Question

For the? following, assume the normal case that bond coupons are? semi-annual: ?

a) What is the yield to maturity? (YTM) on a 9?-year, 6.8?% coupon bond if the bond is currently selling for? $1,000? ? (Assume semi-annual? coupons) %

?b) What is the YTM on the above bond if the value today is ?$961.08?? %

?c) For the bond in ?a) above?, what is your realized? (actual) EAR if immediately after you purchase the bond market? rates, and the rate at which you can reinvest? coupons, change to 4.2?% and you hold the bond for 5 years and then? sell? (remember, coupons and compounding are? semi-annual) %

Answer 1

a) Yield to maturity is equal to coupon rate if bond is selling at par value. Hence, YTM = 6.8%

b) YTM can be calculated using I/Y function on a calculator

N = 9 x 2 = 18, PMT = 6.8% x 1000 / 2 = 34, PV = -961.08, FV = 1000

=> Compute I/Y = 3.70% (semi-annual)

YTM = 2 x 3.70% = 7.40%

c) You purchased the bond at $1,000

Value of the bond after 5 years can be calculated using PV function

N = 4 x 2 = 8, PMT = 34, FV = 1000, I/Y = 4.2%/2 = 2.1%

=> Compute PV = $1,094.82 will be the price of the bond after 5 years

Now, the value of coupon reinvested after 5 years can be calculated FV function

N = 5 x 2 = 10, PMT = 34 , PV = 0, I/Y = 2.1% => Compute FV = $374.00

EAR = ((1094.82 + 374) / 1000)^(1/5) - 1 = 7.99%