Question

Bond X is noncallable and has 20 years to maturity, an 8% annual coupon, and a $1,000 par value. Your required return on Bond X is 9%; if you buy it, you plan to hold it for 5 years. You (and the market) have expectations that in 5 years, the yield to maturity on a 15-year bond with similar risk will be 6.5%. How much should you be willing to pay for Bond X today? (Hint: You will need to know how much the bond will be worth at the end of 5 years.) Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

The price of bond at the end of 5 years will be as follows:

Bonds Price = Coupon payment x [ [ (1 - 1 / (1 + r)ⁿ ] / r ] + Par value / (1 + r)ⁿ

= (8% x $ 1,000) x [ [ (1 - 1 / (1 + 0.09)¹⁵ ] / 0.09 ] + $ 1,000 / 1.09¹⁵

= $ 80 x 8.06068843 + $ 274.5380413

= $ 919.3931157

So, the current price will be as follows:

Bonds Price = Coupon payment x [ [ (1 - 1 / (1 + r)ⁿ ] / r ] + Par value / (1 + r)ⁿ

= (8% x $ 1,000) x [ [ (1 - 1 / (1 + 0.065)⁵ ] / 0.065 ] + $ 919.3931157 / 1.065⁵

= $ 80 x 4.155679438 + $ 671.0474164

= $ 1,003.50 Approximately

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