Concept explainers
Calculating the Cost of Debt. Ying Import has several bond issues outstanding, each making semiannual interest payments. The bonds are listed in the table below. If the corporate tax rate is 34 percent, what is the aftertax cost of the company’s debt?
Bond | Coupon Rate | Price Quote | Maturity | Face Value |
1 | 6.5% | 105.0 | 5 years | $30,000,000 |
2 | 5.3 | 95.4 | 8 years | 50,000,000 |
3 | 6.9 | 103.8 | 15½ years | 65,000,000 |
4 | 7.3 | 105.7 | 25 years | 85,000,000 |
To determine: The weighted average after-tax cost of debt.
Introduction:
The cost of debt refers to the return that the bondholders or lenders expect on their principal. In other words, it refers to the borrowing costs of the company.
Answer to Problem 22QP
The weighted average after-tax cost of debt is 4.21 percent.
Explanation of Solution
Given information:
Company Y has four bond issues. All the bonds make semiannual coupon payments. The corporate tax rate is 34 percent. Assume that the face value of one bond is $1,000. It issued Bond 1 with a coupon rate of 6.5 percent. The remaining time to maturity of the bond is 5 years. The market price of the bond is 105 percent of the face value. The total face value of Bond 1 is $30,000,000.
It issued Bond 2 with a coupon rate of 5.3 percent. The remaining time to maturity of the bond is 8 years. The market price of the bond is 95.4 percent of the face value. The total face value of Bond 2 is $50,000,000.
It issued Bond 3 with a coupon rate of 6.9 percent. The remaining time to maturity of the bond is 15.5 years. The market price of the bond is 103.8 percent of the face value. The total face value of Bond 3 is $65,000,000.
It issued Bond 4 with a coupon rate of 7.3 percent. The remaining time to maturity of the bond is 25 years. The market price of the bond is 105.7 percent of the face value. The total face value of Bond 4 is $85,000,000.
Formulae:
The formula to calculate the market value of debt:
The formula to calculate the total market value of the debt:
The formula to calculate annual coupon payment:
The formula to calculate the current price or the market value of the debt:
The formula to calculate the yield to maturity:
Where,
“C” refers to the coupon paid per period
“F” refers to the face value paid at maturity
“r” refers to the yield to maturity
“t” refers to the periods to maturity
The formula to calculate the after-tax cost of debt:
Where,
“RD” refers to the cost of debt
“TC” refers to the corporate tax rate
The formula to calculate the weighted average cost of debt:
Compute the market value of Bond 1:
Hence, the market value of Bond 1 is $31,500,000.
Compute the market value of Bond 2:
Hence, the market value of Bond 2 is $47,700,000.
Compute the market value of Bond 3:
Hence, the market value of Bond 3 is $67,470,000.
Compute the market value of Bond 4:
Hence, the market value of Bond 4 is $89,845,000.
Compute the total market value of the debt:
Hence, the total market value of debt is $236,515,000.
Compute the cost of debt for Bond 1:
Compute the annual coupon payment:
Hence, the annual coupon payment is $65.
Compute the current price of the bond:
The face value of the bond is $1,000. The bond value is 105% of the face value of the bond.
Hence, the current price of the bond is $1,050.
Compute the semiannual yield to maturity of Bond 1 as follows:
The bond pays the coupons semiannually. The annual coupon payment is $65. However, the bondholder will receive the same is two equal installments. Hence, semiannual coupon payment or the 6-month coupon payment is $32.5
The remaining time to maturity is 5 years. As the coupon payment is semiannual, the semiannual periods to maturity are 10
Finding “r” in Equation (1) would give the semiannual yield to maturity. However, it is difficult to simplify the above the equation. Hence, the only method to solve for “r” is the trial and error method.
The first step in trial and error method is to identify the discount rate that needs to be used. The bond sells at a premium in the market if the market rates (Yield to maturity) are lower than the coupon rate. Similarly, the bond sells at a discount if the market rate (Yield to maturity) is greater than the coupon rate.
In the given information, the bond sells at a premium because the market value of the bond is higher than its face value. Hence, substitute “r” with a rate that is lower than the coupon rate until one obtains the bond value close to $1,050.
The coupon rate of 6.5 percent is an annual rate. The semiannual coupon rate is 3.25 percent
The attempt under the trial and error method using 2.674 percent as “r”:
The current price of the bond is $1,049.96 when “r” is 2.674 percent. The value is close to $1,050. Hence, 2.674 percent is the semiannual yield to maturity.
Compute the annual yield to maturity:
Hence, the yield to maturity is 5.35 percent.
Compute the after-tax cost of Bond 1:
The pre-tax cost of debt is equal to the yield to maturity of the bond. The yield to maturity of the bond is 5.35 percent. The corporate tax rate is 34 percent.
Hence, the after-tax cost of Bond 1 is 3.53 percent.
Compute the cost of debt for Bond 2:
Compute the annual coupon payment:
Hence, the annual coupon payment is $53.
Compute the current price of the bond:
The face value of the bond is $1,000. The bond value is 95.4% of the face value of the bond.
Hence, the current price of the bond is $954.
Compute the semiannual yield to maturity of Bond 2 as follows:
The bond pays the coupons semiannually. The annual coupon payment is $53. However, the bondholder will receive the same is two equal installments. Hence, semiannual coupon payment or the 6-month coupon payment is $26.5
The remaining time to maturity is 8 years. As the coupon payment is semiannual, the semiannual periods to maturity are 16
Finding “r” in Equation (1) would give the semiannual yield to maturity. However, it is difficult to simplify the above the equation. Hence, the only method to solve for “r” is the trial and error method.
The first step in trial and error method is to identify the discount rate that needs to be used. The bond sells at a premium in the market if the market rates (Yield to maturity) are lower than the coupon rate. Similarly, the bond sells at a discount if the market rate (Yield to maturity) is greater than the coupon rate.
In the given information, the bond sells at a discount because the market value of the bond is lower than its face value. Hence, substitute “r” with a rate that is higher than the coupon rate until one obtains the bond value close to $954.
The coupon rate of 5.3 percent is an annual rate. The semiannual coupon rate is 2.65 percent
The attempt under the trial and error method using 3.254 percent as “r”:
The current price of the bond is $953.96 when “r” is 3.017 percent. The value is close to $954. Hence, 3.017 percent is the semiannual yield to maturity.
Compute the annual yield to maturity:
Hence, the yield to maturity is 6.03 percent.
Compute the after-tax cost of Bond 2:
The pre-tax cost of debt is equal to the yield to maturity of the bond. The yield to maturity of the bond is 6.03 percent. The corporate tax rate is 34 percent.
Hence, the after-tax cost of Bond 2 is 3.98 percent.
Compute the cost of debt for Bond 3:
Compute the annual coupon payment:
Hence, the annual coupon payment is $69.
Compute the current price of the bond:
The face value of the bond is $1,000. The bond value is 103.8% of the face value of the bond.
Hence, the current price of the bond is $1,038.
Compute the semiannual yield to maturity of Bond 3 as follows:
The bond pays the coupons semiannually. The annual coupon payment is $69. However, the bondholder will receive the same is two equal installments. Hence, semiannual coupon payment or the 6-month coupon payment is $34.5
The remaining time to maturity is 15.5 years. As the coupon payment is semiannual, the semiannual periods to maturity are 31
Finding “r” in Equation (1) would give the semiannual yield to maturity. However, it is difficult to simplify the above the equation. Hence, the only method to solve for “r” is the trial and error method.
The first step in trial and error method is to identify the discount rate that needs to be used. The bond sells at a premium in the market if the market rates (Yield to maturity) are lower than the coupon rate. Similarly, the bond sells at a discount if the market rate (Yield to maturity) is greater than the coupon rate.
In the given information, the bond sells at a premium because the market value of the bond is higher than its face value. Hence, substitute “r” with a rate that is lower than the coupon rate until one obtains the bond value close to $1,038.
The coupon rate of 6.9 percent is an annual rate. The semiannual coupon rate is 3.45 percent
The attempt under the trial and error method using 3.254 percent as “r”:
The current price of the bond is $1,037.91 when “r” is 3.254 percent. The value is close to $1,038. Hence, 3.254 percent is the semiannual yield to maturity.
Compute the annual yield to maturity:
Hence, the yield to maturity is 6.51 percent.
Compute the after-tax cost of Bond 3:
The pre-tax cost of debt is equal to the yield to maturity of the bond. The yield to maturity of the bond is 6.51 percent. The corporate tax rate is 34 percent.
Hence, the after-tax cost of Bond 3 is 4.30 percent.
Compute the cost of debt for Bond 4:
Compute the annual coupon payment:
Hence, the annual coupon payment is $73.
Compute the current price of the bond:
The face value of the bond is $1,000. The bond value is 105.7% of the face value of the bond.
Hence, the current price of the bond is $1,057.
Compute the semiannual yield to maturity of Bond 4 as follows:
The bond pays the coupons semiannually. The annual coupon payment is $73. However, the bondholder will receive the same is two equal installments. Hence, semiannual coupon payment or the 6-month coupon payment is $36.5
The remaining time to maturity is 25 years. As the coupon payment is semiannual, the semiannual periods to maturity are 50
Finding “r” in Equation (1) would give the semiannual yield to maturity. However, it is difficult to simplify the above the equation. Hence, the only method to solve for “r” is the trial and error method.
The first step in trial and error method is to identify the discount rate that needs to be used. The bond sells at a premium in the market if the market rates (Yield to maturity) are lower than the coupon rate. Similarly, the bond sells at a discount if the market rate (Yield to maturity) is greater than the coupon rate.
In the given information, the bond sells at a premium because the market value of the bond is higher than its face value. Hence, substitute “r” with a rate that is lower than the coupon rate until one obtains the bond value close to $1,057.
The coupon rate of 7.3 percent is an annual rate. The semiannual coupon rate is 3.65 percent
The attempt under the trial and error method using 3.411 percent as “r”:
The current price of the bond is $1,056.97 when “r” is 3.411 percent. Hence, 3.411 percent is the semiannual yield to maturity.
Compute the annual yield to maturity:
Hence, the yield to maturity is 6.82 percent.
Compute the after-tax cost of Bond 4:
The pre-tax cost of debt is equal to the yield to maturity of the bond. The yield to maturity of the bond is 6.82 percent. The corporate tax rate is 34 percent.
Hence, the after-tax cost of Bond 4 is 4.50 percent.
Compute the overall after-tax cost of the debt of Company Y:
Hence, the overall cost of debt of the firm is 4.21 percent.
Want to see more full solutions like this?
Chapter 12 Solutions
Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
- Ying Import has several bond issues outstanding, each making semiannual interest payments. The bonds are listed in the following table. If the corporate tax rate is 32 percent, what is the aftertax cost of Ying's debt? Bond Coupon Rate Price Quote Maturity Face Value 1 6.1% 104 4 years $17,000,000 234 7.2 111 7 years 38,000,000 6.3 104 16 years 46,000,000 7.3 115 26 years 58,000,000arrow_forwardYing Import has several bond issues outstanding, each making semiannual interest payments. The bonds are listed in the following table. Bond 1 234 Coupon Rate Price Quote 6.9% 8.4 8.1 7.7 106.86 115.42 113.97 103.21 Cost of debt Maturity 5 years 8 years 15.5 years 25 years % Face Value $ If the corporate tax rate is 24 percent, what is the aftertax cost of the company's debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) 49,000,000 44,000,000 64,000,000 71,000,000arrow_forwardYing Import has several bond issues outstanding, each making semiannual interest payments. The bonds are listed in the following table. If the corporate tax rate is 32 percent, what is the aftertax cost of Ying's debt? Bond 1 2 3 4 Coupon Rate Price Quote 102 109 101 116 6.3% 7 6.1 7.2 4.24% 3.88% 3.84% 5.94% 4.04% Maturity 4 years 9 years 22 years 35 years Face Value $ 16,000,000 40,000,000 40,000,000 58,000,000arrow_forward
- Cost of debt. Kenny Enterprises has just issued a bond with a par value of $1,000, a maturity of twenty years, and a coupon rate of 10.7% with semiannual payments. What is the cost of debt for Kenny Enterprises if the bond sells at the following prices? What do you notice about the price and the cost of debt? a. $967.34 b. $1,000.00 c. $1,045.83 d. $1, 189.10% (Round to two decimal places.)arrow_forwardYing Import has several bond issues outstanding, each making semiannual interest payments. The bonds are listed in the table below. Bond 1 2 1234 3 Coupon Rate 8.90% 6.90 8.60 9.10 Aftertax cost of debt Price Quote 106.4 94.0 105.2 95.0 % Maturity 3 years 6 years 13.5 years 23 years If the corporate tax rate is 24 percent, what is the aftertax cost of the company's debt? Note: Do not round Intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16. Face Value $ 23,000,000 35,000,000 40,000,000 55,000,000arrow_forwardYing Import has several bond issues outstanding, each making semiannual interest payments. The bonds are listed in the table below. Bond Coupon Rate Maturity Face Value. $ 8.60% 6.90 8.30 8.80 3 Aftertax cost of debt Price Quote 105.1 95.3 103.9 105.8 % 6 years 9 years 16.5 years 26 years If the corporate tax rate is 21 percent, what is the aftertax cost of the company's debt? Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16. 21,000,000 41,000,000 46,000,000 61,000,000arrow_forward
- Cost of debt. Kenny Enterprises has just issued a bond with a par value of $1,000, a maturity of twenty years, and a coupon rate of 10.5% with semiannual payments. What is the cost of debt for Kenny Enterprises if the bond sells at the following prices? What do you notice about the price and the cost of debt? a. b. $1,000.00 c. $1,036.72 d. $1,161.82 $977.21arrow_forwardCost of debt. Kenny Enterprises has just issued a bond with a par value of $1,000, a maturity of twenty years, and a coupon rate of 10.2% with semiannual payments. What is the cost of debt for Kenny Enterprises if the bond sells at the following prices? What do you notice about the price and the cost of debt? a. $938.10 b. $1,000.00 c. $1,041.98 d. $1,187.22 ..... a. What is the cost of debt for Kenny Enterprises if the bond sells at $938.10? % (Round to two decimal places.)arrow_forwardCote Import has several bond issues outstanding, each making semiannual interest payments. The bonds are listed in the following table. Bond 1 2 3 4 Coupon Rate 7.50 % 9.00 8.70 8.30 Cost of debt Price Quote 103.48 110.80 110.15 103.05 Maturity 5 years 8 years % 15.5 years 25 years If the corporate tax rate is 34%, what is the after-tax cost of the company's debt? (Do not round intermediate calculations. Round the final answer to 2 decimal places.) Face Value $ 45,000,000 40,000,000 50,000,000 65,000,000arrow_forward
- Ying Import has several bond issues outstanding, each making semiannual interest payments. The bonds are listed in the table below. Coupon Rate Maturity Face Value $ 8.90% Bond 1 2 3 6.80 8.60 9.20 Aftertax cost of debt Price Quote 106.8 93.4 105.8 96.5 % 4 years 6 years 14.5 years 25 years If the corporate tax rate is 25 percent, what is the aftertax cost of the company's debt? Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16. 28,000,000 31,000,000 36,000,000 55,000,000arrow_forwardUse the following data to calculate the Cost of Debt for the bond issues of Martin Corporation (one perecentage that represents the after tax cost for all the debt). Tax Rate = Face Value Current Price Coupon Rate Coupon payments per year Years remaining until maturity 20% Bond #1 $ 200,000,000 106.50 6.20% 2 12 Bond #2 $ 180,000,000 99.20 5.30% 2 15arrow_forwardYing Import has several bond issues outstanding, each making semiannual Interest payments. The bonds are listed in the following table. If the corporate tax rate is 31 percent, what is the aftertax cost of Ying's debt? (Do not round your intermediate calculations.) Bond Coupon Rate Price Quote 102 111 103 116 1234 4 6.3% 7 6.1 6.8 4.19% 5.78% 3.79% 3.83% 3.99% Maturity 7 years 12 years 21.5 years 32.5 years Face Value $ 21,000,000 40,000,000 47,000,000 58,000,000arrow_forward
- Intermediate Financial Management (MindTap Course...FinanceISBN:9781337395083Author:Eugene F. Brigham, Phillip R. DavesPublisher:Cengage Learning