3. Solve the following problems: i. Renfro Rentals has issued bonds that have a
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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? iiii. 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? 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? iiii. 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? 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? iiii. 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. 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?
The bond price of today can be calculated with the help of following formula
Bond price P0 = C* [1- 1/ (1+i) ^n] /i + M / (1+i) ^n
Where
Price of the bond, P0 =?
C = coupon payment or annual interest payment = 10% per annum but it makes coupon payments on semiannual basis therefore coupon payment = 10%/2 of $1000 = $50
n = number of payments or time remaining for the maturity of bond = 16 (8*2 for semiannual payments)
i = yield to maturity (YTM) = 8.5% per annum or 4.25% per semiannual
M = value at maturity, or par value = $ 1000
Therefore,
Price of bond P0 = $50* [1 – 1 / (1+4.25%) ^16] /4.25% + 1000 / (1+4.25%) ^16
= $572.02 + $513.79
= $1085.80
Therefore the price of bond is $1085.80
2. 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?
The bond price of after two years can be calculated with the help of following formula
Bond price P2 = C* [1- 1/ (1+i) ^n] /i + M / (1+i) ^n
Where
Price of the bond, P2 =?
C = coupon payment or annual interest payment = 10% per annum but it makes coupon payments on semiannual basis therefore coupon payment = 10%/2 of $1000 = $50
n = number of payments or time remaining for the maturity of bond = 16 ((10-2)*2 for semiannual payments)
i = interest rate = 6% per annum or 3% per semiannual
M = value at maturity, or par value = $ 1000
Therefore,
Price of bond P2 = $50* [1 – 1 / (1+3%) ^16] /3% + 1000 / (1+3%) ^16
= $628.06 + $623.17
= $1251.22
Therefore the bond will sell after two years of issue at the price of $1251.22
b. Suppose that 2 years after the initial offering, the going interest rate had risen to 12%. At what price would the bonds sell?
The bond price of after two years can be calculated with the help of following formula
Bond price P2 = C* [1- 1/ (1+i) ^n] /i + M / (1+i) ^n
Where
Price of the bond, P2 =?
C = coupon payment or annual interest payment = 10% per annum but it makes coupon payments on semiannual basis therefore coupon payment = 10%/2 of $1000 = $50
n = number of payments or time remaining for the maturity of bond = 16 ((10-2)*2 for semiannual payments)
i = interest rate = 12% per annum or 6% per semiannual
M = value at maturity, or par value = $ 1000
Therefore,
Price of bond P2 = $50* [1 – 1 / (1+6%) ^16] /6% + 1000 / (1+6%) ^16
= $505.29 + $393.65
= $898.94
Therefore the bond will sell after two years of issue at the price of $898.94
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?
C = coupon payment or annual interest payment = 10% per annum but it makes coupon payments on semiannual basis therefore coupon payment = 10%/2 of $1000 = $50
i = interest rate = 6% per annum or 3% per semiannual
M = value at maturity, or par value = $ 1000
The price of the bond is summarized in following table for time remaining to maturity from 8 years to 0 year
Remaining years to maturity
Bond price
8
$1,251.22
7
$1,225.92
6
$1,199.08
5
$1,170.60
4
$1,140.39
3
$1,108.34
2
$1,074.34
1
$1,038.27
0
$1,000.00
Remaining years to maturity
Bond price
8
$1,251.22
7
$1,225.92
6
$1,199.08
5
$1,170.60
4
$1,140.39
3
$1,108.34
2
$1,074.34
1
$1,038.27
0
$1,000.00
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