You are considering investing in a standard fixed-rate corporate bond with 25 years remaining to maturity. The bond pays annual coupons of 5% and just made its most recent coupon payment. The face value of the bond is $1000. a. What is the current price of coupon bond if its current yield to maturity is 4%? b. In exactly five years the yield to maturity of the coupon bond will have increased to 7% because the Fed has increased interest rates and because the company has become more risky. What is the price of the coupon bond in five years immediately after it made the coupon payment? c. What is the Internal Rate of Return (IRR) if you purchase the bond now at the price given in part (a), hold on to the bond for five years, and sell the bond after five years at the price computed in part (b).

Question

Valeria

Business

12 December, 09:40

You are considering investing in a standard fixed-rate corporate bond with 25 years remaining to maturity. The bond pays annual coupons of 5% and just made its most recent coupon payment. The face value of the bond is $1000. a. What is the current price of coupon bond if its current yield to maturity is 4%? b. In exactly five years the yield to maturity of the coupon bond will have increased to 7% because the Fed has increased interest rates and because the company has become more risky. What is the price of the coupon bond in five years immediately after it made the coupon payment? c. What is the Internal Rate of Return (IRR) if you purchase the bond now at the price given in part (a), hold on to the bond for five years, and sell the bond after five years at the price computed in part (b).

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Answers (1)

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Michelle Moore · Answer 1

a. $1,156.22

b. $788.12

c. - 2.35%

Explanation:

a. The current price of coupon bond:

It will be equals to the present value discounted at yield to maturity (4% in this case) of 25 coupon payment at the end of each year, $50 each (1,000 x 5%) and repayment of the face value of $1,000 at maturity. Calculation as below:

PV of 25 coupon payment = (50 : 4%) x (1 - (1+4%) ^-25) = $781.10

PV of face value's repayment = 1,000 / (1+4%) ^25 = $375.12

Current price = $781.10 + $375.12 = $1,156.22

b. The price of the coupon bond in five years:

It will be equals to the present value discounted at yield to maturity (7% in this case) of 20 coupon payment at the end of each year, $50 each (1,000 x 5%) and repayment of the face value of $1,000 at maturity. Calculation as below:

PV of 20 coupon payment = (50 : 7%) x (1 - (1+7%) ^-20) = $529.70

PV of face value's repayment = 1,000 / (1+7%) ^20 = $258.42

Current price = $529.70 + $258.42 = $788.12

c. Internal Rate of Return (IRR):

The transactions described in (c) will generate the following cashflow:

- Innitial investment of bond purchase of $1,156.22

- 5 coupon payments at the end of each year of $50 each;

- Selling proceed of bond at the end of year 5: $788.12

Denote x is IRR needs to be found. We have the NPV of the cashflows will be equal to 0 if the cashflows is discounted at IRR:

-1,156.22 + (50 : x) x (1 - (1+x) ^-5) + 788.12 / (1+x) ^5 = 0

x = - 2.35%