Question 1

Part A

A.1) Consider the silver futures (contract size 1 ounce, quotation $=ounce). Suppose that a firm sells 30 contracts when the futures price is F0 = 35. The initial margin is 20% of the overall value of the future position. The maintenance margin is 75% of the initial margin. Suppose that the following settlement prices are recorded in the subsequent days: F1 = 45, F2 = 40; F3 = 42; F4 = 48; F5 = 43; F6 = 50:

i.      Describe the evolution of the margin account over these 6 days assuming that the firm answers all margin calls.                                                                                           (5%)

ii.      Describe the evolution of the margin account over these 6 days if the firm is long 20 contracts.                                                                                                                   (5%)

A.2) Describe an example of portfolio diversification in the Capital Asset Pricing Model

(CAPM) context. What type of risk cannot be diversified away? Discuss.                         (5%)

A.3) What kind of strategy would you adopt to hedge your portfolio against the risk that cannot

be diversified away? Discuss.                                                                                            (10%)

Part B

B. 1) Top100 Corp. has just issued:

▪   a $1,000 par value bond

▪   with 7% annual coupon

▪   with 4 years to maturity

▪   Assume that term structure is flat at 8%

▪   The bond is currently trading at $966.88

▪   Macaulay Duration is 3.62 years

i.      Estimate the Modified Duration for the bond                                                        (3%)

ii.      Suppose that the term structure of interest rates moved down by 10 basis points. Assume that this decrease in interest rates is parallel over the term structure. What is the new price of the bond?                                                                                                    (4%)

iii.      Suppose that the term structure of interest rates moved down by  100 basis points. Assume that this decrease in interest rates is parallel over the term structure. What is the new price of the bond?                                                                                        (4%)

iv.      Compute  the   approximate  price   change   in   (iii)   and   (ii)  using  the  Duration approximation and compare these prices to the actual price changes. Discuss, how well the duration works under each case, and if it does not, provide an explanation.        (8%)

B.2) Discuss the disadvantage of the Internal rate of return (IRR) Rule as an investment

appraisal method.                                                                                                                  (6%)

Question 2

Part A

A portfolio of 2 zero-coupon bonds (bond 1 and bond 2) with weights w1 = 30% (proportion invested in the first bond), w2 = 70%. The first bond has a face value of $1000, the second has a face value of $900. All of them have the same maturity of 2 years. The risk-free rate is 3% per year with continuous compounding and it is the same for all maturities

i.      Find the current market price of the portfolio.                                                         (5%)

ii.      Find the forward price on a forward contract with a delivery date in 1 year and written on the above portfolio.                                                                                              (5%)

iii.      Find the price of the existing forward contract with the same characteristics as in ii) and delivery price K = $800.                                                                                           (5%)

iv.     Now suppose that the 2 bonds are characterized by semimanual coupons ($30 for bond

1 and 35 for bond 2). The face values are still $1000 for the first bond and $900 for the second. All of them have the same maturity of 2 years. Calculate the forward (delivery in 1 year) price of the portfolio.                                                                              (10%)

Part B

B.1) Storico Co. just paid a dividend of $3.85 per share. The company will increase its dividend by 20 per cent next year and will then reduce its dividend growth rate by 5 percentage points per year until it reaches the industry average of 5 per cent dividend growth, after which the company will keep a constant growth rate forever. If the required return on Storico stock is 13

per cent, what will a share of stock sell for today?                                                                 (5%)

B.2) Ramsay Corp. currently has an EPS of $2.35, and the bench-mark PE for the company is 21. Earnings are expected to grow at 7 per cent per year.

i.      What is your estimate of the current stock price?                                                    (7%)

ii.      What is the target stock price in one year?                                                               (8%)

B.3) Because of financial stress, the bonds of Intelo have been downgraded by Moody’s from A to BBB. What is the predicted effect on the bonds’ price? What is the predicted effect on the

bonds’ yield to maturity?                                                                                                     (5%)

Question 3

Part A

A.1) Discuss the basic motivations for a counterparty to enter a currency swap.                (3%)

A.2) Suppose that the standard deviation of quarterly changes in the prices of a commodity is $0.65, the standard deviation of quarterly changes in a futures price on the commodity is $0.81, and the coefficient of correlation between the two changes is 0.8. What is the optimal hedge

ratio for a three-month contract? What does it mean?                                                          (5%)

A.3) A company has a $20 million portfolio with a beta of 1.2. It would like to use futures contracts on a stock index to hedge its risk. The index futures is currently standing at 1080, and each contract is for delivery of $250 times the index. What is the hedge that minimizes risk?

(5%)

A.4) A one-year-long forward contract on a non-dividend-paying stock is entered into when the stock price is $40 and the risk-free rate of interest is 5% per annum with continuous compounding.

i.      What are the forward price and the initial value of the forward contract?               (5%)

ii.      Six months later, the price of the stock is $45 and the risk-free interest rate is still 5%. What are the forward price and the value ofthe forward contract?                            (7%)

Part B

B.1) Suppose that a firm is trying to decide between two different microprocessor assembly facilities. Facility A, which is highly automated, and facility B, which is less automated and

more labour intensive.

Facility A:

▪   Fixed costs of $8 million annually and

▪   Unit variable costs of $4/unit.

Facility B:

▪   Fixed costs of $4 million annually and

▪   Unit variable costs of $10/unit.

If the sale price is $20/unit for both products, Estimate EBIT for Facility A and Facility B if a

total of 600,000 units are sold by each facility.                                                                    (5%)

B.2) Top100 Corp. has just issued:

▪   a $1,000 par value bond

▪   with 10% semi-annual coupon rate

▪   and 8% yield-to-maturity

▪   with 20 years to maturity

▪   Assume, for now, that the term structure is flat.

i.      Estimate the price of this bond                                                                           (5%)

ii.      Is the bond trading at premium or discount or par? Explain why                      (4%)

iii.     Assume now that, all else remaining the same, you have invested in this bond at    time zero. What will the price of the bond be in 4 years?                                  (5%)

B.3) Alpha.Inc is debating using Payback Period versus Discounted Payback Period for small- dollar projects. The Information Officer (IO) has submitted a new computer project of $15,000 cost. The cash flows will be $5,000 each year for the next five years. The cut-off period used by Alpha.Inc is three years. The Information Officer states it does not matter what model the company uses for the decision; it is an acceptable project. Demonstrate for the IO that the

selection of the model does matter, the discount rate is 1%!                                               (6%)

Question 4

Part A

A.1) Suppose that a European call option to buy a share for $100.00 costs $5.00 and is held until maturity. Under what circumstances will the holder of the option make a profit? Under what circumstances will the option be exercised? Draw a diagram illustrating how the profit from a long position in the option depends on the stock price at maturity of the option.    (7%)

A.2) Suppose that the term structure of risk-free interest rates is flat in the United States and Australia. The USD interest rate is 7% per annum and the AUD rate is 9% per annum. The current value of the AUD is 0.62 USD. Under the terms of a swap agreement, a financial institution pays 8% per annum in AUD and receives 4% per annum in USD. The principals in the two currencies are $12 million USD and 20 million AUD. Payments are exchanged every year, with one exchange having just taken place. The swap will last two more years.

i.      What is the value of the swap to the financial institution using the Par yield approach? Assume all interest rates are continuously compounded.                                          (8%)

ii.      What is the value of the swap to the financial institution using the forward contract approach? Assume all interest rates are continuously compounded.                        (5%)

A.3) Calculate the price of a three-month European put option on a non-dividend-paying stock with a strike price of $50 when the current stock price is $50, the risk-free interest rate is 10% per annum, and

the volatility is 30% per annum                                                                                                           (5%)

Part B

B.1) Kelvin Limplin created a portfolio by investing $24,000 in Stock A, $6,000 in Stock B, and $10,000 in the riskless asset.  The correlation between Stock A and Stock B is 0.5.

What are the expected return and standard deviation of Kelvin’s portfolio?                       (5%)

B.2) Suppose you have been hired as a financial consultant to Defense Electronics, Inc. (DEI), a large, publicly-traded firm that is the market share leader in radar detection systems (RDSs). The company is looking at setting up a manufacturing plant overseas to produce a new line of RDSs. This will be a five-year project. The company bought some land three years ago for $4million in anticipation of using it as a toxic dump site for waste chemicals, but it built a