Question

Consider an 8% coupon bond selling for $953.10 with three years until maturity making annual coupon payments. the interest rates in the next three years will be, with certainty, r1 = 8%, r2 = 10%, and r3 = 12%. calculate the bond's (a) yield to maturity and (b) realized compound yield

Answer 1

Answer:

a) YTM = 9.8%

b) realized compound yield is 9.9%

Explanation:

a) PMT = 80

par value FV = 1000

coupon rate = 8%

curent price PV = 953.1

years to maturity n = 3

Yield to maturity (YTM) = $\frac{PMT+(FV-PV)/n}{(FV+PV)/2}$ = $\frac{80+(1000-953.1)/3}{(1000+953.1)/2}$= 9.8%

b) r2 = 10% = 100%+10%=1.1

r3 = 12% = 100%+12%=1.12

Realized compound yield:First, find the future value (FV. of reinvested coupons and principal

FV =  ($80 *1.10 *1.12) + ($80 * 1.12) + $1080 = $1268.16

let a be the rate that makes the future value $1268.16

953.1(1+y)³ =$1268.16

(1+y)³=1.33

1+y=1.099

y = 0.099 = 9.9%