P6–18 Bond value and time: Constant required returns Pecos Manufacturing has jus

Question

P6–18 Bond value and time: Constant required returns Pecos Manufacturing has just issued
a 15-year, 12% coupon interest rate, $1,000-par bond that pays interest annually.
The required return is currently 14%, and the company is certain it will remain
at 14% until the bond matures in 15 years.
a. Assuming that the required return does remain at 14% until maturity, find the
value of the bond with (1) 15 years, (2) 12 years, (3) 9 years, (4) 6 years, (5) 3
years, and (6) 1 year to maturity.
b. Plot your findings on a set of “time to maturity (x axis)–market value of bond
(y axis)” axes constructed similarly to Figure 6.5 on page 252.
c. All else remaining the same, when the required return differs from the coupon
interest rate and is assumed to be constant to maturity, what happens to the
bond value as time moves toward maturity? Explain in light of the graph in
part b.

Explanation / Answer

A) We have required return or yield to maturity of bond given as 14%, coupon rate 12%, future value $1,000. We have to calculate the price using different time periods. Calculating bond price is quite simple using excel. Using the pv function, we enter the ytm figure in rate, period in nper, annual coupon payment in pmt and future value in fv.

1) when nper is 15, bond price is calculated as $877.16

2) nper is 12, bond price $886.79

3) nper is 9, bond price $901.073

4)  nper is 6, bond price $922.227

5)  nper is 3, bond price $953.57

6)  nper is 1, bond price $982.46

B) please do part b on your own

C) the required return or ytm and coupon rates are inversely related and have similar affect on price of bond. When coupon rate of a bond is less than the ytm or lets say the market interest rate as the case here, the price of bond drops and it sells at a discount. This is because no investor in their right state of mind will buy a bond at face value with a lower interest rate when they can get a greater interest by purchasing it in open market. When the coupon rate of bond is greater than the market yield, investor will rush to purchase the bond even though now it will sell at premium because they will get greater yield on this purchase than elsewhere. With a constant yield, the time to maturity is also to watch for as shown by calculations in part a. The greater is the time to maturity, the more discount the bond offers.

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