Question

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.

Old Chicago's 15-year bonds should show a greater price change than Red Frog's bonds. Witheverything the same except for maturity, the longer the maturity, the greater the price fluctuationassociated with a given change in market required return. The closer in time that you are to therelatively large maturity value being realized, the less important are interest payments indetermining the market price, and the less important is a change in market required return on themarket price of the security

b.

(Red Frog):

Formula:

V=I(PVIFAi,n) + MV(PVIFi,n)

V = Valuation of Bond

MV = Market Value

P0= $45(PVIFA4%,10) + $1,000(PVIF4%,10)

Po = $45(8.111) + $1,000(.676)

Po = $365 + $676

Po= $1,041 Ans.

(Old Chicago):

Formula:

V=I(PVIFAi,n) + MV(PVIFi,n)

V = Valuation of BondMV = Market Value

P0= $45(PVIFA4%,30) + $1,000(PVIF4%,30)

Po= $45(17.292) + $1,000(.308)

Po= $778.14 + $308

Po= $1,086.14 Ans.

Old Chicago's price per bond changes by ($1.086.14 - $1,000)

= $86.14,

while Red Frog's priceper bond changes by less than half that amount, or ($1,041 - $1,000)

= $41.