a)
To determine: The bond’s issue price
Introduction:
A bond refers to the debt securities issued by the governments or corporations for raising capital. The borrower does not return the face value until maturity. However, the investor receives the coupons every year until the date of maturity.
If the bond sells at a steep discount during the issue and does not make any coupon payments during its life, then the bond is a zero coupon bond.
a)
Answer to Problem 28QP
The company will issue the bond at $239.4591 per bond.
Explanation of Solution
Given information:
Company I wants to raise debt for its expansion plans. It wants to issue 25-year zero coupon bonds with a par value of $1,000. The market requires a return of 5.8 percent on similar bonds. The bond will follow semiannual compounding.
The formula to calculate the issue price of zero coupon bonds:
Where,
“r” refers to the market rate expected by the investors
“t” refers to the periods of maturity
Compute the issue price of zero coupon bonds:
The market rate required on the bond is 5.8 percent. It is an annual rate. In the given information, the company follows semiannual compounding. Hence, the semiannual or 6-month market rate is 2.9 percent
Hence, the issue price of the zero coupon bond will be $239.4591.
b)
To determine: The interest deduction in the first and last year based on “Internal revenue service” (IRS) amortization rule
Introduction:
The “Internal revenue service” (IRS) amortization rule requires the company to amortize the zero coupon bonds and consider the difference between the ending value of the bond and the beginning value of the bond as an interest deduction.
b)
Answer to Problem 28QP
The interest deduction at the end of the first year is $14.09. The interest deduction at the end of the last year is $55.5711.
Explanation of Solution
Required information:
The company will issue the zero coupon bonds at $239.4591 (Refer Part (a) of the solution). The face value of the 25-year zero coupon bonds is $1,000. The bond follows semiannual compounding and the required rate is 5.8 percent.
The formula to calculate the price of zero coupon bonds:
Where,
“r” refers to the market rate expected by the investors
“t” refers to the periods of maturity
The formula to calculate the interest deduction:
Compute the price at the beginning of the first year:
The price at the beginning of the first year will be the issue price. The issue price of the zero coupon bond is $239.4591 (Refer Part (a) of the solution).
Compute the price at the end of the first year:
The market rate required on the bond is 5.8 percent. It is an annual rate. In the given information, the company follows semiannual compounding. Hence, the semiannual or 6-month market rate is 2.9 percent
The remaining time to maturity is 24 years
Hence, the price of the zero coupon bond at the end of the first year will be $253.5491.
Compute the interest deduction for the first year:
Hence, the interest deduction for the first year is $14.09.
Compute the price at the beginning of the last year:
The market rate required on the bond is 5.8 percent. It is an annual rate. In the given information, the company follows semiannual compounding. Hence, the semiannual or 6-month market rate is 2.9 percent
The bond has 25 years of life. The year before 25 is the 24th year. The price at the end of the 24th year is equal to the price at the beginning of the 25th year. Hence, the remaining time to maturity is 1 year
As the coupon payment is semiannual, the semiannual periods to maturity are two
Hence, the price at the end of the 24th year or the price at the beginning of the 25th year is $944.4289.
Compute the price at the end of the last year:
The last year is the 25th year. As the end of the last year, the investor receives the face value of the bond. Hence, the price at the end of the last year is $1,000.
Compute the interest deduction for the last year:
Hence, the interest deduction for the last year is $55.5711.
c)
To determine: The interest deduction in the first and last year based on straight-line amortization
Introduction:
The straight-line amortization method amortizes the total interest in equal installments over the life of the bond.
c)
Answer to Problem 28QP
Under the straight-line method, the interest deduction will be equal in all the years. Hence, the interest deduction at the end of the first year and last year is $30.4216.
Explanation of Solution
Required information:
The company will issue the zero coupon bonds at $239.4591 (Refer Part (a) of the solution). The face value of the 25-year zero coupon bonds is $1,000.
The formula to calculate the total interest paid on the bond:
The formula to calculate the interest deduction based on straight-line method:
Compute the total interest paid on the bond:
Hence, the total interest paid during the life of the bond is $760.5409.
Compute the interest deduction based on straight-line method:
Hence, the interest deduction every year is $30.4216.
d)
To determine: The interest amortization preferred by the company
Introduction:
A bond refers to the debt securities issued by the governments or corporations for raising capital. The borrower does not return the face value until maturity. However, the investor receives the coupons every year until the date of maturity.
If the bond sells at a steep discount during the issue and does not make any coupon payments during its life, then the bond is a zero coupon bond.
d)
Explanation of Solution
Required information:
The interest deduction at the end of the first year is $14.09, and the interest deduction at the end of the last year is $55.5711 under the “Internal revenue service” (IRS) amortization rule. Under the straight-line method, the interest deduction at the end of the first year and last year is $30.4216.
The company will prefer the straight-line method of amortization to the “Internal revenue service” (IRS) amortization rule. The company can avail higher value deductions in the early years of the bond under the straight-line method. However, the interest deduction is lower in the early years under the “Internal revenue service” (IRS) amortization rule.
Hence, the company would prefer the straight-line method of amortization.
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Chapter 7 Solutions
Fundamentals of Corporate Finance
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