Question

Part 2 1. You have collected information about firm XYZ as follows: • The debt of the firm: par value = $800, annual coupon = $100 (paid once a year), maturity = 3 years. • The total value of the firm (including equity and the debt) = $1,000 now. • The firm's future values follow a two-state path with Up state growth multiple u = 1.3 and Down state growth multiple d = 0.769 each year. • The annual risk-free rate = 2%. You do not have to answer questions (b) and (e). (a) What is the value of the firm's debt, if it is a straight corporate debt? ( 40 points) fb) Suppose now that instead of a straight corporate debt as in (1) the firm's debt is convertible for 40% of the firm's value. What is the value of the convertible corporate debt? (20 points) (c) There is a treasury bond with the par value of $800, annual coupon f $100, and the maturity of 3 years. Suppose that the term structure of spot rates is flat 2%. What is the value of the Treasury bond? (20 points) (d) Which bond, the Treasury bond or the straight corporate bond, has higher price and why? Calculate the yield spread between the straight corporate bond and the Treasury bond (20 points) tel Which bond, the straight corporate bond or the convertible corporate bond, has higher price and why? (10 points)

Answer 1

a) Annual Interest paid = $100

Interest rate = $100/$800 = 0.125 = 12.5%

So, Value of Corporate Debt which pays annual coupon every year along with par value at maturity

V = 100/ (1+0.125) +100/ (1+0.125)^2 +100/ (1+0.125)^3 +800/ (1+0.125)^3

= $800

Value of straight corporate debt is $800

c) Value of Treasury Bond = 100/ (1+0.02) +100/ (1+0.02)^2 +100/ (1+0.02)^3 +800/ (1+0.02)^3

=$1042.25

d) The treasury bond is selling at a higher price than straight corporate debt because the yield of Treasury Bond is lower(2%) as compared to straight corporate debt with a yield of 12.% As yield has an inverse relationship with price , the price of Treasury bond is higher.

The Yield spread between straight corporate debt and Treasury bond = 12.5% -2%

=10.5%