Up in Smoke Tobacco Shops' bond carries a 9 percent coupon, pays interest semiannually, and has 10 years to maturity. What is the bond's yield to maturity if the bond is selling for $937.75 (rounded to the nearest whole percent)

Question

Singleton

Business

13 November, 12:29

Up in Smoke Tobacco Shops' bond carries a 9 percent coupon, pays interest semiannually, and has 10 years to maturity. What is the bond's yield to maturity if the bond is selling for $937.75 (rounded to the nearest whole percent)

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Answers (1)

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Bridger Carey · Answer 1

10%

Explanation:

Since the bond is selling at a discount, it means that the coupon rate is blow the market rate, so the actual rate must be higher. Since there is only one option with an interest rate above 9%, we must check to see if it works.

10% yearly interest rate = 5% semiannual interest rate

we must determine the PV of the 20 coupons paid and the face value at maturity.

to calculate the PV of the 20 coupons ($45 each) we can use an excel spreadsheet and the NPV function with a 5% discount rate: PV of the coupons = $560.80

the PV of the face value in 10 years = $1,000 / 1.05²⁰ = $376.89

the present value of the coupons and the bond at maturity = $560.80 + $376.89 = $937.69. The PV using a 5% semiannual rate is very similar to $937.75, and since the question asked us to round up to the nearest whole percent, we can assume it is correct.