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L. Muralidharan

BPCL requiring $20,00,000 to settle by 90 days for the crude oil commitments. The following rates are available.

Spot

INR/$48.95: 49.00

90 days swap:15 - 20

US interest rate per cent: 5 - 5.25

Bank of Baroda, the chief banker for BPCL advises Yen loan for settlement. Yen Loan is available at 2.5 per cent per annum. BPCL finds the exchange rate as follows:

Spot

¥/$123.50: 124

90 days swap: 20-10.

What is the borrowing currency for BPCL. The Board of BPCL expresses that the bottom line will be affected very much on assuming any fluctuation risk what so ever. Discuss.

Solution: To solve this problem, fundamental knowledge on IFM will suffice. The crux is that one must find out the payment to be made in INR if the company borrows in US $ and the payment to be made when borrowal is made in Japanese Yen. Then these amounts must be compared to find out the most beneficial alternative source.

Borrow in US $:

Repayment of Exposure in 90days = (2 million x [1+{lcub}(5.25/100)x 90/360{rcub}])

= 2.02625 million $

Forward rate of $ = Rs 49.20 (i.e. 49 + 0.20)

Payment to be made to the Banker

= 2.02625 million $ x Rs.49.20

= Rs 99.6915 million

Borrow in Yen:

Repayment to be made in 90 days = ({lcub}2 million x124{rcub} x [1+{lcub}(2.5/100)x 90/360{rcub}])

= 249.55 million Yen

Payment to be made to the banker in Rs

Therefore, INR /¥ = INR/$ x $/¥

Bid rate of INR/¥ * = (48.95+0.15 x [1/1.2390]) = Rs.39.63

Offer rate of INR/¥ * = (49 + 0.20 x [1/1.2330]) = Rs.39.90

* always 100 unit of yen is represented as 1 unit

To repay Yen the offer rate of INR must be used

Hence the payment to be made

= 249.55 million x (39.90 / 100)

= 99.57045 million

From the above details it is beneficial to the company if it borrows JPY rather than $.

Estimating beta

A phone company is planning to invest in projects in multimedia. The beta for the telephone company is 0.75 and has a debt/equity ratio of 1.00; the after-tax cost of borrowing is 4.25 per cent. The multimedia business is considered to be much riskier than the phone business; the average beta for comparable firms is 1.30; and the average debt/equity ratio is 50 per cent. Assuming that the tax rate is 40 per cent (the risk free rate is 7 per cent and risk premium is 5.5 per cent), estimate the unlevered beta of being in the multimedia business. Estimate the beta and cost of equity if the phone company finances its multimedia projects with the same debt/equity ratio as the rest of its business.

Assume that a multimedia division is created to develop these projects, with a debt/equity ratio of 40 per cent. Estimate the beta and cost of equity for the projects with this arrangement.

Solution: The solution drawn here is self-explanatory. Firstly the Beta of unlevered business should be ascertained and thereafter, the beta shall be reworked in accordance to the desired debt equity mix of the company concerned.

(a)

ß of the unlevered business = ß of the levered business x Equity/ [Equity + Debt (1-tax)]

=1.3 x 2/[ 2 + (1 x 0.6)]

ß of the Unlevered Business = 1.

(b) 1 = ß of levered x 1/[1 + (1 x 0.6)]

ß of the levered business=1 x 1.6/1 = 1.6

Cost of capital= r{-f} + (risk premium) x ß

= 7 + (5.5) x 1.6

= 15.8 per cent.

(c) 1 = ß of levered x 1/[1 + (0.4 x 0.6)]

ß of the levered business = 1 x (1.24/1)= 1.24

Cost of capital = r{-f} + (risk premium) x ß

= 7 + (5.5) x 1.24

=13.82 per cent.

Opportunity cost

Significant Ltd. is evaluating the viability of a capital investment that it is interested in. The project will require an initial investment of Rs 5,00,000 and the projected revenues are Rs 4,00,000 a year for five years. The projected cost-of-goods-sold is 40 per cent of revenues, and the tax rate is 40 per cent. The initial investment is primarily in plant and equipment and can be depreciated straight line over five years. (The salvage value is zero.) The project makes use of other resources that your company already owns:

Two employees of the company, each with a salary of Rs 40,000 a year, who are currently employed by another division will be transferred to this project. The other division has no alternative use for them, but they are covered by a union contract that will prevent them from being retrenched for three years (during which they would be paid their current salary).

The project will use excess capacity in the current packaging plant. Although this excess capacity has no alternative use now, it is estimated that the company will have to invest Rs 2,50,000 in a new packaging plant in year 4 as a consequence of this project using up excess capacity (instead of year 8 as originally planned).

The project will use a van currently owned by the company. Although the van is not now being used, it can be rented out for Rs 3,000 a year for five years. The book value of the van is Rs 10,000, and it is being depreciated straight line (with five years remaining for depreciation).

The discount rate to be used for this project is 10 per cent.

What (if any) is the opportunity cost associated with using the two employees from another division?

What, if any, is the opportunity cost associated with the use of excess capacity of the packaging plant?

What, if any, is the opportunity cost associated with the use of the van?

What is the after-tax operating cash flow each year on this project?

What is the net present value of this project?

Solution: No opportunity cost involved with respect to the two employees for the first 3 years, but during the last 2 years they can be retrenched. So, the opportunity cost for the last 2 years is = (80000 x 0.6)/1.1{+4} + ((80000 x 0.6)/1.1{+5}) = Rs 62589.

(b) The difference in PV of investing in year 4 between and in year 8 = (250000/1.1{+4} - 250000 /1.1{+8}) = Rs 54126.

(c) The Present Value of after-tax rental payments over five years is the opportunity cost = (3000 x 0.6) x (annuity factor of 10per cent for 5 years) = Rs 6,823.

(d) PV of Gross Profit (After Tax)

(400000 - 160000) x 0.6 x AF for 5 years = 5,45,873

Less: Opportunity cost of Employees (a) = (62589)

Opportunity cost on Van (c) = (6823)

Add: PV of Tax savings on Depreciation

(100000 x 40 per cent x AF for 5 years) = 1,51,631

Total Operating cash flow for 5 years = 6,28,092

Less: Timing difference in the Investment made (b) = (54126)

Initial Cash outflow = (500000)

(e) NPV of the project= 73966

Notes:

i) The answer for subdivision (b) has to be analysed carefully. The quantum of expenditure is not undergoing any change, but only in the timing of expenditure. The difference in the PV factor of Year 4 and 8 on the expenditure is relevant flow for capital budgeting expenditure.

ii) Generally, depreciation is not a relevant cash flow. But when the tax rates are given depreciation gains importance as there is tax savings on it. In the instant case despite the presence of taxation, depreciation proves to be irrelevant. Since the benefit of tax saving on depreciation remaining undisturbed for either of the alternatives, it is ignored.

Number of contracts

A UK Company is expecting to receive $3,00,000 in three months' time on April 1. Being concerned about the pound strengthening against the dollar, it decides to use futures to hedge its transaction risk.

Current spot rate: $1.54-$1.55

Sterling futures price (1st April): $1.535

Standard size of futures contracts: £ 62,500

Find out the number of contract to be sold or bought?

(b) You are given the following information: Current Market price of the share Rs.150; Exercise price of the share = Rs 120; Risk-free rate (RF) = 10 per cent; the term = 90 days; and the S D = 0.6. Assuming that the share pays no dividends, find out the value of the call and the put option with the help of Black-scholes model, also confirm the finding through Put-call parity relationship.

(LN (1.25) = 0.2231; Normal table value of 0.98 = 0.8366; Normal table value of 0.6828 = 0.7526; e {+(}{+-}{+0}{+.}{+0}{+2}{+4}{+6}{+6}{+)} = 0.9756)

Solution: (a) The first thing to establish is whether the company should buy or sell futures. Given that holding a futures contract allows future delivery of a foreign currency and that in this case sterling is the foreign currency, the company should buy US Sterling futures. This allows the company to take delivery of sterling in return for the dollars it expects to receive. The futures price quoted is the amount of US dollars needed to buy one unit of the foreign currency. Translating the expected dollar receipt into sterling at the exchange rate implicit the currency future, we have:

$3,00,000 / 1.535 = £1,95,440

Number of contracts required = £195440 / 62500 = 3.13 contracts

The company is advised to purchase three contracts, allowing it to take delivery of £187500 in return for a payment of $ 287813. Given that the company is to receive $3,00,000, it will have to sell the $12,187 surplus, either in the foreign exchange market in three month's time, or by means of a forward exchange contract.

(b) Pricing of an Option under Black Scholes Model

Value of a Call Option =P x N(d{-1}) - (X) x e{+frac12}{+r}{+t}{+f} x N(d{-2})

Value of a Put Option =(X) x e{+frac12}{+r}{+t}{+f} x N (-d{-2}) - P x N(-d{-1})

Where d{-1} = [Ln (P/X) + (r{-f} +(<108,SYM,115>{+2} /2)) x t]/ <108,SYM,115> x <108,SYM,214>t

d2 =d1 - <108,SYM,115> x <108,SYM,214>t

N(d{-1}) =Normal table value of d{-1}

X = Strike Price (also denoted by K)

t = Time (in years)

r{-f} = Risk free Interest rate

N (d{-2}) =Normal table value of d{-2}

<108,SYM,229>= Standard deviation

Put - call parity:

Buy a stock + buy a put = Present value of exercise price + buy a call

By using the above formula,

The value of a call option = 37.38

The value of a put option = 0.89

(Students are advised to pick the values from the natural log table and normal distribution table to solve B/S model questions.)

Merger of companies

The following data relate to Companies A and B:

Company A

Profit after tax (Rs 000s): 100

Equity Shares (000s): 50

Price Earning Ratio: 20

Company B

Profit after tax (Rs 000s): 20

Equity Shares (000s): 5

Price Earning Ratio: 10.

If A and B merge by exchanging one share of Company A for each share of Company B, how will earnings per share of the two companies be affected? What is the market value exchange ratio?

If the exchange ratio were 3 shares of A for two shares of B, what would be the impact of earnings per share after merger? Assume that there would be synergy benefits equal to 20 per cent increase in the present earnings due to merger.

Solution: If the instructions are followed logically, the solution is very easy to develop.

Short notes

(a) Write short notes on the usage of interest rate futures as a method of hedging.

(b) Write short notes on Treasury Bills

(c) What are the advantages of Investing in Mutual funds?

Solution: (a) Usage of Interest rate futures as a method of hedging:

Firstly interest rates and the price of the bond are inversely proportional. Rate of interest rise would result in fall in the price of the bond and the vice versa is also true.

The above relationship would create anxiety in the minds of the investor when change is experienced in the interest rates and thereby the value of the securities. The holders of securities would either suffer capital loss or interest rate risk. There one can understand the impact of interest rate risk as an important factor to be hedged.

When hedging interest rate risk, companies would normally buy futures contract if they want to guard against a fall in interest rates and sell futures contracts to guard against a rise in interest rates. Future contracts are priced in nominal terms by subtracting the value of the specified interest rate from 100.

Suppose the interest rate is 10 per cent, then the interest rate contract is said to be at 90. Then 1 per cent is counted as having 100 ticks and a tick is 0.01 per cent.

Lets find out as how it works. The nominal value of a contract is £500000. The value of a tick during 3 months duration shall be worked out as 500000*0.01/100*3/12 = £12.50. When the rate of interest is rising by 3 per cent then it should be construed as 300 * 12.50 causing a loss of £3750.

The company wanting to guard against interest rate rise shall sell the futures contract at 90 (100-10).

When the company had sold at 90 can square its position by buying at 87 resulting in a gain by 3 per cent, which would match exactly the quantum of loss, suffered on account of interest rate rise. (Sold at 90 futures and bought at 87 spot). This can also be standardised in the following form:

When a company wanting to guard against risk of rise in liabilities interest rate then it should sell futures and if a company wants to secure its income from an asset were the interest rates are decreasing then the company should buy futures.

(b) Treasury Bills:

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