Question

Workman Software has 8.8 percent coupon bonds on the market with 19 years to maturity. The bonds make semiannual payments and currently sell for 107.2 percent of par. a. What is the current yield on the bonds? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What is the YTM? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) c. What is the effective annual yield? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

current yield 8.2089552%

YTM = 8.05%

effective annual yield = 4.92%

Explanation:

(A)

current yield = C/P

coupon payment / market price

8.8/107.2 = 0.082089552 = 8.2089552%

(B)

$P = \frac{C}{2} \times\frac{1-(1+YTM/2)^{-2t} }{YTM/2} + \frac{CP}{(1+YTM/2)^{2t}}$

First par being the present value of the coupon payment and second the redeem of the face value at the end of the bond.

market price 107.2

face value 100

time = 19

rate 8.8%

C = annual coupon payment 100 x 8.8% = 8.8

You solve this using a financial calculation and get the semiannual rate

YTM/2 = 0.040268160

then multiply by 2 to get the annual YTM

0.040268160  x 2 =

YTM = 0.08053632 = 8.05%

(C)

Effective Annual Yield

$(1+HPR)^{365/time} -1 = EAY$

where:

Holding period return:

$\frac{Net \: Return}{Investment} = HPR$

In this case:

coupon payment + redem - investment = net return

8.8 * 19 + 100 - 107.2 = 160

160/107.2 = 1.492537313

Then

$(1+HPR)^{365/time} -1 = EAY$

$(1+1.142537313)^{\frac{365}{19\times365}} -1 = EAY$

EAY = 0.049242509 = 4.9242509%