Edrona Exams | Complete examination management system

## SFM Final

Strategic Financial Management

Q 1 TMC is a venture capital financier. It received a proposal for financing requiring an investment of Rs.45 cr which returns Rs.600 cr after 6 years if succeeds. However, it may be possible that the project may fail at any time during the six years. The following table provides the estimates of probabilities of the failure of the projects.

 Year 1 2 3 4 5 6 Probability of Failure 0.28 0.25 0.22 0.18 0.18 0.1

In the above table the probability that the project fails in the second year is given that it has survived throughout year 1, similarly for year 2 and so forth.

TMC is considering an equity investment in the project. The beta of this type of project is 7. The market return and risk free rate of return are 8% and 6% respectively. You are required to compute the expected NPV of the venture capital project and advice the TMC.

(i) First we shall find out the probability the venture capital project survives to the end of six years.

 Year Probability Project survives 1 (1– 0.28) = 0.72 2 (1– 0.28)(1– 0.25)=0.72×0.75=0.54 3 (1– 0.28)(1– 0.25)(1-0.22)=0.72×0.75×0.78=0.4212 4 (1–0.28)(1–0.25)(1– 0.22)(1– 0.18)=0.72×0.75×0.78×0.82=0.3454 5 (1–0.28)(1–0.25)(1–0.22)(1–0.18)(1–0.18)=0.72x0.75×0.78x0.82x0.82=0.2832 6 (1–0.28)(1–0.25)(1–0.22)(1–0.18)(1–0.18)(1–0.10)=0.72x0.75x×0.78x0.82x0.82x0.90 = 0.255

Thus, probability of project will fail = 1 – 0.255 = 0.745

(ii) Next using CAPM we shall compute the cost of equity to compute the Present Value of Cash Flows

Ke= Rf +β (Rm – Rf)

= 6% +7 (8% – 6%)

= 20%

(iii) Now we shall compute the net present value of the project The present value of cash inflow after 6 years

(Rs.600 Cr. ×PVIF 20%)              Rs. 201 Cr.

Less:- Present value of Cash outflow Rs. 45 Cr.

Rs.156 Cr.

Net Present Value of project if it fails   Rs. 45 Cr.

And expected NPV = (0.255)(156) + (0.745)(-45) Rs.6.255 Cr.

Since expected NPV of the project is positive it should be accepted

Q 2 Trouble Free Solutions (TFS) is an authorized service center of a reputed domestic air conditioner manufacturing company. All complaints/ service related matters of Air conditioner are attended by this service center. The service center employs a large number of mechanics, each of whom is provided with a motor bike to attend the complaints. Each mechanic travels approximately 40000 kms per annum. TFS decides to continue its present policy of always buying a new bike for its mechanics but wonders whether the present policy of replacing the bike every three year is optimal or not. It is of believe that as new models are entering into market on yearly basis, it wishes to consider whether a replacement of either one year or two years would be better option than present three year period. The fleet of bike is due for replacement shortly in near future. Cost of capital is 10%

The purchase price of latest model bike is Rs. 55,000. Resale value of used bike at current prices in market is as follows:

 Period Rs. 1 Year old 35,000 2 Year old 21,000 3 Year old 9,000

Running and Maintenance expenses (excluding depreciation) are as follows:

 Year Road Taxes Insurance Petrol Repair Maintenance 1 3,000 30,000 2 3,000 35,000 3 3,000 43,000

In this question the effect of increasing running cost and decreasing resale value have to be weighted up to against the purchase cost of bike. For this purpose we shall compute Equivalent Annual Cost (EAC) of replacement in different years shall be computed and compared.

 Year Road Taxes Petrol etc. Total PVF @10% PV Cumulative PV PV of Resale Price Net Outflow 1 3,000 30,000 33,000 0.909 29,997 29,997 31,815 (1,818) 2 3,000 35,000 38,000 0.826 31,388 61,385 17,346 44,039 3 3,000 43,000 46,000 0.751 34,546 95,931 6,759 89,172

 Year Purchase Priceof Bike Net Outflow Total Outflow PVAF @ 10% EAC 1 55,000 (1,818) 53,182 0.909 58,506 2 55,000 44,039 99,039 1.735 57,083 3 55,000 89,172 1,44,172 2.486 57,993

Computation of EACs

Thus, from above table it is clear that EAC is least in case of 2 years; hence bike should be replaced every two years.

Q 3 Following are the data on a capital project evaluated by the managing of X Ltd:

Project M

Annual cost saving   RS.40,000

Useful life       4 years

Profitable index (PI)       1.064

NPV                                  ?

Cost of capital                    ?

Cost of project                   ?

Payback                            ?

Salvage value                    0

(a) Given:

Annual Cost Saving Rs 40000

Useful life       4 years

IRR                    15%

Cost of Project M

At 15% IRR, the sum total of cash inflows = Cost of project

[or at 15% IRR, PV of cash inflows = PV of cash outflows]

Considering the discount table @ 15% cumulative present value of cash inflow for 4 years is 2.855

Therefore, Total of cash inflow for 4 years for project M is (Rs. 40,000 x 2.855) = Rs. 1,14,200

Hence, Cost of project = Rs. 1,14,200

Payback period of Project M = Cost of the Project / Annual cost saving

Payback period =1,14,200 / 40,000

= 2.855 Or 2 years 11 months (Approx.)

Cost of Capital:

If the profitability Index (PI) is 1.064.

PI = Discounted cash inflow / Cost of the Project

or 1.064 = Discounted cash inflow / 1,14,200

or 1.064xRs. 1,14,200 = Discounted Cash inflow

Hence, cumulative factor for 4 years = 3.038

Discount table at discount rate of 12% the cumulative discount factor for 4 years is 3.038 Hence the Cost of Capital is 12%

NPV of the project

NPV = Present Value of cash inflow – Present Value of cash outflows

= Rs. 1,21,509 – 1,14,200= Rs. 7,309

Q 4 XYZ Ltd., an infrastructure company is evaluating a proposal to build, Operate and Transfer a section of 35kms of road at a project cost of Rs 200 Cr. to be financed as follows: Equity share capital Rs50 Cr. loans at the rate of interest of 15%p.a from financial Institutions Rs150 Cr. The project after completion will be opened to traffic and a toll will be collected for a period of 15 years from the vehicles using the road. The company is also required to maintain the road during the above 15years and after the collections of that Period; it will be handed over to the highway authorities at zero value. It is estimated that the toll revenue will be RS 50 Cr. per annum and the annual toll collection expenses including maintenance of the road will amount 5%p.a of the project cost. The company considers to write-off the total cost of the project straight line basis. For corporate income-tax purposes the company is allowed to take depreciation @10% on WDV basis.

The financial institutions are agreeable for the repayment of the loan in 15 equal annual installment consisting of principal and interest. Calculate project IRR and Equity IRR. Ignore corporate taxation.

Working Note :

(i) Net cash inflow of the Project Cash Inflow

Total Revenue 50 Cr. p.a. for 15 year

Cash Outflow

To collection expenses 10 Cr. p.a. for 15 years (including maintenance of road)

(5% of 200 Cr.)

Net Cash Inflow      40 Cr. p.a. for 15 years

Computation of Equity IRR Cash Inflow @ zero

date from equity shareholders = Cash Inflow available for equity shareholders ÷ (1+r)n

where r = Equity IRR

n = life of project

50 Cr. = =Rs. 14.35 Cr. / (1+r)15

From PVAF table at 28% the cummulative discount factor for 1-15 years is 3.484.

thus, Equity IRR is 28%

(ii) Equated annual instalment (i.e. principal + interest) of loan from financial institution:

Amount of loan from financial institution    150 Cr

Rate of interest         15% p.a.

No. of years           15

Cumulative discount factor for 1-15 years    5.847

Hence, equated annual installment is 150Cr./5.847 =    25.65 Cr.

(iii) Cash inflow available for equity shareholders:

Net cash inflow of the project 40.00 Cr (From working note (i)

Equated yearly instalment of the project 25.65 Cr (From working note (ii)

Cash inflow available for equity shareholders 14.35 Cr

Difference in Project IRR & Equity IRR

Project IRR = 18.4% Equity IRR = 28%

XYZ ltd is earning 18.4% on loan but paying only 15% Now, 18.4% - 15% = 3.4%

Q 5 A firm has projected the following cash flows from a project under evaluation:

 Year Rs. lakhs 0 (70) 1 30 2 40 3 30

The above cash flows have been made at expected prices after recognizing inflation. The firm‘s cost of capital excluding inflation is 10 % and the expected annual rate of inflation is 5% show how the viability of the project is to be evaluated.

It is given that the cash flows have been adjusted for inflation; hence they are ―nominal C/Fs‖. The cost of capital or discount rate is ―real‖. In order to find real terms NPV, the cash flows should be converted into ―real terms cash flow‖. This is done as below:

 Year Nominal C/F D/F- Inflation rate Real C/F D/F@10% Disc C/F 0 (70) 1.000 (70) 1.000 (70) 1 30 0.952 28.56 0.909 25.96 2 40 0.907 36.28 0.826 29.97 3 30 0.864 25.92 0.751 19.47 NPV (+) 5.40

As the real terms NPV is positive, Company can take up the project.

Q 6 ABC Ltd. is considering a project in US, which will involve an initial investment of US $1,10,00,000. The project will have 5 years of life. Current spot exchange rate is Rs.48 per US$. The risk free rate in US is 8% and the same in India is 12%. Cash inflow from the project is as follows:

 Year Cash inflow 1 US$20,00,000 2 US$ 25,00,000 3 US$30,00,000 4 US$ 40,00,000 5 US$50,00,000 Calculate the NPV of the project using foreign currency approach. Required rate of return on this project is 14%. Answer Computation of risk premium of the company For Rupee Investment, (1+Risk free)(1+risk premium)= (1+ required return) (1+0.12) (1+risk premium) = (1+0.14) (1+risk premium) = 1.0179 For USD Investment, (1+Risk free)(1+risk premium)= (1+ required return) (1.08) (1.0179) = (1.099) Hence,$ required return is 9.9%

Computation of NPV

 Year Cash flow $D/F @ 9.9% Disc C/F 0 -11 1 -11 1 2 0.91 1.82 2 2.5 0.828 2.07 3 3 0.753 2.259 4 4 0.686 2.744 5 5 0.624 3.12 NPV in$ 1.013 NPV in Rupees =1.013*48=48.624Rs.

Q 7 XY Limited is engaged in large retail business in India. It is contemplating for expansion into a country of Africa by acquiring a group of stores having the same line of operation as that of India. The exchange rate for the currency of the proposed African country is extremely volatile. Rate of inflation is presently 40% a year. Inflation in India is currently 10% a year.

Management of XY Limited expects these rates likely to continue for the foreseeable future. Estimated projected cash flows, in real terms, in India as well as African country for the first three years of the project are as follows:

 Year-0 Year-1 Year-2 Year-3 Cash flows in Indian Rs.(000) -50,000 -1,500 - 2,000 - 2,500 Cash flows in African Rands (000) -2,00,000 +50,000 +70,000 +90,000

XY Ltd. assumes the year 3 nominal cash flows will continue to be earned each year indefinitely. It evaluates all investments using nominal cash flows and a nominal discounting rate. The present exchange rate is African Rand 6 to Rs. 1. You are required to calculate the net present value of the proposed investment considering the following:

1. African Rand cash flows are converted into rupees and discounted at a risk adjusted rate.
2. All cash flows for these projects will be discounted at a rate of 20% to reflect it's high risk. Answer

Present value of cash flows:

 Year 0 1 2 3 Inflation factor in India 1.00 1.10 1.21 1.331 Inflation factor in Africa 1.00 1.40 1.96 2.744 Exchange Rate( as per IRP) 6.00 7.6364 9.7190 12.3696 Cash Flows in Rs. '000 Real cash flow -50000 -1500 -2000 -2500 Nominal (1) cash flow -50000 -1650 -2420 -3327.50 Cash Flows in African Rand '000 Real cash flow -200000 50000 70000 90000 Nominal cash flow -200000 70000 137200 246960 In Indian Rs. '000 (2) -33333 9167 14117 19965 Net Cash Flow in Rs. '000 (1)-(2) -83333 7517 11697 16637 PVF@20% 1 0.833 0.694 0.579 PV cash flow -83333 6262 8118 9633

NPV of 3 years = -59320 (Rs.'000)

NPV of Terminal Value = Perpetuity/TVM= {16637/0.20}*0.579= 48164(Rs.'000) Total NPV of the Project = -59320 (Rs.'000) + 48164 (Rs.000) = -11156 (Rs.'000)

Q 8 L.B, Inc., is considering a new plant in the Netherlands the plant will cost 26 Million Euros. Incremental cash flows are expected to be 3 Million Euros per year for the first 3years, 4 Million Euros the next three, 5 Million Euros in year 7 through 9, and 6 Million Euros In years 10 through 19, after which the project will terminate with no residual value. The present exchange rate is 1.90 Euros per $. The required rate of return on repatriated$ is 16%.

1. If the exchange rate stays at 1.90, what is the project’s net present value?
2. If the Euro appreciates to 1.84 for years 1-3, to 1.78 for years 4-6, to 1.72for years 4-6, to

1.72 for years 7-9, and to 1.65 for years 10-19, what happens to the present value?

Evaluation of projects

 b. Capital budgeting Analysis statement Year CFAT-€ Exchange rate $/€ CFAT-$ D/F @16% Disc CFAT 0 -26.00 1.90 -13.68 1.00 -13.68 1-3 3.00 1.84 1.63 2.25 3.67 4-6 4.00 1.78 2.25 1.44 3.23 7-9 5.00 1.72 2.91 0.92 2.67 10-19 6.00 1.65 3.64 1.27 4.62 NPV 0.51

As the NPV is –ve, if exchange rate remains constant, company should not take up the project, If the exchange rate changes as given, Company can take up the project as the NPV is +ve.

Q 9 XY Limited is engaged in large retail business in India. It is contemplating for expansion into a country of Africa by acquiring a group of stores having the same line of operation as that of India. The exchange rate for the currency of the proposed African country is extremely volatile. Rate of inflation is presently 40% a year. Inflation in India is currently 10% a year.

Management of XY Limited expects these rates likely to continue for the foreseeable future. Estimated projected cash flows, in real terms, in India as well as African country for the first three years of the project are as follows:

 Year-0 Year-1 Year-2 Year-3 Cash flows in Indian Rs.(000) -50,000 -1,500 - 2,000 - 2,500 Cash flows in African Rands (000) -2,00,000 +50,000 +70,000 +90,000

XY Ltd. assumes the year 3 nominal cash flows will continue to be earned each year indefinitely. It evaluates all investments using nominal cash flows and a nominal discounting rate. The present exchange rate is African Rand 6 to Rs 1.

You are required to calculate the net present value of the proposed investment considering the following:

(i) African Rand cash flows are converted into rupees and discounted at a risk adjusted rate.

(ii) All cash flows for these projects will be discounted at a rate of 20% to reflect it‘s high risk.

(iii) Ignore taxation.

 Year – 1 Year – 2 Year – 3 PVIF@20% .833 .694 .579 NPV of 3 years = -59320 (Rs ‗000)

NPV of Terminal Value = × 0.579= 48164 (Rs‘000)

Total NPV of the Project = -59320 (Rs ‘000) + 48164 (Rs‘000) = -11156 (Rs‘000)

Q 10 IPL already in production of Fertilizer is considering a proposal of building a new plant to produce pesticides. Suppose, the PV of proposal is Rs 100 crore without the abandonment option. However, it market conditions for pesticide turns out to be favourable the PV of proposal shall increase by 30%. On the other hand market conditions remain sluggish the PV of the proposal shall be reduced by 40%. In case company is not interested in continuation of the project it can be disposed off for Rs 80 crore.

If the risk free rate of interest is 8% than what will be value of abandonment option

Decision Tree showing pay off First of all we shall calculate probability of high demand (P) using risk neutral method as follows:

8% = p x 30% + (1-p) x (-40%)

0.08 = 0.30 p - 0.40 + 0.40p P = 0.48/0.70

= 0.686

The value of abandonment option will be computed as follows:

Expected Payoff at Year 1 = p x 0 + [(1-p) x 20] = 0.686 x 0 + [0.314 x 20] = Rs 6.28 crore

Since expected pay off at year 1 is 6.28 crore. Present value of expected pay off will be:

= 6.28/ 1.08

= Rs 5.80 crore

Thus the value of abandonment option (Put Option) is Rs 5.80 crore.

Q 11 Raghu Electronics wants to take up a new project involving manufacture of an electronic device which has good market prospects. Further details are given below:

 (i) Cost of the project (as estimated): - Land (to be incurred at the beginning of the year 1) 2.00 - Buildings (to be incurred at the end of the year 1) 3.00 - Machinery (to be incurred at the end of the year 2) 10.00 - Working capital (margin money) 5.00 (to be incurred at the beginning of the year 3) 20.00

(ii) The project will go into production from the beginning of year 3 and will be operational for a period of 5 years. The annual working results are estimated as follows:

 (Rs in lakhs) Sales 24 Variable Post 8 Fixed Cost (excluding depreciation) 5 Depreciation of Assets 2

(iii) At the end of the operational period, it is expected that the fixed assets can be sold for Rs 5 lakh (without any profit).

(iv) Cost of capital of the firm is 10%. Applicable tax rate is 33.33% inclusive of surcharge and education cess, etc. You are required to evaluate the proposal using the net present value approach and advise the firm.

 Calculation of cash outflow: Land 2,00,000 Building (3,00,000*0.909) 2,72,700 Machinery (10,00,000*0.826) 8,26,000 Working Capital (5,00,000*0.826) 4,13,000 Total cash outflow Rs   Calculation of cash inflow: 17,11,700

 Particulars Year 1 Year 2 Year 3 Year 4 Year 5 Sales 24,00,000 24,00,000 24,00,000 24,00,000 24,00,000 Variable Cost 8,00,000 8,00,000 8,00,000 8,00,000 8,00,000 Contribution 16,00,000 16,00,000 16,00,000 16,00,000 16,00,000 Fixed Cost 5,00,000 5,00,000 5,00,000 5,00,000 5,00,000 Depreciation 2,00,000 2,00,000 2,00,000 2,00,000 2,00,000

EBT                    9,00,000         9,00,000             9,00,000         9,00,000          9,00,000

 Tax 3,00,000 3,00,000 3,00,000 3,00,000 3,00,000 PAT 6,00,000 6,00,000 6,00,000 6,00,000 6,00,000 Depreciation 2,00,000 2,00,000 2,00,000 2,00,000 2,00,000 Sale of Assets - - - - 5,00,000 Working Capital - - - - 5,00,000 Cash inflows PV Factors PV of Cash inflow 8,00,000 0.751 6,00,800 8,00,000 0.683 5,46,400 8,00,000 0.621 4,96,800 8,00,000 0.564 4,51,200 8,00,000 0.513 9,23,400

Total Cash Inflow = Rs13,06,900 (30,18,600-17-11,700)

Since NPV is +ve, hence the project should be accepted.

Q 12 ABC Chemicals Ltd. is considering two mutually exclusive proposals. Your advice is sought for choice between two options for consideration:

(i) Purchase of petrol truck

(ii) Purchase of a battery powered truck

 Year Petrol truck Batter powered truck Purchase cost (Rs) Operating cost (Rs) 0 1,50,000 2,50,000 1 24,000 12,000 2 34,000 12,000 3 29,000 12,000 4 31,000 12,000 5 -- 12,000

Assume an investment incentive of 100% Initial depreciation allowance and a 30% incidence of corporate tax. No depreciation is allowed on subsequent years. Taxes are promptly paid. A return of 10% after tax as investment incentives is required. You are required to find out equivalent cost for two options.

(i) Petrol Truck

Calculation of present value of outflow:

 PV of purchase cost +PV of operating cost WN 1 = 1,50,000 = 64,996 Less: Depreciation Tax benefit = (40,905) (1,50,000*0.30*0.909) Net PV of cash outflow = 1,74,091

Working Note: 1

 Year Operating Cost Outflow After Tax PV Factor PV 1 24,000 16,800 0.909 15,271 2 34,000 23,800 0.826 19,659 3 29,000 20,300 0.751 15,246 4 31,000 21,700 0.683 14,281 64,996

(ii) Battery Powered Truck

Calculation of present value of outflow:

 PV of Purchase Cost = 2,50,000 PV of Operating Cost = 31,836 {12,000*(10.3)*3.7} Less: Depreciation Tax Benefit = (68,175) (2,50,000*0.30*0.909) Net PV of cash outflow = 2,13,661

ABC Chemicals Ltd. should choose the option for purchase of petrol truck

Q 13 Sagar Ltd. has been in IT business for six years and enjoys a favorable market reputation. Corporate tax is 30%. They anticipated that the demand for IT solutions would increase considerably since many foreign firms are setting-up their BPO centres in India. For an expansion project, they propose to invest Rs 22 crore to be funded by new debt and equity on 50:50 basis. Enquiries with merchant bankers reveal that funds can be available at following rates:

Debt                     Rate

First Rs 5 crore     10%

Next Rs 5 crore      12%

Equity       12%

Risk gradation by company 2% over cost of capital

You are required to compute the appropriate risk adjusted discount rate.

Total fund required = 22 crores

Debt = 11 crores Equity = 11 crores Cost of Debt

 Amt. (in crores) Rate Kd Amount 5 5 1 10 12 15.72 7 8.4 11 35 42 11 11 88

Kd = 88/11 = 8% Ke = 12%

Weighted average cost of capital:

= (8*0.5)+(12*0.5)

= 4+6

= 10%

Risk adjusted discount rate = 10%+2% = 12%

Q 14 Jumble Consultancy Group has determined relative utilities of cash flows of two forthcoming projects of its client company as follows:

 Cash Flow in Rs -15000 -10000 -4000 0 15000 10000 5000 1000 Utilities -100 -60 -3 0 40 30 20 10

The distribution of cash flows of project A and Project B are as follows

 Project A Cash Flow (Rs) Probability   Project B Cash Flow (Rs) Probability -15000 0.1     -10000 0.1 -10000 0.2     -4000 0.15 -15000 0.4     -15000 0.4 -10000 0.2     -5000 0.25 -5000 0.1     -10000 0.1

Which project should be selected and why?

Evaluation of project utilizes of Project A and Project B

 Project A Cash flow (in Rs) Probability Utility Utility value -15,000 0.1 -100 -10 -10,000 0.2 -60 -12 15,000 0.4 40 16 10,000 0.2 30 6 5,000 0.1 20 2 2

 Project A Cash flow (in Rs) Probability Utility Utility value -15,000 0.1 -60 -6 -10,000 0.15 -3 -0.45 15,000 0.4 40 16 10,000 0.25 20 5 5,000 0.1 30 3 17.55

Project B should be selected as its expected utility is more.

Q 15 Sumathi Ltd is considering an investment of Rs. 250m in a new technology. The total amount has to be paid initially, though its installation will take one year. There is only seven per cent probability that the new technology will work. If it works it will generate a cash flow of Rs.2,700m at the end of the each of the second and third year. If the technology does not work, the investment will be a dead loss. Cost of capital is 10%. Should the investment be made?

Now suppose the technology does not work, its supplier will return Rs.180m in the beginning of the second year. Compute NPV? find the Value of abandonment option?

NPV (without abandonment facility) = -250rn + 2700 X (0.826+0.751) X 0.07 + 0 X 0.93 = Rs. 48.053m

The investment is recommended as the NPV is Positive.

• NPV (with abandonment facility) -250m + 2700 X (0.826+0.751) X 0.07 + 180 X 0.93 X 0.909 = Rs. 200.2196m
• Value of abandonment option = 200.2196 48.053=Rs. 152.17m

Q 16 Vishakha Ltd. has been considering the establishment of a manufacturing unit with the domestic market as the target customer. Life of the project is 7 years.The finance department reports the expected NPV to be ‗Minus RS.3m‘. The Chairman refers the project to a Project Consultancy Group (PCG).

The PCG brings a new fact to the management – it is expected that at the end of 2nd year the Government may allow the export of the out put of the manufacturing unit. Probability of this happening is 0.78. In that case, Vishakha Ltd. shall have the option to increase the production and sale of output of the plant. This will require new investment. The NPV of the new investment will be Rs 14m at the end of 2nd year. What will be the value of option assuming cost of capital =12%

A) Value of option = 14M x 0.797 x 0.78= Rs. 8.7M

B) NPV = -5M + 0.85x5.092 =-0.6718

Value of option=NPV on follow on investment=-1Mx0.516+0.85Mx2.402= 1.525

Q 17 Udhavji Ltd. is considering a project requiring initial cash investment of Rs. 12m. The project is expected to generate annual cash inflow for 2 years, the details given below:

 Annual cash flow Probability Rs. 12m 0.31 Rs. 8m 0.45 Rs. 1m 0.31

Cost of capital is 16%. Find NPV?

Suppose the experience gained by implementing the project will provide the company an option to start a new venture at the end of 2nd year. The required investment would be Rs. 8m. The new venture is expected to generate annual cash inflow of 3 and 4, the details given below:

 Annual cash flow Probability Rs. 10m 0.20 Rs. 9m 0.45 Rs. 2m 0.35

The amount of required investment is certain and hence, it should be discounted on the basis of risk free rate of return which is 7%. Find the Value of the option?

NPV = -12m + (12m x 0.24 + 8m x 0.45 + 1m x 0.31) x (1.605) = -1.24615m

Value of Option = NPV of follow on investment = -8m x 0.873 + (10m x 0.20 + 9 m x 0.45 + 2m x 0.35) x (1.193) = 1.06875m

Q 18 Hyderabad Industries Ltd. has been considering the establishment of a manufacturing unit with the domestic market as the target customer. Life of the project is 7 years. The finance department reports the expected NPV to be ‗Minus Rs. 3m‘. The Chairman refers the project to Project Consulting Group (PCG).

The PCG brings a new fact to the notice of the management – it is expected that at the end of 1st year the Government will announce its export policy. In that case, Hyderabad Industries Ltd. shall have the option to increase the production and sales of output of the plant. This will require new investment of RS.20m in the beginning of 2nd year (from today). If the policy announcement is on the expected lines, cash inflows at the end of 2nd year will be Rs. 40m; in the otherwise situation this amount will be only Rs.12m instead of Rs. 40m. the following on project will have a life of only 1 year and it can be undertaken only if the original proposal is implemented. Risk free rate of interest is 10%. Find the Value of Option?

Calculation of probability of announcement being on favourable lines: P = (r-d) / (u-d) = [20(1.1) - 12] / (40-12) = 0.3571

 Situation Gain Prob. Expected Gain Favourable policy 40-12=28 0.3571 9.99 UnFavourable policy 0 0.6429 0 Value of the Option at the end of Year II 6.4278

Value of the Option = 6.4278x0.826 = 5.309

Q 19 ANP Plan, a hedge fund currently has assets of Rs. 20 Cr. CA. X, the manager of fund charges fee of 0.10% of portfolio asset. In addition to it he charges incentive fee of 2%. The incentive will be linked to gross return each year in excess of the portfolio maximum value since the inception of fund. The maximum value fund achieved so far since inception of fund about one and half year was Rs. 21 Cr.

You are required to compute the fee payable to CA. X, if return on the fund this year turns out to be(a) 29% (b) 4.5% (c) -1.8%.

(a)If return is 29% Q 20 For a given share, the prices are observed for 7 days and are recorded below along with the index values on those days.

You are required to calculate the returns on the share on the returns on the index. What does the beta indicate?

 Day Share Price Index Price of Share 1 1376.15 818.35 2 1388.75 811.75 3 1408.85 819.85 4 1418.00 836.05 5 1422.85 815.65 6 1445.15 804.30 7 1438.65 801.30

Computed the returns, find the Beta of the stock as usual

 MKT-M Stock-X 0.92 -0.81 1.45 1 0.65 1.98 0.34 -2.44 1.57 -1.39 -0.45 -0.37

Q 21 Assuming that two securities X and Y are correctly priced on security market line (SML) and expected return from these securities are 9.4% and 13.40% respectively. The Beta of these securities are 0.80 and 1.30 respectively.

Mr. A an investment manager states that the return on market index is 9%. You are required to determine,

1. Whether the claim of Mr. A is right. If not then what is the correct return on market index.
2. Risk free rate of return.

When CAPM assumptions are holding good, actual return =CAPM return

• 9.4=Rf+0.8 (Rm-Rf)… (1)
• 13.4=Rf+1.3(Rm-Rf)… (2) ,

Solving 1 and 2 equations

• Rf=3%, Rm=11%
• His context is wrong, hence Rf=3% and Rm=11%

Q 22 Mr.V decides to sell short 10000 shares of ABC plc, when it was selling at yearly high of £

5.60. His broker requested him to deposit a margin requirement of 45% and commission of £ 1550 while Mr. V was short the share, the ABC paid a dividend of £ 0.25 per share.At the end of one year Mr. V buys 10000 Shares of ABC plc at £4.50 to close out position and was charged a commission of £ 1450.

You are required to calculate the return on investment of Mr.V. Answer

Sell 10000 shares @ 5.6          56000 £

Buy 10000 shares @ 4.5          45000 £

 Sell 10000 shares @ 5.6 56000 £ Buy 10000 shares @ 4.5 45000 £ Gain due to short selling 11000 £ Margin deposited = 56000 x 45% 25200£ Gain due to short selling 11000 £ Less: Commission on sale ( 1550) Less: Dividend payable by Mr V ( 2500) Less: Commission on purchase ( 1450) Net gain 5500 £ Return % = (5500/25200) x 100 = 21.82%

Q 23 Closing values of BSE Sensex from 6th to 17th day of the month of January of the year 2012 were as follows

 Days Date Day Sensex 1 6 Thu 14522 2 7 Fri 14925 3 8 Sat No Trading 4 9 Sun No Trading 5 10 Mon 15222 6 11 Tue 16000 7 12 Wed 16400 8 13 Thu 17000 9 14 Fri No Trading 10 15 Sat No Trading 11 16 Sun No Trading 12 17 Mon 18000

Calculate Exponential Moving Average (EMA) of Sensex during the above period. The 30 days simple moving average of Sensex can be assumed as 15,000: The value of exponent for 30 days EMA is 0.062.

Exponential Moving Average(EMA) = EMA of Previous Day + Smoothing Factor [ Sensex Current close-Previous EMA]

 Days (a) (b) (c) EMA = c + b *[a - c]
 Sensex Smoothing Factor Simple Moving Average 1 14522 0.062 15000 15000+0.062(14522-5000)=14970 2 14925 0.062 14970 14970+0.062(14925-14970)=14967 5 15222 0.062 14967 14967+0.062(15222-14967)=14983 6 16000 0.062 14983 14983+0.062(16000-14983)=15046 7 16400 0.062 15046 15046+0.062(16400-15046)=15130 8 17000 0.062 15130 15130+0.062(17000-15130)=15246 12 18000 0.062 15246 15246+0.062(18000-15246)=15417

The exponential moving average shows that the stock is clearly in the up-trend.

Q 24 Data for finding out optimal portfolio are given below.

 Security Mean return β Unsystemantic Risk σ2€i Grasim 19 1.0 20 Infosys 11 0.5 10 Indian oil 25 2.0 40 Hero motor 23 1.5 30 SBI 13 1.0 20 Dr Reddy‘s 9 0.5 50 Tech Mah 14 1.5 30

The risk free rate is 5% and the market risk (variance) is 10%. Determine the cut-off point and optimum portfolio.

Ranking is based on (Rs-Rf)/β

Investor should buy stocks of Grasim, Hero Motor Corp, and Infosys as the benefiting is in increasing trend due to diversification

Q 25 Mr. X, is a Senior Portfolio Manager at ABC Asset Management Company. He expects to purchase a portfolio of shares in 90 days. However he is worried about the expected price increase in shares in coming day and to hedge against this potential price increase he decides to take a position on a 90- day forward contract on the Index. The index is currently trading at 2290. Assuming that the continuously compounded dividend yield is 1.75% and risk free rate of interest is 4.16%, you are required to determine:

(a) Calculate the justified forward price on this contract.

(b) Suppose after 28 days of the purchase of the contract the index value stands at 2450 then determine gain/ loss on the above long position.

(c) If at expiration of 90 days the Index Value is 2470 then what will be gain on long position. Note: Take 365 days in a year and value of e0.005942 = 1.005960, e0.001849 = 1.001851.

a) The Forward Price shall be = S0en(r – y) Where

S0 = Spot price n = period

r = risk free rate of interest y = dividend yield Accordingly, Forward Price = 2290 e90/365(0.0416 – 0.0175)

= 2290 e0.005942

= 2290(1.005960)

= 2303.65

b) Gain/loss on Long Position after 28 days

= 2450 – 2290 e28/365(0.0416 – 0.0175)

= 2450 – 2290 e0.001849

= 2450 – 2290(1.001851)

= 155.76

(c ) Gain/loss on Long Position at maturity

= Sn – S0e(r – y)t

= 2470.00 – 2303.65 = 166.35

Q 26 From the following data relating to investment made by a company for the past 5 years, ascertain the expected return for the 6th year

 Years 1 2 3 4 5 Closing market price (Rs) 50 64 85 100 125 Dividend yield (Rs) 4 8 10 15 15

Opening market price in year 1 was Rs45. Also ascertain the compounded annual growth rate. What would be the capital annual growth rate if there were no dividend payouts at all ?

Computation of total return and return %

 Year Opening price (Rs) Closing price (Rs) Dividend (Rs) Capital appreciation (Rs) Total return (Rs) Return % 1 2 3 4 5 = 3-2 6 = 4 + 5 7 = 6 ÷ 2 1 45.00 50.00 4.00 5.00 9.00 20.00% 2 50.00 64.00 8.00 14.00 22.00 44.00% 3 64.00 85.00 10.00 21.00 31.00 48.44% 4 85.00 100.00 15.00 15.00 30.00 35.29% 5 100.00 125.00 15.00 25.00 40.00 40.00%

Expected return = average return

= (20.00% + 44.00% + 48.44% + 35.29% +40.00%) ÷ 5 = 187.73 ÷ 5 =37.55 %

Q 27 Calculate the value of share from the following information:

 Profit of the company Equity capital of company Par value of share Debt ratio of company Growth rate of the company for first 5 years Growth rate of the company for the 6 year and onward Beta 0.1; risk free interest rate Market returns Capital expenditure per share Depreciation per share Rs290 crores Rs 1,300 crores Rs40each 27 8% 5% 8.7% 10.3% Rs47 Rs39
 Change in Working capital Rs 3.45 per share Q 28 Assuming that shares of ABC Ltd. and XYZ Ltd. are correctly priced according to Capital Asset Pricing Model. The expected return from and Beta of these shares are as follows:

 Share Beta Expected return ABC XYZ 1.2 0.9 19.8% 17.1%

You are required to derive Security Market Line. Answer

CAPM = Rf+ β(Rm -Rf)

According

RABC = Rf+1.2 (Rm - Rf) = 19.8 RXYZ = Rf+ 0.9 (Rm - Rf) = 17.1

19.8 = Rf+1.2 (Rm - Rf)                    --(1)

17.1 = Rf+0.9(Rm- Rf)                      --(2)

Deduct (2) from (1)

2.7 = 0.3 (Rm- R f) Rm - Rf = 9 Rf = Rm - 9

Substituting in equation (1)

19.8 = (Rm - 9) + 1.2 (Rm - Rm+ 9)

19.8 = Rm - 9 + 10.8

19.8 = Rm+1.8

Then Rm=18% and Rf= 9%

Security Market Line = Rf + β (Market Risk Premium) = 9%+ β x 9%

Q 29 Suppose that economy A is growing rapidly and you are managing a global equity fund and so far you have invested only in developed-country stocks only. Now you have decided to add stocks of economy A to your portfolio. The table below shows the expected rates of return, standard deviations, and correlation coefficients (all estimates are for aggregate stock market of developed countries and stock market of Economy A).

 Developed Country Stocks Stocks of Economy A Expected rate of return (annualized percentage) 10 15 Risk [Annualized Standard Deviation (%)] 16 30 Correlation Coefficient (p) 0.30

Assuming the risk-free interest rate to be 3%, you are required to determine:

(a) What percentage of your portfolio should you allocate to stocks of Economy A if you want to increase the expected rate of return on your portfolio by 0.5%?

(b) What will be the standard deviation of your portfolio assuming that stocks of Economy A are included in the portfolio as calculated above?

(c) Also show how well the Fund will be compensated for the risk undertaken due to inclusion of stocks of Economy A in the portfolio?

a) Let the weight of stocks of Economy A is expressed as w, then (1- w)×10.0 + w ×15.0 = 10.5

i.e. w = 0.1 or 10%.

(b) Variance of portfolio shall be:

(0.9)2 (0.16) 2 + (0.1)2 (0.30) 2+ 2(0.9) (0.1) (0.16) (0.30) (0.30) = 0.02423

Standard deviation is (0.02423)½= 0.15565 or 15.6%.

1. The Sharpe ratio will improve by approximately0.04, as shown below: With inclusion of stocks of Economy A: $$10.5-3 \over15.6$$

= 0.481

Q 30 Mr. Nirmal Kumar has categorized all the available stock in the market into the following types:

1. Small cap growthstocks
2. Small cap valuestocks
3. Large cap growth stocks
4. Large cap valuestocks

Mr. Nirmal Kumar also estimated the weights of the above categories of stocks in the market index.

Further, more the sensitivity of returns on these categories of stocks to the three important factor are estimated to be:

 Category of Stocks Weight in the Market Index Factor I (Beta) Factor II (Book Price) Factor III (Inflation) Small  cap Small cap value Large cap Large cap value Risk Premium 25% 10% 50% 15% 0.80 0.90 1.165 0.85 6.85% 1.39 0.75 2.75 2.05 -3.5% 1.35 1.25 8.65 6.75 0.65%

The rate of return on treasury bonds is 4.5% Required:

(a)Using Arbitrage Pricing Theory, determine the expected return on the market index.

(b)Using Capital Asset Pricing Model (CAPM), determine the expected return on the market index.

(c)Mr. Nirmal Kumar wants to construct a portfolio constituting only the ‗small cap value‘ and ‗large cap growth‘ stocks. If the target beta for the desired portfolio is 1, determine the composition of his portfolio.

(a)Method I

Portfolio‘s return

Small cap growth = 4.5 + 0.80 x 6.85 + 1.39 x (-3.5) + 1.35 x 0.65 = 5.9925%

Small cap value = 4.5 + 0.90 x 6.85 + 0.75 x (-3.5) + 1.25 x 0.65 = 8.8525%

Large cap growth = 4.5 + 1.165 x 6.85 + 2.75 x (-3.5) + 8.65 x 0.65 = 8.478%

Large cap value = 4.5 + 0.85 x 6.85 + 2.05 x (-3.5) + 6.75 x 0.65 = 7.535%

Expected return on market index

0.25 x 5.9925 + 0.10 x 8.8525 + 0.50 x 8.478 + 0.15 x 7.535 = 7.7526%

Method II

Expected return on the market index

= 4.5% + [0.1x0.9 + 0.25x0.8 + 0.15x0.85 + 0.50x1.165] x 6.85 + [(0.75 x 0.10 + 1.39 x 0.25 + 2.05 x 0.15 + 2.75 x 0.5)] x (-3.5) + [{1.25 x 0.10 + 1.35 x 0.25 + 6.75

x 0.15 + 8.65 x 0.50)] x 0.65

= 4.5 + 6.85 + (-7.3675) + 3.77 = 7.7525%.

b) Using CAPM,

Small cap growth = 4.5 + 6.85 x 0.80 = 9.98%

Small cap value = 4.5 + 6.85 x 0.90 = 10.665%

Large cap growth = 4.5 + 6.85 x 1.165 = 12.48%

Large cap value = 4.5 + 6.85 x 0.85 = 10.3225% Expected return on market index

= 0.25 x 9.98 + 0.10 x 10.665 + 0.50 x 12.45 + 0.15 x 10.3225 = 11.33%

(c) Let us assume that Mr. Nirmal will invest X1% in small cap value stock and X2% in large cap growth stock

X1 + X2 = 1

0.90 X1 + 1.165 X2 = 1

0.90 X1 + 1.165(1 - X1) = 1

0.90 X1 + 1.165 - 1.165 X1 = 1

0.165 = 0.265 X1

0.165/ 0.265= X1

0.623 X1, X2 = 0.377

% in small cap value 37.7% in large cap growth

Q 31 You are considering investing in one of following 2 NFOs of 2 Mutual funds, issue price per unit = RS.10.

 Redemption on or before the expiry of 1 year 0.50%
 Redemption of the expiry of 1 year but before the expiry of 2 years 0.40% Redemption on or after the expiry of 2 years but before the expiry of 3 years 0.30% Redemption on or after the expiry of 3 years but before the expiry of 4 years 0.20% Redemption on or after the expiry of 4 years 0.10%

In which MF you will invest if your time horizon of the investment is 1 year, 4 years? Assume that rate of ROI of the mutual fund will be 12% per annum (Net of expenses).

Computation of One year return

 A B FV =10 P0 = 10.225 FV = 10 P0 = 10.09 P1 = 10*(1.12) = 11.2 P1 =10*(1.12)-11.2*(0.5/100) = 11.144 (11.2−10.225) ∗100 Return % = 10.225 = 9.535% (11.144−10.09) ∗100 Return % = 10.09 = 9.669% Computation of Four year return

 A B FV =10 P0 = 10.225 FV = 10 P0 = 10.09 P1 = 10*(1.12)4 = 15.7351 P1 =10*(1.12)4 - EXIT load = 15.7351 - 15.7351* 0.1% 53.89 Return % = 4 = 13.4725% 55.8 Return % = 4 = 13.95%

Q 32 Gopika invested Rs.10,000 in the new Fund offer of a close ended Scheme of Vaibha Mutual fund. The fund is listed in stock exchange. Consider the following details:

 End of the year NAV Market price as a % of Discount or premium over the NAV 1 10.90 -0.20 2 12.00 -0.10 3 14.00 +0.20 4 15.70 +0.30
 5 18.9 0.5

a)Calculate the annualized return if her time horizon is 5 years.

(b) What is the annually compounded growth rate of NAV over 4 years?

(c) Calculate the % annual return of a person who invested in the scheme at the end of 1st year and disinvested at the end of the 2nd year.

(d) What is the annually compounded growth rate of return of person who invested at the end of 1st year.

(d) What is the annually compounded growth rate of return of person who invested at the end of 1st year and disinvested at the end of 5th year?

a)  18.9 + 18.9*(0.5/100) = 18.9945

Holding Period Return = 89.94% for 5 years

b) NAV of 10 has become 15.7 in future value terms

15.7 X PVIF (x %, 4 y)= 10, therefore Return is 12%

c)  P0 = 10.9 - 10.9*0.2 = 10.8782

P1 = 12 - 12(0.1/100) = 11.988, Rate of return = 10.2%

d) P0 = 10.8782 P1= 18.9945

NAV of 10.87 has become 18.99 in future value terms,

18.99 X PVIF (x %, 4 y)= 10.8782 hence return is 15 %

Q 33 Columbus Surgicals Inc. is based in US, has recently imported surgical raw materials from the UK and has been invoiced for £ 480,000, payable in 3 months. It has also exported surgical goods to India and France.

The Indian customer has been invoiced for £ 138,000, payable in 3 months, and the French customer has been invoiced for € 590,000, payable in 4 months.

Current spot and forward rates are as follows:

£ / US$Spot: 0.9830 – 0.9850 Three months forward: 0.9520 – 0.9545 US$ / €

Spot: 1.8890 – 1.8920

Four months forward: 1.9510 – 1.9540 Current money market rates are as follows:

UK: 10.0% – 12.0% p.a.

France: 14.0% – 16.0% p.a.

USA: 11.5% – 13.0% p.a.

You as Treasury Manager are required to show how the company can hedge its foreign exchange exposure using Forward markets and Money markets hedge and suggest which the best hedging technique is.

Given:£ Exposure

Since Columbus has a £ receipt (£ 138,000) and payment of (£ 480,000) maturing at the same time i.e. 3 months, it can match them against each other leaving a net liability of £ 342,000 to be hedged.

(i)Forward market hedge

Buy 3 months' forward contract accordingly, amount payable after 3 months will be

£ 342,000 / 0.9520 = US$359,244 (ii)Money market hedge To pay £ after 3 months' Columbus shall requires to borrow in US$ and translate to £ and then deposit in £.

For payment of £ 342,000 in 3 months (@2.5% interest) amount required to be deposited now (£ 342,000 ÷ 1.025) = £ 333,658

With spot rate of 0.9830 the US$loan needed will be = US$ 339,429. Loan repayable after 3 months (@3.25% interest) will be = US$350,460. In this case the money market hedge is a cheaper option. € Receipt Amount to be hedged = € 590,000 Now Convert exchange rates to home currency € / US$ Spot 0.5285 – 0.5294

4 months forward 0.5118 – 0.5126

(i)Forward market hedge

Sell 4 months' forward contract accordingly, amount receivable after 4 months will be(€ 590,000 / 0.5126) = US$1,150,995 (ii)Money market hedge For money market hedge Columbus shall borrow in € and then translate to US$ and deposit in US$For receipt of € 590,000 in 4 months (@ 5.33% interest) amount required to be borrowed now (€590,000 ’ 1.0533) = € 560,144 With spot rate of 0.5294 the US$ deposit will be = US$1,058,073 deposit amount will increase over 3 months (@3.83% interest) will be = US$ 1,098,597

In this case, more will be received in US$under the forward hedge. Q 34 Following are the rates announced by the dealing room at 9.00am.  T.T. Selling Bills Selling USD 44.60 44.70 Euro 53.80 53.90 T.T. Selling Bills Selling USD 44.10 44.00 Euro 52.80 52.70 Traveller Cheques  Selling Rate Buying Rate USD 44.90 43.60 Euro 54.05 52.55 Foreign Currency notes  Selling Rate Buying Rate USD 45.10 43.40 Euro 54.30 52.30 1. The rate quoted for issue of traveler cheque of EURO 5,000? 2. The rate for issue of foreign currency notes for travelling abroad to the customer? 3. Which rates will you quote for remittance of USD 20000 for studies abroad? 4. What rate will you apply for a gift (currency) received from his relative abroad? 5. Your customer going abroad for Business purpose asks you to issue Traveller‘s cheque for 50000 Euro & Currency Notes of USD 10000. You will debit his A/c by Rs? Answer 1. Cost of buying 5000€ in traveller's cheques = 5000€ * 54.05 = Rs. 270250/- 2. The rate of issue of Foreign currency notes for travelling abroad to Customer: (a) If the customer is going to USA , the relevant rate is 45.10 Rs/$

(b)If the customer is going to Europe , the relevant rate is 54.3 Rs/€

3. Cost of Buying TT of 20,000$= 20,000$ * 44.6 = Rs. 8,92,000/-

4.  If the customers relative is in USA, relevant rate is 43.4 Rs./ $If the customers relative is in Europe, relevant rate is 52.3 Rs./$

5. Traveller Cheques = 50000€ * 54.05 = Rs. 27,02,500/-

Foreign Currency Notes = 10000$* 45.1 = Rs. 4,51,300/- Total cash to Debit his account is = Rs. 31,53,500/- Q 35 Imagine you are a British arbitrageur, holding sterling, in the following example: Actual exchange rates GBB/USD £1 =$ 1.5715-721 USD/JPY $1 = ¥ 106.090-120 GBP/JPY £ 1 = ¥ 176.720-831 Start with £ 1,000,000. 1. List the steps you need to take a profit. 2. Calculate the rate of profit you will make. Answer Given: Implied Cross rates are £1 = ¥166.720- 831.Thus, in the actual market, Sterling is overpriced in relation to yen and we must sell sterling for yen. Thus: Use £ to buy yen; Step B: Use Yen to buy$ ; Step C: Use $to buy £ Step A: Sell £ for yen; Banker sells the foreign currency (¥) at the bid rate of ¥176.720. This gives ¥176,720,000. Step B: Sell ¥ for$; Banker sells dollars at the offer rate of ¥106.120. This gives $1,665,284.58 Step C: Sell$ for the Banker buys dollars at the higher rate of $1.5721, which gives £1,059,273.95 or a profit of 5.9%. Q 36 Following are the rates quoted at Bombay for British pound:  £/Rs. 52.60/70 Interest Rates India London 3 m Forward 6 m Forward 20/70 50/75 3 months 6 months 8% 10% 5% 8% Verify whether there is any scope for covered interest arbitrage if you borrow rupees. Answer Forward Rates:  3 month forward rate 6 month forward rate Spot 52.6 52.7 Spot 52.6 52.7 ADD: Swap 20 70 ADD: Swap 50 75 3 mth fwd rate(Rs./ £) 52.8 53.4 6 mth fwd rate (Rs./ £) 53.1 53.45 Case A : Step 1: Borrow Rs. 100000 from on 1/1/14 @ 8% p.a. for 3 months Step 2: Convert Rs. to £ at spot rate = 52.6 -52.7 ( Here ask rate is relevant) =100000/52.7 = 1897.5£ Step 3: Deposit in London @ 5% p.a. for 3 months Step 4: Take forward to sell £ at 52.8 Rs./ £ Step 5: On 31/3/14, redeem deposits 1897.5 £ (1+ 5%*3/12) = 1920.7£ Step 6: Reconvert £ to Rs.@ 52.8 Rs./ £= 1920.7£*52.8= Rs. 101413/- Step 7: Repay Rs. loan= 100000 (1+ 8%*3/12) = Rs. 102000/- Arbitrage loss = 101413-102000 = Rs. 587/- Hence there is no arbitrage profit. Case B : Step 1: Borrow Rs. 100000 from on 1/1/14 @ 10% p.a. for 6 months Step 2: Convert Rs. to £ at spot rate = 52.6 -52.7 ( here ask rate is relevant) =100000/52.7 = 1897.5£ Step 3: Deposit in London @ 8% p.a. for 6 months Step 4: Take forward to sell £ at 53.1 Rs./ £ Step 5: On 31/6/14, redeem deposits 1897.5£(1+ 8%*6/12) = 1973.4£ Step 6: Reconvert £ to Rs.at 53.1 Rs./ £= 1973.4£*53.1= Rs.104787/- Step 7: Repay Rs. loan= 100000 (1+10%*6/12) = Rs. 105000/- Arbitrage loss = 104787-105000 = Rs. 213/- Hence there is no arbitrage profit. Q 37 ABN-Amro Bank, Amsterdam, wants to purchase Rs. 15 million against US$ for funding their Vostro account with Canara Bank, New Delhi. Assuming the inter-bank, rates of US$is Rs. 51.3625/3700, what would be the rate Canara Bank would quote to ABN-Amro Bank? Further, if the deal is struck, what would be the equivalent US$ amount.

Given: Here Canara Bank shall buy US$and credit Rs. to Vostro account of ABN-Amro Bank. Canara Bank‘s buying rate will be based on the Inter-bank Buying Rate (as this is the rate at which Canara Bank can sell US$ in the Interbank market)

Accordingly, the Interbank Buying Rate of US$will be Rs.51.3625(lower of two) Equivalent of US$ for Rs. 15 million at this rate will be

= 15,000,000 / 51.3625 = US$2,92,041.86 Q 38 Trueview plc a group of companies controlled from the United Kingdom includes subsidiaries in india, Malaysia and the United States. As per the CFO’s forecast that, at the end of the june 2010 the position of inter-company indebtness will be as follows: • The Indian subsidiary will be owed Rs. 1,44,38,100 by the Malaysian subsidiary and will to owe the US subsidiary US$ 1,06,007.
• The Malasian subsidiary will be owed MYR 14,43,800 by the US subsidiary and will owe it US $80,000. Suppose you are head of central treasury department of the group and you are required to net off inter-company balances as far as possible and to issue instructions for settlement of the net balances. For this purpose, the relevant exchanges rates may be assumed in terms of £ 1 are US$ 1.415; MYR 10.215; Rs. 68.10.

What are the net payments to be made in respect of the above balances?

Statement showing the inter company dues in Mutli currency and in single currency £

 India Malaysia USA 14438100*1/68.10=212013 (1443810*1/68.10)= (212013) - (106007*1/1.415)=(74916) - 106007*1/1.415= 74916 - 1443800*1/10.215= 141341 (1443800*1/10.215)=(141341) - (80000*1/1.415)= (56537) 80000*1/1.415=56537

NET    137097£                            (127209)£                      (9888)£

Malaysian subsidiary will pay 1,27,209£ and US subsidiary will pay 98,888£ to Indian subsidiary.

Q 39 Alpha Geo Ltd. has imported goods for US$5,00,000 which is payable after 3 months. The company also has a receivable for US$3,00,000in 2 months for which a forward contract is already taken at Rs. 36.60. The market rates are as under:

Spot        36.20/40Rs

1m          20/25 Points

2m          30/35 Points

3m          45/50 Points

In order to cover the risk, the company is having two options :

i) To cover payables in the forward market; and

ii) To lag the receivables by l month and cover the exposure only for the net amount Evaluate both the options if the cost of Rupee funds is 16% and no interest is earned on delaying the receivable.

Take today as 1/1/14 and an amount of 5L $is due to be received in 3 mths and an amount of 3L$ is due to be paid in 2 mths.

i) To cover payables in the forward market:

Company will receive 3L $on 28/2 and convert the$ into Rs. at the forward rate

Amt. of Rs. receivable = 3L $x 36.6 =10980000/- Deposit this for 1 mth @16 % p.a Amount receivable on 31/3 = 10980000 + (10980000 x 16% x 1/12) Rs 1112600 The company has to pay 5L$ on 31/3

For this the company should enter 3 mth forward contract to buy $Amt. of Rs. payable to buy 5L$ = 5L $x 36.9 =Rs.18450000/- Net amount payable =Rs. 7323600/- ii) The company can delay the receivables by 1 mth so that receivables and payables fall on the same day i.e. on 31/3 So, the company can take forward cover only for balance amount of 2L$

Amt. of Rs. payable to buy 2L $= 2L$ x 36.9 = Rs. 7380000/-

But for the receivable (of 3L$), the company has already entered into a forward contract. The company should cancel it now Gain or loss: On entering Sell$ at 2 mth forward   = 36.60

On cancellation Buy at 2 mth forward = 36.75

Loss = (0.15) x 300000$= Rs 45000/- Q 40 Pepsi Company, a US-based soft drink giant, has subsidiaries in UK and USA Each subsidiary handles its exposure and financing needs. Corporate policy is to cover all exposures. At present, the situation is as follows: U.S. subsidiary needs working capital, HQ also needs financing for which credit is readily available in the US. There are nocapital or exchange controls but HQ's cost of borrowing in the US is somewhat lower than in the London market. The following rates are prevailing:$/ £ spot £ 2.2795 &

One month forward is .75 points discount on £. US Interest rates: 4.5% p.a.

UK Interest rates: 7.75% - 8.00% p.a. Advice Pepsi Company

Given, US Interest rates : 4.5% p.a. UK Interest rates : 7.75% - 8.00% p.a. Spot = 2.2795$/£ One month forward rate = 2.2720$/£ (2.2795-.0075)

US Subsidiary needs funds

 Product = $/£ 2.272-2.2795/2.2795*100*12/1 = -3.94% Calculation of Net Cost of funds in UK company: UK Interest rate Less: Foreign Currency appreciation Net Cost of funds 8% - (3.94)% - 4.06% As the cost of funds borrowed from UK is lesser (i.e 4.06% < 4.5%), it is advised to borrow in UK. Q 41 An American investor purchased stocks worth$ 1 Mln in Hero motor corp when stock wasRs. 1945 and the spot rate was 47.00R/$. However, Stock up toRs. 2100 in one month. While rupee depreciated to Rs. 52/$. What is the gain or loss to FIIs if he decides to liquidate the investment?

Given:

Step 1: No. of shares purchased with 1 million $On 1/1/14, Amt recd. = 1 million$ * 47 = Rs.47 million CMP of share = Rs. 1945/-

Shares purchased = 47million Rs. / 1945 = 24165 shares Step 2: On 1/2/14,

Sale proceeds from sale of shares = 24165 * 2100 = Rs. 50746500/-

Spot rate= 52 Rs/  received = 50746500/52 = 9, 75,894 $Loss = 975894-1000000 =24146$

Return % -24146/1000000*100 = -2.416%

Q 42 Z Ltd. importing goods worth USD 2 million, requires 90 days to make the payment. The overseas supplier has offered a 60 days interest free credit period and for additional credit for 30 days @ interest of 8% per annum.

The bankers of Z Ltd offer a 30 days loan at 10% per annum and their quote for foreign exchange is as follows:

Spot 1 USD                 - 56.50

60 days forward for 1 USD - 57.10

90 days forward for 1 USD - 57.50

You are required to evaluate the following options

(i) Pay the supplier in 60 days, or

(ii) Avail the supplier‘s offer of 90 days credit.

(i)Paying the supplier in 60 days

 If the payment is made to supplier in 60 days the applicable forward rate for 1 USD Payment Due Outflow in Rupees (USD 20,00,000 x Rs. 57.10) Add: Interest on loan for 30 days @ 10% p.a. Rs. 57.10 USD 22,00,000 Rs. 11,42,00,000 Rs. 9,51,667 Total Outflow in Rs. Rs 11,51,51,667

(ii) Availing supplier‟s offer of 90 days credit

 Amount Payable Add: Interest on credit period for 30 days @ 8% p.a. Total Outflow in USD Applicable forward rate for 1 USD TOTAL Outflow in Rs. (USD 20,13,333 x Rs. 57.50) USD 20,00,000 USD 13,333 USD 20,13,333 Rs. 57.50 Rs.11,57,66,648

Alternative 1 is better as it entails lower cash outflow.

Q 43 Management of an Indian company is contemplating to import a machine from USA at a cost of US$15,000 at today‘s spot rate of$0.0227272 per Rs.. Finance manager opines that in the present foreign exchange market scenario, the exchange rate may shoot up by 10% after two months and accordingly he proposes to defer import of machine. Management thinks that deferring import of machine will cause a loss of Rs.50,000 to the company in the coming two months. As the Chartered Accountant, you are asked to express your views, giving reasons, as to whether the company should go in for purchase of machine right now or defer purchase for two months.

Given:

Indian importer

Exposure 15000$Spot rate 0.227272$/Rs. .

Expected spot =.0227272*110% =0.02499$/Rs.  Payment at spot Payment at expected spot Benefit Due to postponement Loss due to import machine after two months Net benefit =15000*1/0.227272=660000 Rs. =15000*1/0.2499 = 600240 Rs. 59761 Rs. 50000 Rs. 9761 Rs. As net benefit is positive company should defer the purchase of machinery by two months. Q 44 Biogen, a U.S. company, expects to receive royalty payments totaling £1.25 million next month. It is interested in protecting these against a drop in the value of the pound. It can sell 30-day pound futures at a price of$1.6513 per pound or it can buy pound. The spot price of the pound is currently $1.6560, and the pounds is expected to trade in the range of$1.6250 to $1.6400. How many futures contracts will Biogen need to protect its receipts? Answer Given: The company is a US exporter Receipt = £ 1.25 million Due in 1 month 1 mth £ futures Price = 1.6513 The expected range of £ is 1.6250 - 1.6400$ and 30 days futures price = 1.6513

As the amt. of $receivable is higher, the company should take future contract to sell £. Q 45 XYZ Bank, Amsterdam, wants to purchase Rupees 25 million agains t £ for funding their Nostro account and they have credited LORO account with Bank of London, London. Calculate the amount of £‘s credited. Ongoing inter-bank rates are per$, Rs. 61.3625/3700 & per £, $1.5260/70. Answer Given: XYZ bank, Amsterdam is buying Rs. in exchange of £ Bank of London is Buying £ in exchange of Rs. Hence the bid rate is relevant. Bid Rs./ £ = Bid Rs./$ * Bid $/£ = 61.3625 * 1.5260 = 93.639 Rs./ £ Amt of £ required to buy 25 Million Rs. = 25 million /93.639 = 266982.27 £ Q 46 ABC technologies is expecting to receive a sum of$400,000 after 3month. The company decided to go for future contract to hedge against the risk. The Standard Size of the future contract available in the market is $1000. As on date spot and future$ contract are quoting at Rs44 and Rs45 respectively. Suppose after 3months the company closes out its position futures are quoting at Rs44.5 and spot rate is also quoting at Rs 44.50. You are required to calculate effective realization for the company while selling the receivable. Also calculate how company has been benefited by using the futures contract.

Given: Company is an Indian exporter Exposure = 400000$Due = 3 mths Lot size = 1000$ Spot = 44 Rs./ $3 mth futures 45.00 Rs. /$ --Sell $3 mth futures close 44.50 Rs. /$ --Buy $at maturity spot and square off Gain0.50 Rs./$

Total Gain = 400000 x 0.50 = 200000$Sell at spot 400000 x 44.5 = 17800000 + Gain on futures = 200000 Total Receipt = 18000000 Rs. Q 47 A British firm will have following two cash transactions after 2 months: 1. Cash payment for purchase of Machinery$ 5,14,000
2. Cash receipt of dividend income,             $1,10,000 Exchange data Spot rate 1 £ =$ 1.6000/1.6050

2 months forward             10/11 Cent

Interest rates (Pound)           12% p.a.

2 months maturity Option Date (lot size £ 25,000)

 Strike Price ($/£) call put 1.65 1.3 cents 1.4 cents 1.70 1.4 cents 1.60 cents 1.75 1.5 cents 1.75 cents Using the data given above suggests the mode of foreign exchange risk management Answer Given: Net amount payable is 404000$ If paid using Forward contract:

404000/1.7 = 237647/-

If paid using Option:

Fwd @ 1.7000, Hence Put option to sell £ can be bought at 1.75 Buy Put options (£250000 lot ) = 404000/1.75 = 230857£ 225000*1.75 = 393750 - Minimum $Proceeds 10857 @ Fwd @ 1.7 i.e. 6029 £ Put Premium = 0.0175$ / £ i.e. Total premium = 3937.5 $payable in$ Buy $at Spot = 2461 £ Time value of money = £ 2.510 Option Outflow: Exercise price = 225000 £ 10250 @ Fwd = 6029 £ Put Premium = 2510 £ Total cost = 233539 £ Q 48 Suppose that sterling – U.S. dollar spot and forward exchange rates are as follows:  Spot: 90-day forward: 180-day forward: 1.8470 1.8381 1.8291 What opportunities are open to an investor in the following situation: a. A 180-day European call option to buy £1 for$1.80 cost $0.0250? b.A 90-day European put option to sell £1 for$1.86 cost $0.0200? Answer Spot = 1.8470  90 days forward rate =1.8381 180 days forward rate = 1.8921 90 days PUT 1.86 = 0.02 180 days CALL1.80 = 0.025 Bay PUT Break Even Price = (1.86 – 0.02) =1.84 Buy forward @ 1.8381 (Less) Sell PUT @ 1.8400 Min Arbi Gain 0.0019 Buy CALL Break Even Price=(1.80+0.025)= 1.8250 Buy CALL @ 1.8250 (Less) Sell Forward @ 1.8291 Min Arbi Gain 0.0041 Q 49 An exporter requests his bank to extend the forward contract for US$ 20,000 which is due for maturity on 31st October, 2014, for a further period of 3 months. He agrees to pay the required margin money for such extension of the contract. Contracted Rate – US$1= Rs 62.32 The US Dollar quoted on 31-10-2014:- Spot 61.5000/61.5200 3 months‘ Discount -0.93% /0.87% Margin money from bank‘s point of view for buying and selling rate is 0.45% and 0.20% respectively. Compute: i) The cost to the importer in respect of the extension of the forward contract, and ii) The rate of new forward contract. Answer i) The contract is to be cancelled on 31-10-2014 at the spot selling rate of US$ 1 = Rs 61.5200

Add: Margin Money 0.20%    = Rs0.1230

= Rs 61.6430 or Rs 61.64

US$20,000 @ Rs 61.64 = Rs 12,32,800 US$ 20,000 @ Rs 62.32              = Rs 12,46,400

The difference in favour of the Customer         = Rs 13,600

ii) The Rate of New Forward Contract

Spot Selling Rate US$1 = Rs 61.5000 Less: Discount @ 0.93% = Rs(0.5720) = Rs 60.9280 Less: Margin Money 0.45% = Rs (0.2742) = Rs 60.6538 or Rs 60.65 Q 50 An edible oil importer wants to import edible il worth US$ 1,00,000 and places his import order on july 15, 2013, with the delivery date being 3 months ahead. At the time when the contract is placed, in the spot market, one US $was worth Rs 44.50. The Rupee depreciates to Rs 44.75 per US$ when the payment is due in October 2013. The value of the payment for the importer goes up to 44,75,000 rather than Rs 44,50,000. Design a hedging strategy for the importer given that one contract is for $1,000. Answer Appropriate hedging strategy would be to buy$ 1,00,000 in futures market as follows:

 Current Spot Rate (15th Juy '13) Rs44.5000 Buy 100 US $-Rs Oct. '13 Contracts (1000 x 44.5000) X 100 = Rs 44.50,000 Sell 100 US$-Rs oct. '13 Contracts in Oct 13 Rs 44.7500 Profit/Loss (futures market) 1000 x (44.75 -44.500)= Rs 25,000 Purchases in spot market @ 44.75 Rs 44.75 x 1,00,000 = Rs 44,75,000 Total cost of hedged transaction 1,00,000 x 44.75 = Rs 44,50,000

Q 51 The Spot rate for £ is $1.4710 - 1.4810 and swap points for 1 - month, 3- months and 6- months forward are 65/44, 145/123 and 290/222 respectively. Find out the outright rates for all three forward periods. Is the £ selling at premium or discount for these periods? How many$ would be required to buy £ 1,00,000 spot and after 3-months?

In all the three swap points sets, the first rate is more than the second point. So, the swap points are to be deducted from the spot rate to find out the forward rates as follows:

 Swap point Bid Price Ask price Spot Rate - $1.4710$ 1.4810 1- month forward 65/44 $1.4645 1.4766 3-month forward 145/123$ 1.4565 1.4687 6-month forward 290/222 $1.4420 1.4588 As the forward rate in terms of$ are decreasing, the $are at a forward premium$ required after 3 – months = 1,00,000 X $1.4687 =$ 1,46,870

$required spot = 1,00,000 X$ 1.4810 = $1,48,100 This$ is at forward premium and less $required to buy £ in future. Q 52 XYZ Ltd. which is exporting gold jewellery worth US$ 50,000, wants protection against possible Indian Rupee appreciation in Dec .'14, i.e., when it receives the payment. Currently, $are being traded at Rs44.65 which is expected to decline to Rs 44.30 till Dec.'14. In the futures market, Dec.'14 futures are available at Rs 44.65. It wants to lock in the exchange rate for the above transaction. Design an appropriate strategy. Answer In this case, the appropriate strategy for XYZ Ltd. would be to sell the$ futures maturing in Dec.'14. The Position would be as follows:

One US $- INR Contract size US$ 1,000

Sell 50 US$-INR Dec,'14. Contracts Rs 44.6500 Buy 50 US$ -INR Dec.'14 contracts in Dec.'14                       Rs 44.3000

Profit/Loss from futures                  50 x 1,000 x (44.65 - 44.30)

= 0.35 x 50 x 1000 = 17,500

Sell US $50,000 in spot market @ Rs 44.30 in Dec.'14. The net receipt in Rs for the hedged transaction would be : 50,000 x 44.30 +17,500 = 22,32,500 Had he not participated in futures market, he would have got only Rs 22,15,000. Thus he kept his sales unexposed to foreign exchange rate risk. Q 53 A bank enters into a forward purchase TT covering an export bill for Swiss Francs 1,00,000 at Rs 32.4000 due 25th April and covered itself for same delivery in the local inter bank market at Rs 32.4200. However, on 25th March, exporter sought for cancellation of the contract as the tenor of the bill is changed. In Singapore market, Swiss Francs were quoted against dollars as under: Spot USD 1 = Sw. Fcs. 1.5076/1.5120 One month forward 1.5150/ 1.5160 Two months forward 1.5250 / 1.5270 Three months 1.5415/ 1.5445 and in the interbank market US dollars were quoted as under:  Spot Spot / April Spot/May Spot/June USD 1 = Rs 49.4302/.4455 .4100/.4200 .4300/4400 .4500/4600 Calculate the cancellation charges, payable by the customer if exchange margin required by the bank is 0.10% on buying and selling. Answer First the contract will be cancelled at TT Selling Rate USD/ Rupee Spot Selling Rate Rs 49.4455 Add: Premium for April Rs 0.4200 Rs 49.8655 Add: Exchange Margin @ 0.10% Rs 0.04987 Rs 49.91537 or USD/ Sw. Fcs OneMonth Buying Rate Sw. Fcs. 1.5150 Sw. Fcs. Spot Selling Rate (Rs49.91537/1.5150) Rs 32.9474 Rounded Off Rs 32.9475 Bank buys Sw. Fcs. Under original contract Rs 32.4000 Bank Sells under Cancellation Rs 32.9475 Difference payable by customer Rs 00.5475 Exchange difference of Sw. Fcs. 1,00,000 payable by Rs 54,750 (Sw. Fcs. 1,00,000 x Rs 0.5475) Q 54 Suppose you are a treasurer of XYZ plc in the UK. XYZ have two overseas subsidiaries, one based in Amsterdam and one in Switzerland. The Dutch subsidiary has surplus Euros in the amount of 725,000 which it does not need for the next three months but which will be needed at the end of that period (91 days). The Swiss subsidiary has a surplus of Swiss Francs in the amount of 998,077 that, again, it will need on day 91. The XYZ plc in UK has a net balance of £75,000 that is not needed for the foreseeable future. Given the rates below, what is the advantage of swapping Euros and Swiss Francs into Sterling Rs Spot Rate (€) £0.6858- 0.6869 91 day Pts 0.0037 0.0040 Spot Rate(£) CHF 2.3295- 2.3326 91 day Pts 0.0242 0.0228 Interest rates for the Deposits  Amount of Currency 91 day Interest Rate Pa £ € CHF 0 - 100,000 1 ¼ 0 100,001 - 500,000 2 1 ½ ¼ 500,001 - 1,000,000 4 2 ½ Over 1,000,000 5.375 3 1 Answer Individual Basis  Interest Amt. after 91 days Conversion in £ Holland £502,414.71 € 725,000 x 0.02 x 91/360 = € 3,665.28 € 728,665.28 (728,665.28 x 0.6895) Switzerland £432,651.51 CHF 998,077 x 0.005 x (999,338.46 / 2.3098) 91/360 = CHF CHF 999,338.46 UK £ 75,000 x 0.01 x 91/36 = £ 189.58 £ 75,189.83 £ 75,189.83 Total GBP at 91 Days £ 1,010,256.05 Swap to Sterling  Sell € 7,25,000 (Spot at 0.6858) buy £ £ 4,97,205.00 Sell CHF 9,98,077(Spot at 2.3326) buy £ £ 4,27,881.76 Independent GBP amount £ 75,000.00 £ 1,000,086.76 Interest (£ 1,000,086.76 x 0.05375 x 91/360) £ 13,587.98 Total GBP at 91 Days £ 1,013,674.74 Less : Total GBP at 91 days as per Individual Basis £ 1,010,256.05 Gain £ 3,418.69 Q 55 On 3rd April 2016, a Bank quotes the following –  Spot Exchange Rate (US$1) INR 66.2525 INR 67.5945 2 months‘ Swap Points                              70                                                        90     3 month‘s Swap Points                             160                                                      186

In a spot transaction, delivery is made after two days.

Assuming Spot Date as 5th April 2016, and assuming 1 Swap Point = 0.0001, you are required to–

(a) Ascertain Swap Points for 2 months and 15 days. (For 20thJune 2016),

(b) Determine Foreign Exchange Rate for 20thJune 2016, and

(c) Compute the Annual Rate of Premium / Discount of US$on INR, on an Average Rate. Answer  (a) Swap points for 3rd month 160 – 70 = 90 186 – 90 = 96 (b) Swap points for 15 days = (a) / 2 45 48 (c) Swap points for 2 month and 15 days 70 + 45 = 115 90 + 48 = 138 (d) Foreign Exchange Rate for 2 months and 15 days 66.2525 + 0.0115 = 66.2640 67.5945 + 0.0138 = 67.6083 (e) Annual rate of premium / Discount (Taking 3 Month Ask swap points 0.0186 as base) Q 56 An Indian telecom company had approached Punjab National Bank for forward contract of £5,00,000 delivery on 31st May, 2008. The bank had quoted a rate of Rs61.60/£ for the purchase of pound sterling from the customer. But on 31st May, 2008, the customer informed the bank that it was not able to deliver the pound sterling as anticipated receivable from London has not materialized and requested the bank to extend the contract for delivery by 31st July, 2008. The following are the market quotes available on 31st May, 2008:  Spot (Rs/£) 1-month forward premium 2-month forward premium 3-month forward premium 62.60/65 20/25 42/46 62/68 Flat charges for cancellation of forward contract are Rs500. You are required to find out the extension charges payable by the telecom company. Answer Indian Company enters into forward purchase contract @ Rs61.60/- However, on 31st i.e. on due date, customer requests bank to extend the contract for delivery by 31st July 2008i.e. 2 months after 31st May. Thus, new contract will be booked at 1 £ = Rs 62.60 2month premium = 0.42 =63.02 Also, charges will be required tobe paid in relation to cancellation of the existing contract: Flat charges for cancellation Rs 500 Charges on account of exchange difference 5,00,000 (62.65-61.6) 5,25,000 5,25,000 Thus, Indian telecom company will be required to pay Rs 5,25,000 and new contract @ Rs 63.02 will be booked. Q 57 On September 1, 2011, the Rs/$ spot rate in New York is Rs 51.90 and December £ futures are trading at $1.5950. The Rs/£ spot rate on that day is Rs 78.90. Neel Corporation has a 3-month sterling receivable of £ 1,00,000. You are given that the standard size of sterling futures contracts is £ 62,500 and Neel Corporation decides to hedge its risk by trading in two sterling futures contracts. By December 1, 2011 the spot dollar has appreciated to Rs 52.80, while the spot pound sterling has depreciated to Rs 78.20. If December futures are trading at £ 1.5720. what is the profit or loss incurred by Neel Corporation? Answer On September 1, 2011: One US dollar = 51.90 INR and One Pound = 78.90 INR. This gives that One pound = 78.90/51.90 =1.5202 US dollars. On December 1, 2011: One US dollar = 52.80 INR and One Pound = 78.20 INR. This gives that One pound = 78.20/52.80 = 1.4811 US dollars. From above it is clear that One pound has depreciated from 1.5202 US dollar to 1.4811 US dollars in the spot market. The size of the order is for 1,00,000 pounds. Hence the loss due to depreciation would be = 1 ,00,000*(1.5202 -1.4811) = 3910 dollars. The hedge is required for 1,00,000 dollars but contract size is not equal to this amount. The contract size is for 62,500 dollars, Two contracts amounting to 1,25,000 dollars would be taken. Gain by trading in futures is given by: Gain = 2*62.500*(1.5950 -1.5720) = 2875 dollars. Net loss to Neil corporation: 3910 - 2875 = 1035 dollars. Note: The impact of hedge of extra 25.000 dollars (125,000 -100,000) has been ignored Q 58 The foreign exchange market price for US Dollar ($) against Indian Rupees (Rs) are quoted as under:

 Buying Selling Spot 65.30 65.50 Three months’ forward 66.35 67.20

Calculate the cost of forward cover.

When customer is buying dollar under 3 months forward cover: 1.05/66.35*12/3*100 = 6.33%

When customer is selling dollar under 3 moths forward cover: 1.70/67.20*12/3*100 = 10.12%

Cost of forward cover will be:

(6.33%+10.12%)/2 = 8.22%

Q 59 Bharat Silk Limited, an established exporter of silk materials, has a surplus of US$20 million as on 31st May 2015. The banker of the company informs the following exchange rates that are quote at three different forex markets:  GBP/ INR INR/ GBP USD/ INR INR/ USD USD/ GBP GBP/ USD 99.1 0.01 64.1 0.02 0.65 1.553 at London at London at Mumbai at Mumbai at New York at New York Assuming that there are no transaction costs, advice the company how to avail the arbitrage gain from the above quoted spot exchange rates. Answer The company can proceed in the following ways to realize arbitrage gain: (i) Buy Rupees from US$ at Mumbai: Rs 64.10*US$2,00,00,000 = Rs 128,20,00,000 (ii) Convert Rupees from US$ at London: Rs 128,20,00,000/99.10 = GBP 1,29,36,427.85

(iii) Convert GBP into US$at New York = GBP 1,29,36,427.85*1.5530 = US$ 2,00,90,272.45 There is a Net Gain of = US$2,00,90,272.45 - US$ 2,00,00,000 = US$90,272.45 Q 60 Suppose current price of an index is Rs. 13,800 and yield on index is 4.8% (p.a.). A 6- month future contract on index is trading at Rs. 14,340. Assuming that Risk Free Rate of Interest is 12%, show how Mr. X (an arbitrageur) can earn an abnormal rate of return irrespective of outcome after 6 months. You can assume that after 6 months index closes at Rs. 10,200 and Rs. 15,600 and 50% of stock included in index shall pay divided in next 6 months. Also calculate implied risk free rate. Answer Given: The fair price of the index future contract can calculated as follows: Theoretical futures price = =13,800+[(13,800×0.12×-13,800×4.8%×0.50)]6/12 - 13,800+[828 –331.20]= Rs. 14,296.80 Since presently index is trading at Rs. 14,340, hence it is overpriced. To earn an abnormal rate of return, Mr. X shall take following steps: 1. Mr. X shall buy a portfolio which comprising of shares as index consisted of. 2. Mr. X shall go for short position on index future contract. Now we shall calculate return to Mr. X under two given situations: (i)Return of Mr. X, if index closes at Rs. 10,200  Particulars Rs. Profit from short position of futures (Rs 14,340 – Rs. 10,200) Cash Dividend on Portfolio (Rs. 13,800 × 4.8% × 0.5) Loss on sale of portfolio (Rs. 10,200– Rs.13,800) 4,140.00 331.20 (3,600.00) 871.20 (ii) Return of Mr. X if index closes at Rs. 15,600  Particulars Rs. Loss from short position in futures (Rs 14,340 – Rs. 15,600) Cash Dividend on Portfolio Profit on sale of underlying portfolio (Rs. 15,600 – Rs.13,800) (1,260.00) 331.20 1800 871.20 Q 61 Mr. Peter Lynch currency trader from USA expects$ will depreciate against €. The current spot rate is 1.0768 $/ €. Strike price 1.1000$/€ 30 Days

Call on €               0.085

Put on €                0.110

(a) What should he do to profit from his anticipation

(b) What is the profit or loss if the rate on settlement after 30 days is $1.220 per € (i) If he bought 30 day call option. (ii) If he sold 30 day put option. Answer Given: Spot rate – 1.0768$/ €. Strike Price – 1.1000 $/€. Call on €- 0.085 Put on € - 0.110$will depreciate against €. It refers to Spot rate in future will be more than 1.1000$/€. Action to be taken to profit from his anticipation (i) Buy call option at a strike price of 1.1000$/€ at a premium of € 0.085. As we expect option will be exercised in future.

(ii) Sell Put option at a Strike price of 1.1000 $/€ at a premium of € 0.110. As the option is expected to be lapsed we can get premium as a profit. a. Profit or loss after 30 days if spot rate is 1.2200$/€.

 Particulars Call Put Option status Exercise Lapse a. GPO 1.220–1.100= 0.12 0 b. Premium - 0.085 +0.110 c. NPO ( a +/- b) 0.035 0.110

Q 62 Ascertain the value of Call Options expiring one year later, of two securities from the following information

 Stock Current Spot Price Exercise Price Expected Price One Year Later X Ltd Rs.1,020 Rs.1,050 Rs.1,100 D Ltd Rs.80 Rs.80 Rs.90

Risk Free Rate may be assumed at 10% for continuous discounting.

CCRFI is given , hence e’ values must be used Computation of Value of Call

 Stock Current Spot Price [SP0 ] Exercise Price PV of EP [EP Xe1x0.10] Value of Call Option [SP0- PV of EP] (1) (2) (3) (4) (5) = (2) – (4) X 1020 1050 1050/1.1052 = 950.05 1,020- 950.05 = 69.95 D 80 80 80/1.1052 = 7.39 80 -72.39 = 7.61

Q 63 A Ltd. has been considering the establishment of a manufacturing plant. Life of the project is 5 years the finance manager reported the expected NPV to be minus RS.50 Lakhs, the proposal is rejected by the management.

The Management Accountant has brought a new fact to the notice of the management- if A Ltd. implements the proposal, it shall have the option to make follow-on investment of RS.900  Lakhs at the end of 3rd year. The present value, of expected cash in flows from the new investment, at the end of 3rd year is RS.800 Lakhs. Cost of capital is 12%. Risk free rate of interest is 10%. The cash flows are highly uncertain and have a standard deviation of 0.36 p.a.

Find the value of the option using Black and Scholes model.

Given: T = 3 yrs

Exercise price = 900L r =10%

SD = 0.36

Spot price = 800 x 0.712 = 569.60 L

In case of (569.6L/900L) = -0.458546

$$d_{1}=\frac{-0.458546+\left\{0.10+0.5(0.36)^{2}\right\} \times 3}{0.36 \times \sqrt{3}}$$

= 0.0575

d2 = 0.5661 N(d1) = 0.71735 N(d2) = 0.285626

Value of ECO = 569.6 x 0.71735 - 900 x 0.741 x 0.285626

= Rs. 218.12 L

Q 64 Assume that a market-capitalization weighted index contains only three stocks A, B and C as shown below. The current value of the index is 1056.

 Company   A Share price (Rs)   120 Market capitalization (Rs Cr.)   12 B 50 30 C 80 24

Calculate the price of a futures contract with expiration in 60 days in this index if it is known that 25 days from today, Company A would pay a dividend of Rs 8 per share. Take the risk-free rate of interest to be 15% per annum. Assume the lost size to be 200 units.

Given:

Log(1+0.15) = 0.1398 = 13.98% CCRFI

Index is at 1056

Total M-Cap is 66 Cr.

The share price will fall after dividend payment

PV of dividend = 8 *

e-rt = 8 * 0.9905 = 7.924/-

Revised spot rate = 120 - 7.925 = 112.076/-

Revised M-Cap of A ltd = 112076000/-

Revised Index M-Cap = 652076000/-

The index fell by 1.2%

Index M−cap / 66 Cr.         Points /1056

65.2076                              ?

Revised Index = 65.2076*1056/66 = 1043.32

Theoretical Futures Price = 1043.32*ert = 1043.32*1.0232 = 1067.53 points

Q – 65 On April 5, BSXMAY2002, (the futures contracts on the BSE SENSEX expiring on 30.05.2002) were selling at 3540.10 while the spot index value was 3500.57. Using these values, obtain the annualized risk-free rate of return implied in the futures.

Given: S0 =3500.57, 55 Day Future = 3540.1

Assuming that Theoretical Futures Price = Actual Futures Price, Annualised Interest rate = S0(1 + r) = TFP

3500.57 [1+ ( x/100) * (55/360)] = 3540.1

1+ ( x/100) * (55/360) = 1.0113 x = (1.0113 - 1)*100*360/55

x = 7.39%

Q 66 The following information is available about standard gold.

 Spot Price (SP) Future price (FP) Risk free interest rate (Rf) Rs.15,600 per 10 gms. Rs.17,100 for one year future contract 8.5%

Present value of storage cost RS.900 per year

From the above information you are required to calculate the present value of Convenience yield of the standard gold.

Present Value of convince yield = spot rate + P.v.of storage cost-p.v. of future price.

= 15600+900-15760= Rs. 740

Q 67 Today is 24th March. A refinery needs 1,050 barrels of crude oil in the month of September. The current price of the crude oil is Rs. 3,000 per barrel. September futures contract at Multi Commodity Exchange (MCX) is trading at Rs. 3,200. The firm experts the price to go up further and beyond Rs.3,200 in September. It has the option of buying the stock now. Alternatively it can hedge through futures contract.

1. If the cost of capital, insurance, and storage is 15% per annum, examine if it is beneficial for the firm to buy now ?
2. Instead, if the upper limit to buying price is Rs. 3,200 what strategy can the firm adopt?
3. If the firm decides to hedge through futures, find out the effective price it would pay crude oil if at the time of lifting the hedge (i) the spot and futures price are Rs. 2,900 and Rs. 2,910 respectively, (ii) the spot and futures price are 3,300 and Rs. 3,315 respectively.

Given:Requirement in September = 1050 barrels Investment cost = 15%

S0 = Rs. 3000/-

Sept. futures price = 3200/-

Theoretical Futures Price = 3000 * e0.15*6/12= 3233.65/- Effective cost of buying at spot= 3233.65/-

Effective cost of buying at futures = 3200/-

 Particulars (i) (ii) Buy at Futures -3200 -3200 Sell at Futures 2910 3315 (loss)/gain -90 115 Buy at spot for delivery 2900 3300 Net Cost 2990 3185

Q 68 The standard derivation of the monthly spot prices of gold is 0.90 the standard deviation of the monthly futures price of gold is 1.20 Coefficient of correlation between these two prices is 0.60. Today is 20thFebruary; 2010.An exporter-jeweler has to purchase 100kgs of gold after one month. Gold futures contracts mature on 20th of every month. How can it be hedged against rise in gold prices?

Given:

SD of Spot = 0.9, SD of futures = 1.2 Correlation (spot, futures) = 0.6 Hedge ratio = (0.69/1.2) * 0.6 = 0.45 Qty. of gold to be purchased = 100 kgs

Amt. of gold futures to buy = Hedge ratio* req. qty.

= 0.45 * 100 = 45 kgs

Hence Hedge Ratio must be 0.45 for perfect hedging with futures.

Q 69 Sensex futures are traded at a multiple of 50. Consider the following quotations of Sensex futures in the 10 trading days during February, 2009:

 Day. High Low Closing 4-2-09 3306.4 3290.00 3296.50 5-2-09 3298.00 3262.50 3294.40 6-2-09 3256.20 3227.00 3230.40 7-2-09 3233.00 3201.50 3212.30 10-2-09 3281.50 3256.00 3267.50

Abhishek bought one sensex futures contract on February, 04. The average daily absolute change in the value of contract is 10,000 and standard deviation of these changes isRs. 2,000. The maintenance margin is 75% of initial margin.

You are required to determine the daily balances in the margin account and payment on margin calls, if any.

Given: Initial Margin = Mean + (3*SD) (considering 99% volatility ofnormal Distribution Cuve)

= 10000 + ( 3* 2000) = 16000/-

Maintenance Margin = 75% of Initial Margin

= 75% of 16000/- = 12000/-

 Day BSE Close Initial Margin Change Shortfall Closing Margin 1 3296.5 16000 - - 16000 2 3294.4 16000 -2.1*50 = -105 - 15895 3 3230.4 15895 -64*50 = -3200 - 12695 4 3212.3 12695 -18.1*50 = -905 4210 16000 5 3267.5 16000 55.2*50 = 2760 - 18760

Q 70 The shares of Mastek Ltd. are currently traded at Rs 20 per share. A call option at a strike price of Rs 18 is available at Rs 3 for an expiration period of 1 year. Analyse the profit of the investor if the riskfree rate of interest is 10% and the investor wants to go short in share and long in the call

In the given case, the strategy of the investor can be presented as follows:

• Short the share at Rs 20
• Long the call option (Premium Rs 3 at strike Price is Rs 18).
• Invest the money from sale of share @ 10%

The profit of the investor can be analysed as follows:

Sale proceeds from sale of share                       Rs 20

Net Proceeds                                                     Rs 17

Invested @ 10% for 1 year grows to 17e0.1 = 17 x e0.1 Rs 18.79

So, the investor will have Rs 18.79 at the end of the year when the call matures. If the market price of the share at this time is more than Rs 18, he would exercise the option, and get a profit of Rs 0.79 (i.e, 18.79- 18).

However, if the market price of the share on the expiration date is less than Rs 18, he should buy the share from the market and his profit would be (Rs 18.79 - Market price). So, the investor would gain irrespective of the market price.

Q 71 A company has to pay Rs. 10m after 6 years from today. The company wants to fund this obligation today only. The current interest rate in the market is 8%. Two zero coupon bonds are traded in the market in the basis of 8% YTM (a) maturity 5 years and (b) maturity 7 years.

Suggest the interest rate risk immunized investment plan.

Amt. req. to fund obligation = 10million/ (1.08)6 = 6.301969 million

 Bond Weight Duration W*D 5 Year X 5 5x 7 Year 1-x 7 7(1-x) 6 years

Invest Rs 3.15 mln in 5 year bond and similar amount in 7 year bond to immunize the obligation.

Q 72 Calculate Market Price of:

a) 10% Government of India security currently quoted at Rs. 110, but interest rate is expected to go up by 1%.

b) A bond with 7.5% coupon interest, Face Value 10,000 & term to maturity of 2 years, presently yielding 6%. Interest payable half yearly.

Given:

a) Coupon = 10%, CMP = 110/-

Current yield = (10/110) *100 = 9.09%

Revised CMP = (10/x)*100 =10.09% (interest rates increased by 1%) x = (100*10)/10.09%=99.108/-

b) Coupon = 7.5% payable half yearly FV = 10,000/-

Time to maturity = 2 yrs YTM = 6%

Fair value of the bond =375*PVAF(3%,4periods)+10000*PVIF(3%,4periods)

= (375 * 3.7171) + (10000 * 0.88999)

= 10293.81/-

Q 73 Following is available in respect of dividend, market price and market condition after one year:

 Market condition Probability Market Price Dividend per share Good .25 115 9 Normal .5 107 5 Bad .25 97 3

The existing market price of an equity share is Rs. 106 (F. V. Re.1); which is cum 10% bonus debenture of Rs. 6 each, per share. M/s. X Finance Company Ltd. has offered the buy-back of debentures at face value.

Find out the expected return and variability of returns of the-equity shares. And also advise-Whether to accept buy back after?

The Expected Return of the equity share may be found as follows:

 Market  condition Probability Total Return Cost(*) Net  return Good 0.25 Rs. 124 Rs.100 Rs. 24 Normal 0.50 Rs. 112 Rs.100 Rs. 12 Bad 0.25 Rs. 100 Rs.100 Rs. 0

Expected Return = (24x0.25) + (12x0.50)+(0x25)

= (12/100)x100 = 12%

The variability of return can be calculated in terms of standard deviation.

Variance= 0.25 (24-12)2+0.50(12-12)2+0.25(0-12)2= 72% , SD = 8.48%

(*) The present market price of the share is Rs. 106 cum bonus 10% debenture of Rs 6 each; hence the net cost is Rs. 100 (There is no cash loss or any waiting for refund of debenture amount)

M/s X Finance company has offered the buy back of debenture at face value. There is reasonable 10% rate of interest compared to expected return 12% from the market. Considering the dividend rate and market price the creditworthiness of the company seems to be very good. The decision regarding buy-back should be taken considering the maturity period and opportunity in the market. Normally, if the maturity period is low say up to 1 year better to wait otherwise to opt buy back option.

Q 74 Pearl Ltd. expects that considering the current market prices, the equity share holders should get a return of at least 15.50% while the current return on the market is 12%. RBI has closed the latest auction for Rs. 2500 Cr. of 182 day bills for the lowest bid of 4.3% although there were bidders at a higher rate of 4.6% also for lots of less than RS.10 Cr. What is Pearl Ltd‘s Beta?

Return of stock = 15.5%

Risk free return = {4.3%+4.6%}/2 = 4.45% Return of the market = 12%

CAPM = Rf + β(Rm-Rf )

15.5%= 4.45%+β(12%-4.45%)

Hence β=1.473

Q 75 Suppose Mr. A is offered a 10% Convertible Bond (par value Rs 1,000) which either can be redeemed after 4 years at a premium of 5% or get converted into 25 equity shares currently trading at Rs 33.50 and expected to grow by 5% each year. You are required to determine the minimum price

Mr. A shall be ready to pay for bond if his expected rate of return is 11%.

First we shall find the Conversion Value of Bond CV = C (1+g)nx R Where:

C = Current Market Price

g = Growth Rate of Price

R = Conversion Ratio

n = No. of years Accordingly,

CV shall be = Rs 33.50 x 1.054 x 25

=Rs 33.50 x 1.2155 x 25 = Rs 1017.98

Value of Bond if Conversion is opted = Rs 100 x PVAF (11%, 4) + Rs1017.98 PVF (11%,4)

= Rs 100 x 3.102 + Rs 1017.98 x 0.659

= Rs 310.20 + Rs 670.85 = Rs 981.05

Since above value of Bond is based on the expectation of growth in market price which may or may not as per expectations. In such circumstances the redemption at premium still shall be guaranteed and bond may be purchased at its floor value computed as follows:

Value of Bond if Redemption is opted

= Rs 100 x PVAF (11%, 4) + Rs 1050 PVF (11%,4)

= Rs 100 x 3.102 + Rs 1050 x 0.659

= Rs 310.20 + Rs 691.95 = Rs 1002.15

Q 76 During a year, the price of British Gilts (Face value £100) rose from £103 to £105 while paying a coupon of £8. At the same time, the exchange rate moved from $/£ 1.70 to$/£ 1 .58. What is the total return to an investor in the US who invested in the abovesecurity?

Amount invested = £ 103 When; 1 £ = 1.70

Hence, amount invested (in $) = 103*1.70 = 175.1 Amount received = £ 105 Coupon (Interest) received = £ 8 Total = £ 113 When; 1 £ = 1.58 So Amount received = 113*1.58 = 178.54 Return = (178.54-1975.1)/175.1 *100 = 1.965% Q 77  Investment X Y Principal Rs 20 Lakhs 20 Lakhs Rate of Yield p.a. 12% 12% Tenor (Years) 3 3 Compounding Monthly Continuous Compounding charges payable at the end of the period Nil Rsm per lakh For what minimum value of ‘m’ will an investor prefer X to Y? Answer 20,00,000 (1+0.12/12)36 > 20,00,000*e0.36 - 20mn 20,00,000 [1.43076878 – 1.4333294] > -20mn 20,00,000 [-0.00256062] > -20mn Or m > Rs256.06 per lac If the continuously compounding facility exceeds Rs256.00 per lac, the investor will prefer monthly compounding. Q 78 The data given below relates to a convertible bond: Face value Rs 250  Coupon rate 12% No. of shares per bond 20 Market price of share 12 Straight value of bond Rs 235 Market price of convertible bond Rs 265 Calculate: (i) Stock value of bond. (ii) The percentage of downside risk. (iii) The conversion premium (iv) The conversion parity price of the stock. Answer (i) Stock value or conversion value of bond 12 * 20 = Rs 240 (ii) Percentage of the downside risk (Rs265 - Rs235)/Rs235 = 0.1277 or 12.77% This ratio gives the percentage price decline experienced by the bond if the stock becomes worthless. (iii) Conversion Premium (Market Value – Conversion Value)/ Conversion Value * 100 (Rs265 - Rs240)/Rs240 * 100 = 10.42% (iv) Conversion Parity Price Bond Price/No. of shares on conversion Rs265/20 = Rs 13.25 This indicates that if the price of shares rises to Rs 13.25 from Rs 12 the investor will neither gain nor lose on buying the bond and exercising it. Observe that Rs 1.25 (Rs 13.25 – Rs 12.00) is 10.42% of Rs 12, the Conversion Premium. Q 79 Sa Re Gama Electronic is in the business of selling consumer durables. In order to promote its sales it also financing the goods to its customer allowing them to make some cash down payment and balance in installments. In a deal of LCD TV with selling price of Rs. 50,000, a customer can purchase it for cash down payment of Rs. 10,000 and balance amount by adopting any of the following option:  Tenure of Monthly Installments Equated Monthly Installment 12 3,800 24 2,140 Answer  12 Months 24 Months 1.TotalAnnual Charges for Loan 3,800X12–40,000=5,600 (2,140X24–40,000)/2=5,680 2. Flat Rate of Int (F) 5,600/40,000 x 100 = 14% 5,680/40,000x100 = 14.20% 3. Effective Int Rate  Q 80 Drilldip Inc. a US based company has a won a contract in India for drilling oil filed. The project will require an initial investment of Rs. 500 Cr.. The oil field along with equipments will be sold to Indian Government for Rs. 740 Cr. in one year time. Since the Indian Government will pay for the amount in Indian Rupee (Rs.) the company is worried about exposure due exchange rate volatility. You are required to: a) Construct a swap that will help the Drilldip to reduce the exchange rate risk. b) Assuming that Indian Government offers a swap at spot rate which is 1US$ = Rs. 50 in one year, then should the company should opt for this option or should it just do nothing. The spot rate after one year is expected to be 1US$= Rs. 54. Further you may also assume that the Drilldip can also take a US$ loan at 8% p.a.

With swap:

Step 1: borrow USD loan of $10 cr @ 8% p.a. Step 2: exchange these$ with Rs. with any Indian Company.

Step 3: Receive 740 Cr Rs. From Indian Govt and swap back Rs. 500 cr with Indian company and receive$10 Cr back. Balance left out is Rs. 240 Cr convert to$ at one year spot rate. Receive $4.444 CR. Now Drill dip has$14.44 CR.

Step 4: Repay the $loan along with Interest ,$ 10.8, balance $gain is 3.6 cr. Without swap: Step 1: borrow USD loan of$10 cr @ 8% p.a.

Step 2: Convert these $with Rs. At spot rate 50Rs. /$ and receive 500 Cr.

Step 3: Receive Rs.740 Cr. And convert @ 1 year spot rate @ 54Rs. /$. Receive, Rs 13.70Cr Step 4: Repay the$ loan along with Interest, $10.8, balance$ gain is 2.904 cr

As the net amount receivable at swap is higher, the company should go for swap arrangement

Q 81 The following details are related to the borrowing requirements of two companies ABC Ltd. And DEF Ltd.

 Company Requirement Fixed Rates Offered Floating Rates Offered ABC Ltd Fixed Rupee Rate 4.5% PLR + 2% DEF Ltd. Floating Rupee Rate 5.0% PLR + 3%

Both Companies are in need of Rs. 2,50,00,000 for a period of 5 years. The interest rates on the floating rate loans are reset annually. The current PLR for various period maturities are as follows:

 Maturity (Years) PLR (%) 1 2.75 2 3.00 3 3.20 4 3.30 5 3.375

DEF Ltd. has bought an interest rate Cap at 5.625% at an upfront premium payment of 0.25%.

a) You are required to exhibit how these two companies can reduce their borrowing cost by adopting swap assuming that gains resulting from swap shall be share equity among them.

b) Further calculate cost of funding to these two companies assuming that expectation theory holds good for the 4 years.

a) The swap agreement will be as follows:

1. ABC Ltd. will borrow at floating rate of PLR + 2% and shall lend it to DEF Ltd. at PLR+2% and shall borrow from DEF Ltd. at Fixed Rate of 4.25%.
2. DEF Ltd. shall borrow at 5% and lend it to ABC Ltd. at 4.25% and shall borrow from ABC Ltd at floating rate of PLR +2%.

Thus net result will be as follows:

Cost to ABC Ltd. = PLR + 2% - (PLR + 2%) + 4.25% = 4.25% Cost to DEF Ltd = 5% - 4.25% + PLR + 2% = PLR +2.75%

b) Suppose if theory of expectations hold good, the cost of fund to DEF Ltd. will be asfollows:

 Year Expected Annual PLR Loading Effective Rate Effectiverate @Cap 1 2.75% 2.75% 5.50% 5.50% 2 (1.032÷1.0275)–1= 3.25% 2.75% 6.00% 5.625% 3 (1.0323÷1.032)–1= 3.60% 2.75% 6.35% 5.625% 4 (1.0334÷1.0323)–1=3.60% 2.75% 6.35% 5.625%

Q 82 Mr. Stanly Joseph has secured from a housing bank, a six year housing loan of Rs. 12,00,000. The loan was structured as follows:

 Loan Amount --- Rs. 12,00,000 Repayment --- Six equated annual installments, payable in arrears. Reference Base --- Prime Lending Rate Reference Rate --- 9% on the date of loan Interest on Loan --- 1 percentage point over reference rate of 9% Annual Installment --- Rs.2,75,530

Two year after the loan was granted, the prime rate moves down to 8% and the effective rate on the loan automatically stood revised to 9%. What action can the bank take?

Determination of Remaining Principal

 Year Opening  balance Int.@ 10% Total Repaid Cl bal. 1 1200000 120000 1320000 275530 1044470 2 1044470 104447 1148917 275530 873387

Determination of Revised Equated Monthly Installment

 New amount 873387 New period 4 years New rate 9 % PVAF 3240 Installment 873387/3240 =   269564/-

Bank shall revise installment from 275530 to 269564/-

Q 83 On January 25, a European Bank wants USD 100 million of 6-month deposit. However, it is offered USD 100 million of 9- month deposit at the bank‘s bid rate. At the current market, the other rates are these:

 Cash FRA Bid Ask Bid Ask 6 Months 10.4375 10.5625 6 x 9 10.48 10.58 9 Months 10.5625 10.6875

Should the bank take the 9- month deposit? Explain with calculations and pay off

The bank wants a six month deposit of $100 million. Therefore it can be understood that it would have funds of$100 million at the end of six months so as to repay the six month deposit if it was available. However, only nine month deposit is available, meaning that it would have the obligation to repay after nine months. Thus the bank would have funds to lend for three months starting 6 months today for the period of three months. Thus the bank can sell 6 x 9 FRA thereby converting the 9-month deposit to a 6-month deposit. That is, the bank sells off (lends) the last 3-month in the FRA market. Days from January 25 to September 25 (9-month deposit) = 273 days. Days from June 25 to September 25 (6 X 9 FRA) = 92 days

The interest that would be paid at the end of nine months to the depositor is:

$100 million x (0.105625) x (273/360) = USD 8,009,895.83. Interest earned on lending for 6-month in the interbank market, then another 3-month at the FRA rate is:$100,000,000x[(1+0.104375x(181/360))x(1+0.1048x(92/360)) - 1] = $8,066,511.50. Thus there is a net profit of$ 56,615.67 at the end of nine months

Q 84 (a) What spot and forward rates are implied in the following bonds? (F.V.RS.100) Bond A Zero-coupon; Maturity 1 year: price Rs.93.46

Bond B coupon 5% Maturity 2 years; Price Rs.98.13 Bond C Coupon 9%; Maturity 3 years; Price Rs. 104.62

(c) A three year bond with a 6 percent coupon is selling at Rs. 99.00. Is there an arbitrage profit opportunity here? Yes, what amount of profit can you make? Assume short sale facility is available.

a. Spot rate (forward rate for the year) : 100/(1+x%)= 93.46 Let forward rate for year 2 : r

5 / (1.07) + 105 / {(1.07)(1+r%)}= 98.13

r = 5%

Let forward rate for year 3 : r

9/(107) + 9 / {(1.07)(1.05) + 109 / {(1.07)(1.05)(1+r)} = -104.62

r = 10%

b. Value of the bond =6/(1.07)+6/(1.07)(1.05)+106/{(1.07)(1.05)(1.10)}= 96.72/-

The bond is overvalued in the market. Arbitrage opportunity exists.

Q 85 Assume that the current rate on a one year security is 7%. You believe that the yield on a 1 year security will be 9% one year from now and 10% 2 years from now. According to expectations hypothesis, what should be yield on a 3 year security?

Current Rate on one year security – 7%

Yield on one year security i.e 12/24 FRA – 9%

Yield on two year security i.e 24/36 FRA – 10%

Yieldon three year security = (1+7%) (1+9%) (1+10%) =(1+x/100)3

1.07 * 1.09 * 1.10 = (1+x/100)3

1.28293 = (1+x/100)3

1.282931/3 = 1+x/100

X = 8.8%

3 year interest rate must be 8.8% to avoid any arbitrage opportunity

Q 86 ABC Bank is seeking fixed rate funding. It is able to finance at a cost of six months LIBOR plus ¼ % for Rs. 200m for 5 years.The bank is able to swap into a fixed rate at 7.50% versus six months LIBOR treating six months as exactly half year.

1. What will be the ―all in cost funds‖ to ABC Bank?
2. Another possibility being considered is the issue of a hybrid instrument which pays 7.5% for the first three years and LIBOR-1/4% for remaining two years.

Given a three year swap rate of 8%, suggest the method by which the bank should achieve fixed rate funding.

a)Calculation of All in Cost:

 Payment by Bank for Borrowing on LIBOR basis -[LIBOR + 0.25] Payment under swap -7.50 Receipt under swap + LIBOR Net cost 7.75%

b) Annual cash flows on Rs. 100/-

 Years 1-3 Years 4-5 Interest on Hybrid instrument -[7.50] -[ L -0.25] I swap -7.50 -7.50 I swap +L +L II swap -L II swap +8 Total 7 7.25

Q – 87 A fund manager Mr. Aditya deposited $200 million on floating basis for 3 years, which pay LIBOR + 50 bps. The interest rates are reset every year. The company buys a 3 year floor on a 1- year LIBOR with a strike rate of 8% and having a face value of$ 200 million. The floor carries a premium of 1.5% of face value of $3 million. Current 1 year LIBOR is 8.60%.if the LIBOR at the end of 1, 2 and 3 years are 7.5%, 9% and 7%, what is the cash flow from floor each year? Amortize premium equity over three years. Answer The strike rate of the floor is Libor which is currently 8.6%. The interest rate applicable on the deposit would be Libor + 50 bps i.e. 50 bps over 7.5%, 9% & 7% respectively for the three years. Thus the interest payable in amount terms over three years would be:$1,60,00,000,

$1,90,00,000 and$1,50,00,000 respectively.

Now, the premium paid for buying this floor is $3 million. As given in the problem equal amortization would involve$10,00,000 each year, The seller of the floor would part with the difference whenever the Libor is below the strike price of 8%.

Therefore we can construct the cash flow table as follows:

 Time Cash - Deposit Amortization of Premium Cash Flow Total from Floor 0 -20,00,00,000 - - -20,00,00,000 1 +1,60,00,000 -10,00,000 +10,00,000 +1,60,00,000 2 +1,90,00,000 -10,00,000 - -1,80,00,000 3 +1,50,00,000 -10,00,000 +20,00,000 +1,60,00,000 4 +20,00,00,000 - - +20,00,00,000

Q 88 Surya holdings ltd. has a portfolio of shares of diversified companies, valued at Rs 10,00,000. It enters into swap arrangement with XYZ swaps with the following terms: Surya holdings Ltd. to get a fixed return of 1.15% per quarter on notional principal of Rs

10,00,000 in exchange of the return on the portfolio which is exactly tracking the NIFTY. The exchange of return is to take place on quarterly basis. Nifty at present is 5400 and on quarterly intervals are 5465,5455,5520,5490. Find out the net payments to be received or paid by Surya Holdings Ltd. at the end of different quarters.

The receipt of Surya Holdings Ltd. is fixed per quarter @ 1.15% on Rs 10,00,000. However, the payment to be made by it depends on the return shown by the movement of NIFTY.

Net cash flow can be calculated as follows:

 Quarter NIFTY NIFTY Return Amount payable Fixed Return Net Amount Receivable 0 5400 - - - - i 5465 1.2037% Rs 12,037 Rs 11,500 Rs 535 ii 5445 -0.3660% - Rs 3660 Rs 11,500 Rs 15,160 iii 5520 1.3774% Rs 13,774 Rs 11,500 - Rs 2,274 iv 5490 -0.5435% - Rs 5,435 Rs 11,500 Rs 16,935

Q 89 Mr.A is thinking of buying shares at Rs.500 each having face value of Rs.100. He is expecting a bonus at the ratio of 1:5 during the fourth year. Annual expected dividend is 20% and the same rate is expected to be maintained on the expanded capital base. He intends to sell the shares at the end of seventh year at an expected price of Rs.900 each. Incidental expenses for purchase and sale of shares are estimated to be 5% of the market price. He expects a minimum return of 12% per annum.

Should Mr. A buy the share? If so, what maximum price should he pay for each share? Assume no tax on dividend income and capital gain.

Given: S0 = 500/- FV = 100

Bonus Ratio = 1:5 DPS = 20

Y7 = P7 = 900 (expected) Brokerage = 5%

Ke= 12%

The value of the share is the PV of future cash flows.

Bonus share for every 1 share held = 1 x 1/5 = 0.2 shares

Dividend on a bonus share = 20 x 1/5 = 4/-

Computation of PV of cash flows of ONE share:

 Year Cash Flow Disc.@ 12% Disc.C/F 1 20 0.8928 17.856 2 20 0.7972 15.944 3 20 0.7118 14.236 4 20 + 4 0.6355 15.252 5 20 + 4 0.5674 13.617 6 20 + 4 0.5063 12.151 7 20 + 4 0.4524 10.857 7 (900x(1+0.2))-5% 0.4524 464.1624 PV of Cash flows 564

To get 12% return, we have to pay 564/- Let FV of stock = x

Share price + commission = x + (x x 5/100) =564 x + 0.05x = 564/- x = 537/-

FV of stock is 537/- Market Price is 500/-

Thus, the stock is undervalued. Buy the stock.

Q 90 Delta Ltd.‘s current financial year‘s income statement reports its net income as Rs 15,00,000.Delta‘s marginal tax rate is 40% and its interest expense for the year was Rs 15,00,000. The company has Rs 1,00,00,000 of invested capital, of which 60% is debt. In addition, Delta Ltd. tries to maintain a Weighted Average Cost of Capital (WACC) of 12.6%.

(i) Compute the operating income or EBIT earned by Delta Ltd. in the current year.

(ii) What is Delta Ltd.‘s Economic Value Added (EVA) for the current year?

(iii) Delta Ltd. HasRs2,50,000 equity shares outstanding. According to the EVA you computed in    , how much can Delta pay in dividend per share before the value of the company would start to decrease? If Delta does not pay any dividends, what would you expect to happen to the value of the company.

(i) Taxable income = Net Income /(1 – 0.40) or,

Taxable income = Rs 15,00,000/(1 – 0.40) = Rs 25,00,000 Again, taxable income = EBIT – Interest

or, EBIT = Taxable Income + Interest

= Rs 25,00,000 +Rs 15,00,000 =Rs 40,00,000

(ii) EVA = EBIT (1 - T) - (WACC x Invested capital)

= Rs40,00,000 (1 - 0.40) - (0.126 xRs 1,00,00,000)

= Rs 24,00,000 - Rs 12,60,000 = Rs11,40,000

(iii) EVA Dividend = Rs 11,40,000/2,50,000 = Rs 4.56

If Delta Ltd. does not pay a dividend, we would expect the value of the firm to increase because it will achieve higher growth, hence a higher level of EBIT. If EBIT is higher, then all else equal, the value of the firm will increase.

Q 91 Following information is available in respect of expected dividend, market price and market condition after one year.

 Market condition Probability Market Price Dividend per share Rs Rs Good 0.25 115 9 Normal 0.50 107 5 Bad 0.25 97 3

The existing market price of an equity share is Rs 106 (F.V. Rs 1), which is cum 10% bonus debenture of Rs 6 each, per share. M/s. X Finance Company Ltd. had offered the buy-back of debentures at face value.

Find out the expected return and variability of returns of the equity shares. And also advise-Whether to accept buy back after?

The Expected Return of the equity share may be found as follows:

 Market condition Probability Total Return Cost (*) Net Return Good 0.25 124 100 24 Normal 0.50 112 100 12 Bad 0.25 100 100 0

Expected Return = (24 x 0.25) + (12 x 0.50) + (0 x 0.25) = 12= (12/100) x 100 = 12%

The variability of return can be calculated in terms of standard deviation. V SD = 0.25 (24 - 12)2 + 0.50 (12 - 12)2 + 0.25 (0 - 12)2

= 0.25 (12)2 + 0.50 (0)2 + 0.25 (-12)2

= 36 + 0 + 36

SD = √72

SD = 8.485 or say 8.49

(*) The present market price of the share is Rs 106 cum bonus 10% debenture of Rs 6 each; hence the net cost is Rs 100 (There is no cash loss or any waiting for refund of debenture amount).

M/s X Finance company has offered the buyback of debenture at face value. There is reasonable 10% rate of interest compared to expected return 12% from the market. Considering the dividend rate and market price the creditworthiness of the company seems to be very good. The decision regarding buy-back should be taken considering the maturity period and opportunity in the market. Normally, if the maturity period is low say up to 1 year better to wait otherwise to opt buy back option.

Q 92 Odessa Limited has proposed to expand its operations for which it requires funds of $15 million, net of issue expenses which amount to 2% of the issue size. It proposed to raise the funds though a GDR issue. It considers the following factors in pricing the issue: (i) The expected domestic market price of the share is Rs 300 (ii) 3 shares underly each GDR (iii) Underlying shares are priced at 10% discount to the market price (iv) Expected exchange rate is Rs 60/$

You are required to compute the number of GDR's to be issued and cost of GDR to Odessa Limited, if 20% dividend is expected to be paid with a growth rate of 20%.

Net Issue Size = $15 million Gross Issue =$15 million / 0.98 = $15.306 million Issue Price per GDR in Rs (300 x 3 x 90%) Rs 810 Issue Price per GDR in$ (Rs 810/ Rs 60) $13.50 Dividend Per GDR (D1) = Rs 2* x 3 = Rs 6 * Assumed to be on based on Face Value of Rs 10 each share. Net Proceeds Per GDR = Rs 810 x 0.98 = Rs 793.80 a) Number of GDR to be issued$15.306 million / $13.50 = 1.1338 million b) Cost of GDR to Odessa Ltd. ke=(6.00/793.80)+0.20 = 20.76% Q 93 A Japanese company is to quote lease rent for 5 aircrafts required by an Indian company. The operating life of the aircrafts may be 5 years; at the end of which it can be disposed of a 10% of it‘s of its cost in US market. The cost of each aircrafts is$ 10m. The Japanese tax system allows sum of digit method depreciation to the lesser. Assume income tax rate in Japan to be 25%. Find the annual lease rent. In yens, to be charged so as provided 4% post return to the lessor. Assume that the lease rent if payable in the begging of each year. The spot rate: 1 $= 120 Yen. Assume thatUSD is expected to depreciate against Yen by 5% p.a. Answer WN-1:Computation of forward rate 5 years forward rate : 1$ = 120 (0.95)5 yen = 108.4705 yen

WN-2:Calculation of depreciation

Cost: 1200 million yen

sale of scrap = 108.4705 million yen. Depreciable Amt: 1091.5295 million yen

 Year Depreciation PV of Tax Savings on  Depreciation 1 1091.5295 x (5/15) = 363.8432 M yens 363.8432 x 0.25 x 0.962 2 1091.5295 x (4/15) = 291.0745M yens 291.0745 x 0.25 x 0.925 3 1091.5295 x (3/15) = 218.3059 M yens 218.3059 x 0.25 x 0.889 4 1091.5295 x (2/15) = 145.5373 M yens 145.5373 x 0.25 x 0.885 5 1091.5295 x (1/15) = 72.7686 M yens 72.7686 x 0.25 x 0.822 Total 250.4878 M yens

PV of Scrap = 108.4705 Million yen

The Lessor wants a return of 4%. Hence the NPV at 4% should be 0. Let annual Lease rent = y

PV of Lease Receipts = y + 3.63y = 4.63y

0 = -Investment +PV of Lease rent - PV of tax on Lease rent + PV of tax savings on depreciation + PV on sale of scrap

0 = -1200 + 4.63y -0.25y (4.452) + 250.4875 + 89.1628 - 3.517y = -860.3494

y = 244.6259 Million yen (PVAF factor for tax will change because tax benefit comes in next year)

Annual Lease rent of Five Aircrafts = 5 x 244.6259 Million yen = 1223.1295 Million yen

Q 94 GKL Ltd. is considering installment sale of LCD TV as a sales promotion strategy. In a deal of LCD TV, with selling price of Rs. 50,000, a customer can purchase it for cash down payment of Rs.10,000 and balance amount by adopting any of the following options:

 Tenure of Monthly  Installments Equated Monthly   Installment 12 Rs.3,800 24 Rs.2140

Required: Estimate the flat and effective rate of interest for each alternative.

PVIFA 2.05%, 12 = 10.5429                  PVIFA2.10%, 12 = 10.5107

PVIFA 2.10%, 24 = 18.7014                  PVIFA2.12%, 24 = 18.6593

 1. Total Annual charges for loan Rs.3,800*12 – Rs.40,000 = Rs.5,600 (Rs.2,140*24–40,000)/2 = Rs.5,680 2.Flat Rate of Interest (F) Rs.5,600/Rs.40,000*100 = 14% Rs.5,680/Rs.40,000 *100 = 14.20% 3.Effective Interest Rate n/(n-1)*2F = 12/13*28 = 25.85% n/(n-1)*2F =24/25 *28.40 = 27.26%

Q 95 Herbal Gyan is a small but profitable producer of beauty cosmetics using the plant Aloe Vera. This is not a high-tech business, but Herbal‘s earnings have averaged around Rs 12 lakh after tax, largely on the strength of its patented beauty cream for removing the pimples.

The patent has eight years to run, and Herbal has been offered Rs 40 lakhs for the patent rights. Herbal‘s assets include Rs 20 lakhs of working capital and Rs 80 lakhs of property, plant, and equipment. The patent is not shown on Herbal‘s books. Suppose Herbal‘s cost of capital is 15 percent. What is its Economic Value Added (EVA)?

EVA = Income earned – (Cost of capital x Total Investment)

Total Investments

 Particulars Amount Working capital Property, plant, and equipment Patent rights Rs 20 lakhs Rs 80 lakhs Rs 40 lakhs Total Rs 140 lakhs

Q 96 Write a short note on

a) Factors that affect Bond’s Duration

b) Process of Portfolio Management

c) Benefits of International Portfolio Investment

d) Benefits of Debit Card

e) Factors affecting the selection of Mutual Funds

a) Following are some of factors that affect bond's duration:

1. Time to maturity: Consider two bonds that each cost Rs 1,000 and yield 7%. A bond that matures in one year would more quickly repay its true cost than a bond that matures in 10 years. As a result, the shorter-maturity bond would have a lower duration and less price risk. The longer the maturity, the higher the duration.
2. Coupon rate: Coupon payment is a key factor in calculation of duration of bonds. If two identical bonds pay different coupons, the bond with the higher coupon will pay back its original cost quicker than the lower-yielding bond. The higher the coupon, the lower is the duration.

b) Portfolio management is a process and broadly it involves following five phases and each phase is an integral part of the whole process and the success of portfolio management depends upon the efficiency in carrying out each of these phases.

1. Security Analysis: Security analysis constitutes the initial phase of the portfolio formation process and consists in examining the risk-return characteristics of individual securities and also the correlation among them. A simple strategy in securities investment is to buy underpriced securities and sell overpriced securities. But the basic problem is how to identify underpriced and overpriced securities and this is what security analysis is all about. There are two alternative approaches to analyse any security viz. fundamental analysis and technical analysis. They are based on different premises and follow different techniques.
2. Portfolio Analysis: Once the securities for investment have been identified, the next step is to combine these to form a suitable portfolio. Each such portfolio has its own specific risk and return characteristics which are not just the aggregates of the characteristics of the individual securities constituting it. The return and risk of each portfolio can be computed mathematically based on the risk-return profiles for the constituent securities and the pair-wise correlations among them.
3. Portfolio Selection: The goal of a rational investor is to identify the Efficient Portfolios out of the whole set of Feasible Portfolios mentioned above and then to zero in on the Optimal Portfolio suiting his risk appetite. An Efficient Portfolio has the highest return among all Feasible Portfolios having identical Risk and has the lowest Risk among all Feasible Portfolios having identical Return.
4. Portfolio Revision: Once an optimal portfolio has been constructed, it becomes necessary for the investor to constantly monitor the portfolio to ensure that it does not lose it optimality. In light of various developments in the market, the investor now has to revise his portfolio. This revision leads to addition (purchase) of some new securities and deletion (sale) of some of the existing securities from the portfolio. The nature of securities and their proportion in the portfolio changes as a result of the revision.
5. Portfolio Evaluation: This process is concerned with assessing the performance of the portfolio over a selected period of time in terms of return and risk and it involves quantitative measurement of actual return realized and the risk borne by the portfolio over the period of investment. Various types of alternative measures of performance evaluation have been developed for use by investors and portfolio managers.

c) Benefits of International Portfolio Investment are as follows:

1. Reduce Risk: International investment aids to diversify risk as the gains from diversification within a country are therefore very much limited, because macro economic factors of different countries vary widely and do not follow the same phases of business cycles, different countries have securities of different industries in their market portfolio leading to correlation of expected returns from investment in different countries being lower than in a single country.
2. Raise Return through better Risk – Return Trade off : International Investment aids to raise the return with a given risk and/or aids to lower the risk with a given rate of return. This is possible due to profitable investment opportunities being available in an enlarged situation and at the same time inter country dissimilarities reduce the quantum of risk.

d) Benefits of Debit cards are as follows:

1. Obtaining a debit card is often easier than obtaining a credit card.
2. Using a debit card instead of writing cheques saves one from showing identification or giving his personal information at the time of the transaction.
3. Using a debit card frees him from carrying cash or a cheque book.
4. Using a debit card means he no longer has to stock up on traveller‘s cheques or cash when he travels
5. Debit cards may be more readily accepted by merchants than cheques, in other states or countries wherever the card brand is accepted.
6. The debit card is a quick, ―pay now‖ product, giving one no grace period.
7. Using a debit card may mean one has less protection than with a credit card purchase for items which are never delivered, are defective, or misrepresented. But, as with credit cards, one may dispute unauthorized charges or other mistakes within 60 days. One should contact the card issuer if a problem cannot be resolved with the merchant.
8. Returning goods or canceling services purchased with a debit card is treated as if the purchase were made with cash or a cheque.

e) Factors affects the selection of Mutual Funds is as follows:

1. Past Performance – The Net Asset Value is the yardstick for evaluating a Mutual Fund. The higher the NAV, the better it is. Performance is based on the growth of NAV during the referral period after taking into consideration Dividend paid. Growth = (NAV1 – NAV0 ) + D1 / NAV0.
2. Timing – The timing when the mutual fund is raising money from the market is vital. In a bullish market, investment in mutual fund falls significantly in value whereas in a bearish market, it is the other way round where it registers growth. The turns in the market need to be observed.
3. Size of Fund – Managing a small sized fund and managing a large sized fund is not the same as it is not dependent on the product of numbers. Purchase through large sized fund may by itself push prices up while sale may push prices down, as large funds get squeezed both ways. So it is better to remain with medium sized funds.
4. Age of Fund – Longevity of the fund in business needs to be determined and its performance in rising, falling and steady markets have to be checked. Pedigree does not always matter as also success strategies in foreign markets.
5. Largest Holding – It is important to note where the largest holdings in mutual fund have been invested.
6. Fund Manager – One should have an idea of the person handling the fund management. A person of repute gives confidence to the investors.
7. Expense Ratio – SEBI has laid down the upper ceiling for Expense Ratio. A lower Expense Ratio will give a higher return which is better for an investor.
8. PE Ratio – The ratio indicates the weighted average PE Ratio of the stocks that constitute the fund portfolio with weights being given to the market value of holdings. It helps to identify the risk levels in which the mutual fund operates.
9. Portfolio Turnover – The fund manager decides as to when he should enter or quit the market. A very low portfolio turnover indicates that he is neither entering nor quitting the market very frequently. A high ratio, on the other hand, may suggest that too frequent moves have lead the fund manager to miss out on the next big wave of investments. A simple average of the portfolio turnover ratio of peer group updated by mutual fund tracking agencies may serve as a benchmark. The ratio is lower of annual purchase plus annual sale to average value of the portfolio.

Q 97 Explain the meaning of the following relating to Swap transactions:

1. Plain Vanila Swaps
2. Basis Rate Swaps
3. Asset Swaps
4. Amortising Swaps

1. Plain Vanilla Swap: Also called generic swap andit involves the exchange of a fixed rate loan to a floating rate loan. Floating rate basis can be LIBOR, MIBOR, Prime Lending Rate etc.
2. Basis Rate Swap: Similar to plain vanilla swap with the difference payments based on the difference between two different variable rates. For example one rate may be 1 month LIBOR and other may be 3-month LIBOR. In other words two legs of swap are floating but measured against different benchmarks.
3. Asset Swap: Similar to plain vanilla swaps with the difference that it is the exchange fixed rate investments such as bonds which pay a guaranteed coupon rate with floating rate investments such as an index.
4. Amortising Swap: An interest rate swap in which the notional principal for the interest payments declines during the life of the swap. They are particularly useful for borrowers who have issued redeemable bonds or debentures. It enables them to interest rate hedging with redemption profile of bonds or debentures.

Q 98 State any four assumptions of Black Scholes Model.

The model is based on a normal distribution of underlying asset returns. The following assumptions accompany the model:

1. European Options are considered,
2. No transaction costs,
3. Short term interest rates are known and are constant,
4. Stocks do not pay dividend,
5. Stock price movement is similar to a random walk,
6. Stock returns are normally distributed over a period of time, and
7. The variance of the return is constant over the life of an Option.

Q 99 AGD Co is a profitable company which is considering the purchase of a machine costing Rs 32,00,000. If purchased, AGD Co would incur annual maintenance costs of Rs 2,50,000. The machine would be used for three years and at the end of this period would be sold for Rs 5,00,000. Alternatively, the machine could be obtained under an operating lease for an annual lease rental of Rs 12,00,000 per year, payable in advance. AGD Co can claim depreciation @ 25% on WDV basis. Annual lease rental will be paid in the beginning of each year. Security Valuation.

(i) Interest payable every six months means that the bank will require 5% every six months accordingly equivalent annual percentage rate shall be calculated as follows:

[(1·05)2 – 1] x 100 = 10·25%

(iii) Amount of installment shall be calculated by using annuity tables as follows:

A = Rs 32,00,000/7·722 = Rs 4,14,400

Q 100 RST Ltd.‘s current financial year's income statement reported its net income as Rs. 25,00,000. The applicable corporate income tax rate is 30%.

Following is the capital structure of RST Ltd. at the end of current financial year:

 Rs. Debt (Coupon rate = 11%)  Equity (Share Capital + Reserves & Surplus)   Invested Capital 40 lakhs  125 lakhs   165 lakhs

Following data is given to estimate cost of equity capital:

 Rs Beta of RST Ltd. Risk –free rate i.e. current yield on Govt. bonds Average market risk premium (i.e. Excess of return on portfolio over risk-free rate) 1.36  8.5%   9%

Required:

1. Estimate Weighted Average Cost of Capital (WACC) of RST Ltd.; and
2. Estimate Economic Value Added (EVA) of RST Ltd.

Cost of Equity as per CAPM

ke = Rf + β x Market Risk Premium

= 8.5% + 1.36 x 9%

= 8.5% + 12.24% = 20.74%

Cost of Debt Kd = 11%(1 - 0.30) = 7.70% =20.74 x 125/165+7.70x40/165

= 15.71 + 1.87 = 17.58%

= Rs. 35,71,429 or Rs. 35.71 lakhs

Operating Income = Taxable Income + Interest

= Rs. 35,71,429 + Rs. 4,40,000

=Rs. 40,11,429 or 40.11 lacs

= Rs. 40,11,429 or Rs. 40.11 lacs

EVA = EBIT (1-Tax Rate) – WACC x Invested Capital

= Rs. 40,11,429 (1 – 0.30) – 17.58% x Rs. 1,65,00,000

= Rs. 28,08,000 – Rs. 29,00,700 = - Rs. 92,700