Question

A 25 year bond issued today by Carris, Inc. has a coupon rate of 11%, a required return of 12% and a face value of $1,000. The bond will be sold 8 years from now when interest rates will be 9%. What is the actual rate of return (or holding period return) over this 8 year period? Round to the nearest percent. (This will be easier to answer if you've already answered the other two questions regarding the Carris bond.)

Answer 1

We need to find the current bond price and bond price in 8 years.

Bond price is the present value of cash inflows from the bond, i.e., Present value of coupon payments and maturity value using YTM (required return) as the discount rate.

Current Bond Price

Annual coupon = $1000 x 11% = $110, No. of years to matuity = 25, YTM = 12%, Maturity value = $1000

Bond price = $110 x PVIFA (12%, 25) + $1000 x (12%, 25) = $110 x 7.84313911208 + $1000 x 0.05882330651 = $921.568608838

Bond price in 8 years

Annual coupon = $110, No. of years to maturity = 25 - 8 = 17, YTM = 9%

Bond price = $110 x PVIFA (9%, 17) + $1000 x (9%, 17) = $110 x 8.54363136933 + $1000 x 0.23107317673 = $1170.87262735

Capital gain on Bond = Sale price - Purchase price = $1170.87262735 - $921.568608838 = $249.30401852

Holding Period Return (HPR)

HPR = [ Total coupon payments + Capital gain ] / Purchase price

or, HPR = [ ($110 x 8) + $249.30401852 ] / $921.568608838 = 1.225415023 or 123%