Concept explainers
Zero Coupon Bonds [LO2] Suppose your company needs to raise $47 million and you want to issue 20-year bonds for this purpose. Assume the required return on your bond issue will be 6 percent, and you’re evaluating two issue alternatives: a semiannual coupon bond with a coupon rate of 6 percent and a zero coupon bond. Your company’s tax rate is 35 percent. Both bonds will have a par value of $1,000.
a. How many of the coupon bonds would you need to issue to raise the $47 million? How many of the zeroes would you need to issue?
b. In 20 years, what will your company’s repayment be if you issue the coupon bonds? What if you issue the zeroes?
c. Based on your answers in (a) and (b), why would you ever want to issue the zeroes? To answer, calculate the firm’s aftertax
a)
To determine: The number of coupon bonds and zero coupon bonds that the company needs to issue
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.
Answer to Problem 29QP
The company needs to issue 47,000 bonds to raise $47,000,000. It needs to issue 153,316 zero coupon bonds to raise $47,000,000.
Explanation of Solution
Given information:
Company X intends to raise $47,000,000 through 20-year bonds. The investors expect 6 percent return on the bond. The bond will pay the coupons semiannually. The company two alternatives to the bond issue. It can either issue a coupon bond at 6 percent coupon rate or a zero coupon bond. The bond’s par value will be $1,000. Company X falls under 35 percent tax bracket.
The formula to calculate the number of coupon bonds that the company needs to issue:
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
The formula to calculate the number of zero coupon bonds that the company needs to issue:
Compute the number of coupon bonds that the company needs to issue:
Hence, the company needs to issue 47,000 bonds to raise $47,000,000.
Compute the issue price of zero coupon bonds:
The market rate required on the bond is 6 percent. It is an annual rate. In the given information, the company follows semiannual compounding. Hence, the semiannual or 6-month market rate is 3 percent
Hence, the issue price of the zero coupon bond will be $306.5568.
Compute the number of zero coupon bonds that the company needs to issue:
Hence, the company needs to issue 153,316 zero coupon bonds to raise $47,000,000.
b)
To determine: The repayment value if the company issues coupon bonds and zero coupon bonds after 20 years
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.
Answer to Problem 29QP
The repayment value of coupon bonds after 20 years is $48,410,000. The repayment value of zero coupon bonds after 20 years is $153,316,000.
Explanation of Solution
Given information:
The company needs to issue 47,000 bonds to raise $47,000,000 (Refer Part (a) of the solution). It needs to issue 153,316 zero coupon bonds to raise $47,000,000 (Refer Part (a) of the solution). The coupon bond has a 6 percent coupon rate. The bond’s par value will be $1,000 and compounding is semiannual.
The formula to calculate the repayment on zero coupon bonds:
The formula to calculate annual coupon payment:
The formula to calculate the semiannual coupon payment:
The formula to calculate the repayment on coupon bonds:
Compute the repayment on zero coupon bonds:
Hence, the repayment value of zero coupon bonds after 20 years is $153,316,000.
Compute the annual coupon payment:
Hence, the annual coupon payment is $60.
Compute the semiannual coupon payment:
Hence, the semiannual coupon payment is $30.
Compute the repayment on coupon bonds:
Hence, the repayment value of coupon bonds after 20 years is $48,410,000.
c)
To determine: The reason why the company would choose to issue zero coupon bonds
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.
Answer to Problem 29QP
There will be a cash outflow every year when the company issues coupon bonds. The after-tax cash outflow is $1,833,000 when the company issues coupon bonds. On the contrary, there will be cash inflow when the company issues zero coupon bonds. The interest payments on zero bonds are notional, and it is just an accounting value. Hence, there is no actual cash outflow.
Moreover, the company can claim interest deduction arising from zero coupon bonds even if there is no actual interest payment. As a result, the tax saved ($1,001,805.8396) by the notional interest of zero coupon bond is the cash inflow. Hence, the company would prefer zero coupon bonds because it would generate cash inflow.
Explanation of Solution
Required information:
The interest payment or coupon payment on coupon bond for the first year is $60 (Refer to Part (b) of the solution). The issue price of the zero coupon bond is $306.5568 (Refer Part (a) of the solution). The bond’s par value will be $1,000 and compounding is semiannual. The required return on zero coupon bonds is 6 percent.
The company needs to issue 47,000 bonds to raise $47,000,000. It needs to issue 153,316 zero coupon bonds to raise $47,000,000. (Refer to Part (a) of the solution).
The formula to calculate the after-tax cash outflow of coupon bonds:
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 payment on zero coupon bonds:
The formula to calculate the cash inflow from zero coupon bonds:
Compute the after-tax cash flow of coupon bonds:
Hence, the after-tax cash outflow is $1,833,000 when the company issues coupon bonds.
Compute the price at the beginning of the first year for the zero coupons bond:
The price at the beginning of the first year will be the issue price. The issue price of the zero coupon bond is $306.5568 (Refer Part (a) of the solution).
Compute the price at the end of the first year:
The market rate required on the bond is 6 percent. It is an annual rate. In the given information, the company follows semiannual compounding. Hence, the semiannual or 6-month market rate is 3 percent
The remaining time to maturity is 19 years. As the coupon payment is semiannual, the semiannual periods to maturity are 38
Hence, the price of the zero coupon bond at the end of the first year will be $325.2261.
Compute the interest payment on zero coupon bonds:
Hence, the interest payment on zero coupon bonds for the first year is $18.6693.
Compute the after-tax cash inflow of zero coupon bonds:
Hence, the after-tax cash inflow from zero coupon bonds is $1,001,805.8396.
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Chapter 7 Solutions
Fundamentals of Corporate Finance
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