BUSI4412 FINANCIAL SECURITY VALUATION A LEVEL 4 MODULE, SPRING SEMESTER 2021-2022

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BUSI4412E1-22

A LEVEL 4 MODULE, SPRING SEMESTER 2021-2022

FINANCIAL SECURITY VALUATION

There are two questions. Each question carries 50 points.

1. This question has three parts:

i. You would like to estimate the cost of capital for a new airline business. Based on its industry asset beta, you have already estimated an unlevered cost of capital for the firm of 11%. However, the new business will be 45% debt financed, and you anticipate its debt cost of capital will be 4%. If its corporate tax rate is 15%, what is your estimate of its cost of capital? (20 points)

ii. The current price of Pineapple stock is $100. In each of the next two years, this stock price can either go up by $39 or go down by $31. The stock pays no dividends. The one-year risk-free interest rate is 5% and will remain constant.

a) Using the Binomial Model, calculate the price of a two-year put option on Pineapple stock with a strike price of $99. (8 points)

b) Using the Binomial Model, calculate the price of a two-year call option on Pineapple stock with a strike price of $101. (7 points)

iii. Assume first that the interest rate for all horizons is 5%.

a) What is the price of a 5-year coupon bond that pays $400 for 4 years and $1,400 in the fifth year? What is its duration? What is the modified duration of this bond? (3 points)

b) Let us assume that the interest rate changes by 25 basis point from 5% to 5.25%, what is the convexity and how the presence of convexity affects the resulting change in its price? (3 points)

c) Let us assume that the interest rate changes by 75 basis points from 5% to 5.75%, how the presence of convexity affects the resulting change in its price? Compare it with part iii and explain the results. (4 points)

d) As CFO of a leading bank, how do interest rate change affect your balance sheet? Hint: think of your balance sheet and debt interest payments on varying maturities of debt. (5 points)

2. This question has three parts:

i. Pineapple stock has a volatility of 40% and a current stock price of $100 per share. Pineapple pays no dividends. The risk-free interest is 5%.

a) Determine the Black-Scholes value of a one-year, at-the-money call option on Pineapple stock. (5 points)

b) What is the impact on the value of this call option when the volatility of the stock goes up by 5% to 45%. Explain your result. (5 points)

c) What is the impact on the value of this call option when the interest rates down up by 1% to 4%. Explain your result. (5 points)

d) What is the impact on the value of this call option when two months elapse, with no other change. Explain your result. (5 points)

ii. Superwoman Corp just announced it will cut its dividend from $4 to $2.50 per share and use the extra funds to expand. Prior to the announcement, Superwoman’s dividends were expected to grow at a 3% rate, and its share price was $50. With the new expansion, Superwoman’s dividends are expected to grow at a 5% rate.

a) What share price would you expect after the announcement? (Assume Superwoman’s risk is unchanged by the new expansion.) (5 points)

b) Is the expansion a positive NPV investment? (5 points)

c) Explain your results. (5 points)

iii. A 8% five-year bond yields 10% and a 6% five-year bond yields 8%. Calculate the fifth-year spot rate. Assume annual coupon payments. Explain your result. (15 points)