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Question 11

Red Frog Brewery has $1,000-par-value bonds outstanding with the following characteristics:

currently selling at par; 5 years until final maturity; and a 9 percent coupon rate

(with interest paid semiannually). Interestingly, Old Chicago Brewery has a very similar

bond issue outstanding. In fact, every bond feature is the same as for the Red Frog

bonds, except that Old Chicago’s bonds mature in exactly 15 years. Now, assume that

the market’s nominal annual required rate of return for both bond issues suddenly fell

from 9 percent to 8 percent.

a.Which brewery’s bonds would show the greatest price change? Why?

b. At the market’s new, lower required rate of return for these bonds, determine the per

bond price for each brewery’s bonds. Which bond’s price increased the most, and by

how much?

Answer 1

a)
A bond with higher maturity period is more sensitive to interest rate changes. Old Chicago Brewery has higher maturity period. Thus, Old Chicago Brewery bonds will have greatest price change.

b)
Calculation of new price of Red Frog Brewery bond:

FV = 1000
PMT = 1000 * 9% / 2 = 45
Nper = 5 * 2 = 10
Rate = 8% / 2 = 4%

Price of the bond can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(4%,10,-45,-1000)
= $1040.55

New price of Red Frog Brewery bond = $1040.55

Calculation of new price of Old Chicago Brewery :

FV = 1000
PMT = 1000 * 9% / 2 = 45
Nper = 15 * 2 = 30
Rate = 8% / 2 = 4%

Price of the bond can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(4%,30,-45,-1000)
= $1086.46

New price of Old Chicago Brewery = $1086.46

Old Chicago Brewery's bond price increased the most.

Old Chicago Brewery's bond price increased by $86.46 ($1086.46 - $1000).