Question

The Brownstone Corporations bonds have 5 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 9%.

a) What is the yield to maturity at a current market price of $849?
$

b) What is the yield to maturity at a current market price of $1,146?
$

c) Would you pay $849 for one of these bonds if you thought that the appropriate rate of YTM was 12%? Explain.

Answer 1

Compute the annual interest, using the equation as shown below:

Annual interest = Face value*Rate of interest

                          = $1,000*9%

                          = $90

Hence, the annual interest is $90.

(a)

Compute the annual yield to maturity (YTM), using the equation as shown below:

Annual YTM = [Annual interest + {(Redemption value – Net proceeds)/ Maturity period}]/ {(Redemption value + Net proceeds)/2}

                       = [$90 + {($1,000 – $849)/ 5}]/ {($1,000 + $849)/2}

                      = ($90 + $30.20)/ $924.50

                      = 13.001622498%

Hence, the annual YTM is 13.001622498%.

(b)

Compute the annual yield to maturity (YTM), using the equation as shown below:

Annual YTM = [Annual interest + {(Redemption value – Net proceeds)/ Maturity period}]/ {(Redemption value + Net proceeds)/2}

                       = [$90 + {($1,000 – $1,146)/ 5}]/ {($1,000 + $1,146)/2}

                      = ($90 - $29.20)/ $1,073

                      = 5.666356011%

Hence, the annual YTM is 5.666356011%.

(c)

Compute the present value annuity factor (PVIFA), using the equation as shown below:

PVIFA = {1 – (1 + Rate)-Number of periods}/ Rate

                 = {1 – (1 + 0.12)-5}/ 12%

             = 3.60477620228

Hence, the present value annuity factor is 3.60477620228.

Compute the present value factor (PVIF), using the equation as shown below:

PVIF factor = 1/ (1 + Discount rate)Time period

                    = 1/ (1 + 0.12)5

                    = 1/ 1.7623416832

                    = 0.56742685571

Hence, PVIF is 0.56742685571.

Compute the bond price, using the equation as shown below:

Bond price = (Annual interest*PVIFA) + (Face value*PVIF)

                   = ($90*3.60477620228) + ($1,000*0.56742685571)

                   = $891.8567

Hence, the bond price is $891.8567.

The current price of the bond is $891.8567 and if the bond if available at $849, then such bond should be purchased.