| 1. | (a) | Following information is available for X Company’s shares and Call option: Current share price
Option exercise price
Risk free interest rate
Time of the expiry of option
Standard deviation | Rs.185
Rs.170
7%
3 years
0.18 |
Calculate the value of option using Black–Scholes formula. | 12 | (0) |
| | (b) | Suppose a dealer quotes ‘All–in–cost’ for a generic swap at 8% against six month libor flat. If the notional principal amount of swap is Rs.5,00,000, | (i) | Calculate semi–annual fixed payment. | | (ii) | Find the first floating rate payment for (i) above if the six month period from the effective date of swap to the settlement date comprises 181 days and that the corresponding libor was 6% on the effective date of swap. |
In (ii) above, if the settlement is on ‘Net’ basis, how much the fixed rate payer would pay to the floating rate payer?
Generic swap is based on 30/360 days basis. | 3 | (0) |
| | (c) | Consider the following information on two stocks, A and B: Year
2006
2007 | Return on A (%)
10
16 | Return on B (%)
12
18 |
You are required to determine: | (i) | The expected return on a portfolio containing A and B in the proportion of 40% and 60% respectively. | (ii)
(iii)
(iv)
(v) | The Standard deviation of return from each of the two stocks.
The covariance of returns from the two stocks.
Correlation coefficient between the returns of the two stocks.
The risk of a portfolio containing A and B in the proportion of 40% and 60%. |
| 3 | (0) |
| 2. | (a) | The following is the Yield structure of AAA rated debenture: Period
3 months
6 months
1 year
2 years
3 years and above | Yield (%)
8.5%
9.25
10.50
11.25
12.00 |
| (i) | Based on the expectation theory calculate the implicit one–year forward rates in year 2 and year 3. | | (ii) | If the interest rate increases by 50 basis points, what will be the percentage change in the price of the bond having a maturity of 5 years? Assume that the bond is fairly priced at the moment at Rs.1,000. |
| 4 | (0) |
| | (b) | RST Ltd. has a capital of Rs.10,00,000 in equity shares of Rs.100 each. The shares are currently quoted at par. The company proposes to declare a dividend of Rs.10 per share at the end of the current financial year. The capitalization rate for the risk class of which the company belongs is 12%. What will be the market price of the share at the end of the year, if | (i) | A dividend is not cleared ? | | (ii) | A dividend is declared ? | | (iii) | Assuming that the company pays the dividend and has net profits of Rs.5,00,000 and makes new investments of Rs.10,00,000 during the period, how many new shares must be issued? Use the MM model. |
| 4 | (0) |
| | (c) | Mr. X established the following spread on the Delta Corporation’s stock : | (i) | Purchased one 3–month call option with a premium of Rs.30 and an exercise price of Rs.550. | | (ii) | Purchased one 3–month put option with a premium of Rs.5 and an exercise price of Rs.450. | | Delta Corporation’s stock is currently selling at Rs.500. Determine profit or loss, if the price of Delta Corporation’s : | (i)
(ii)
(iii) | remains at Rs.500 after 3 months.
falls at Rs.350 after 3 months.
rises to Rs.600. |
Assume the size option is 100 shares of Delta Corporation. | 4 | (0) |
| | (d) | XL Ispat Ltd. has made an issue of 14 per cent non–convertible debentures on January 1, 2007. These debentures have a face value of Rs.100 and is currently traded in the market at a price of Rs.90. Interest on these NCDs will be paid through post–dated cheques dated June 30 and December 31. Interest payments for the first 3 years will be paid in advance through post–dated cheques while for the last 2 years post–dated cheques will be issued at the third year. The bond is redeemable at par on December 31, 2011 at the end of 5 years.
Required : | (i) | Estimate the current yield at the YTM of the bond. | | (ii) | Calculate the duration of the NCD. | | (iii) | Assuming that intermediate coupon payments are, not available for reinvestment calculate the realised yield on the NCD. |
| 6 | (0) |
| 3. | (a) | A company has an old machine having book value zero – which can be sold for Rs.50,000. The company is thinking to choose one from following two alternatives: | (i) | To incur additional cost of Rs.10,00,000 to upgrade the old existing machine. | | (ii) | To replace old machine with a new machine costing Rs.20,00,000 plus installation cost Rs.50,000. |
Both above proposals envisage useful life to be five years with salvage value to be nil.
The expected after tax profits for the above three alternatives are as under : | Year | Old existing Machine (Rs.) | Upgraded Machine (Rs.) | New Machine (Rs.) | 1.
2.
3.
4.
5. | 5,00,000
5,40,000
5,80,000
6,20,000
6,60,000 | 5,50,000
5,90,000
6,10,000
6,50,000
7,00,000 | 6,00,000
6,40,000
6,90,000
7,40,000
8,00,000 |
The tax rate is 40 per cent.
The company follows straight line method of depreciation. Assume cost of capital to be 15 per cent.
P.V.F. of 15%, 5 = 0.870, 0756, 0.658, 0.572 and 0.497. You are required to advise the company as to which alternative is to be adopted. | 8 | (0) |
| | (b) | The data given below relates to a convertible bond : Face value
Coupon rate
No. of shares per bond
Market price of share
Straight value of bond
Market price of convertible bond | Rs.250
12%
20
Rs.12
Rs.235
Rs.265 |
Calculate : (i)
(ii)
(iii)
(iv) | Stock value of bond.
The percentage of downside risk.
The conversion premium
The conversion parity price of the stock. |
| 8 | (0) |
| | (c) | What are the drawbacks of investments in Mutual Funds? | 4 | (0) |
| 4. | (a) | An exporter is a UK based company. Invoice amount is $3,50,000. Credit period is three months. Exchange rates in London are : Spot Rate
3–month Forward Rate | ($/£) 1.5865 – 1.5905
($/£) 1.6100 – 1.6140 |
Rates of interest in Money Market: | Deposit | Loan | $
£ | 7%
5% | 9%
8% |
Compute and show how a money market hedge can be put in place. Compare and contrast the outcome with a forward contract. | 6 | (0) |
| | (b) | An Indian exporting firm, Rohit and Bros., would be cover itself against a likely depreciation of pound sterling. The following data is given : Receivables of Rohit and Bros
Spot rate
Payment date
3 months interest rate | :
:
:
:
: | £500,000
Rs.56,00/£
3–months
India : 12 per cent per annum
UK : 5 per cent per annum |
What should the exporter do? | 6 | (0) |
| | (c) | The closing value of Sensex for the month of October, 2007 is given below: Date Closing
1.10.07
3.10.07
4.10.07
5.10.07
8.10.07
9.10.07
10.10.07
11.10.07
12.10.07
15.10.07
16.10.07
17.10.07
19.10.07
22.10.07
23.10.07
24.10.07
25.10.07
29.10.07
30.10.07
31.10.07 | Sensex Value
2800
2780
2795
2830
2760
2790
2880
2960
2990
3200
3300
3450
3360
3290
3360
3340
3290
3240
3140
3260 |
You are required to test the week form of efficient market hypothesis by applying the run test at 5% and 10% level of significance.
Following value can be used :
Value of t at 5% is 2.101 at 18 degrees of freedom.
Value of t at 10% is 1.734 at 18 degrees of freedom.
Value of t at 5% is 2.086 at 20 degrees of freedom.
Value of t at 10% is 1.725 at 20 degrees of freedom. | 8 | (0) |
|
| 5. | (a) | (i) | The rate of inflation in USA is likely to be 3% per annum and in India it is likely to be 6.5%. The current spot rate of US $ in India is Rs.43.40. Find the expected rate of US $ in India after one year and 3 years from now using purchasing power parity theory. | 4 | (0) |
| | | (ii) | On April 1, 3 months interest rate in the UK £ and US $ are 7.5% and 3.5% per annum respectively. The UK £/US $ spot rate is 0.7570. What would be the forward rate for US $ for delivery on 30th June ? | 4 | (0) |
| | (b) | K. Ltd. is considering acquiring N. Ltd., the following information is available : | Company | Profit after tax | Number of Equity
shares | Market value per
share | K. Ltd.
N. Ltd. | 50,00,000
15,00,000 | 10,00,000
2,50,000 | 200.00
160.00 |
Exchange of equity shares for acquisition is based on current market value as above.
There is no synergy advantage available :
Find the earning per share for company K. Ltd. after merger.
Find the exchange ratio so that shareholders of N. Ltd. would not be at a loss. | 12 | (0) |
| 6. | Write short notes on any four of the following: | 4x5=20 | |
| | (a) | Financial restructuring. | | (0) |
| | (b) | Cross border leasing. | | (0) |
| | (c) | Embedded derivatives. | | (0) |
| | (d) | Arbitrage operations | | (0) |
| | (e) | Rolling settlement. | | (0) |
