Question

Two years ago, Gamma Inc. sold a $250 million bond issue to finance the purchase of new jet airliners. These bonds were issued in $1,000 denominations with an original maturity of 14 years and a coupon rate of 12% with interest paid semiannually. Determine the value today of one of these bonds to an investor who requires a 14 percent return on these securities. Explain why the bond has a value that is not equal to the par value.

Answer 1

Face value = $1,000
Coupon rate = 12%
Frequency of coupon payment = Semiannual
Coupon payment = $1,000*12%*1/2 = $60
Time to maturity now = 14 – 2 = 12 years
Required rate of return = 14%
Value of bond today = $60*PVIFA14%/2, 12*2 + $1,000*PVIF14%/2, 12*2
= $60*PVIFA7%, 24 + $1,000*PVIF7%, 24
= $60*11.46933 + $1,000*0.19715
= $688.16 + 197.15
= $885.31
Since Coupon rate ≠ Required rate of return, bond value is not equal to par value.
Coupon rate < Required rate of return, Bond value < Par value

Answer 2

Face value = $1,000
Coupon rate = 12%
Frequency of coupon payment = Semiannual
Coupon payment = $1,000*12%*1/2 = $60
Time to maturity now = 14 – 2 = 12 years
Required rate of return = 14%
Value of bond today = $60*PVIFA14%/2, 12*2 + $1,000*PVIF14%/2, 12*2
= $60*PVIFA7%, 24 + $1,000*PVIF7%, 24
= $60*11.46933 + $1,000*0.19715
= $688.16 + 197.15
= $885.31
Since Coupon rate ≠ Required rate of return, bond value is not equal to par value.
Coupon rate < Required rate of return, Bond value < Par value