Question

1. Suppose your firm just issued a callable (at par) three-year, 5% coupon bond with semiannual coupon payments. The bond can be called at par in two years or anytime thereafter on a coupon payment date. It is currently priced at 99% of par. What is the bond’s yield to maturity and yield to call?

2. You own a convertible bond with a face value of $1000 and a conversion ratio of 45. What is the conversion price?

3. Suppose a firm with $852 million in debt and $1,287 million in book equity on its balance sheet is considering a $160 million debt issue to fund a major capital expenditure. The firm has 115 million shares outstanding at a current price of $45 per share. The stock beta is 0.85. The firm’s median fixed charge coverage ratio over the past three years is 8.2x and the standard deviation of return on assets over the past five years is 1.1%. Using the model provided with the in-class example, what is the synthetic bond rating for this issue?

4. Suppose the bond in the previous question is a 10-year, noncallable bond and the 10-year T-bond yield is currently 3.43%. Using the credit spread matrix from the in-class example, what coupon rate would be needed for the proposed bond issue to sell at par?

Answer 1

1]

YTM is calculated using RATE function in Excel with these inputs :

nper = 3*2 (3 years to maturity with 2 semiannual coupon payments each year)

pmt = 100 * 5% / 2 (semiannual coupon payment = face value * annual coupon rate / 2. This is a positive figure as it is an inflow to the bondholder)

pv = -99 (current bond price. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 100 (face value of the bond receivable on maturity. This is a positive figure as it is an inflow to the bondholder)

The RATE is calculated to be 2.68%. This is the semiannual YTM. To calculate the annual YTM, we multiply by 2. Annual YTM is 5.37%

2]

conversion price = bond price / conversion ratio

conversion price = $1,000 / 45

conversion price = $22.22

YTC is calculated using RATE function in Excel with these inputs :

nper = 3*2 (3 years to first call date with 2 semiannual coupon payments each year)

pmt = 100 * 5% / 2 (semiannual coupon payment = face value * annual coupon rate / 2. This is a positive figure as it is an inflow to the bondholder)

pv = -99 (current bond price. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 100 (call price of the bond receivable on call date. This is a positive figure as it is an inflow to the bondholder)

The RATE is calculated to be 2.77%. This is the semiannual YTC. To calculate the annual YTC, we multiply by 2. Annual YTC is 5.54%