3. Solve the following problems: i. Renfro Rentals has issued bonds that have a

Question

3. Solve the following problems: i. Renfro Rentals has issued bonds that have a 10% coupon rate, payable semiannually. The bonds mature in 8 years, have a face value of $1,000, and a yield to maturity of 8.5%. What is the price of the bonds?

ii. Suppose Hillard Manufacturing sold an issue of bonds with a 10-year maturity, a $1,000 par value, a 10% coupon rate, and semiannual interest payments.

a. Two years after the bonds were issued, the going rate of interest on bonds such as these fell to 6%. At what price would the bonds sell?

b. Suppose that 2 years after the initial offering, the going interest rate had risen to 12%. At what price would the bonds sell?

c. Suppose that 2 years after the issue date (as in part a) interest rates fell to 6%. Suppose further that the interest rate remained at 6% for the next 8 years. What would happen to the price of the bonds over time?

iii. Fred Tibbits has made a detailed study of the denim clothing industry. He's particularly interested in a company called Denhart Fashions that makes stylish denim apparel for children and teenagers. Fred has done a forecast of Denhart's earnings and looked at its dividend payment record. He's come to the conclusion that the firm will pay a dividend of $5.00 for the next two years followed by a year at $6.50. Fred's investment plan is to buy Denhart now, hold it for three years and then sell. He thinks the price will be about $75 when he sells. What is the most Fred should be willing to pay for a share of Denhart if he can earn 10% on investments of similar risk?

iv. Blackstone Corporation's $7 preferred was issued five years ago. The risk-appropriate interest rate for the issue is currently 11%. What is this preferred stock selling for today?

v. Fox Woodworking Inc. issued preferred shares at a face value of $50 to yield 9% 10 years ago. The shares are currently selling at $60. What return are they earning for investors who buy them today?

Explanation / Answer

1) Bond Price can be calculated using PV function on a calculator

N = 8 x 2 = 16, I/Y = 8.5%/2 = 4.25%, PMT = 10% x 1000/2 = 50, FV = 1000

=> Compute PV = $1,085.80 is the bond price

2 a) - N = 8 x 2 = 16, PMT = 50, FV = 1000, I/Y = 6%/2 = 3%

=> Compute PV = $1,251.22

b) N = 8 x 2 = 16, PMT = 50, FV = 1000, I/Y = 12%/2 = 6%

=> Compute PV = $898.94

c) As the interest rate fell after the issue, the bond price increased above the par value. Over a period of time, the bond price will decline and eventually hit the par value of $1,000 at maturity.

3) Price = D1 / (1 + r) + D2 / (1 + r)^2 + (D3 + P3) / (1 + r)^3

= 5 / 1.1 + 5 / 1.1^2 + (6.5 + 75) / 1.1^3

= $69.91

4) Preferred Stock Price = Dividend / Interest Rate = 7 / 11% = $63.64

5) Return = Dividend / Price = 9% x 50 / 60 = 7.50%

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