Question

Yield to​ maturity)  ​Fitzgerald's 25​-year bonds pay 6 percent interest annually on a ​$1 comma 000 par value. If the bonds sell at $ 845​, what is the​ bond's yield to​ maturity? What would be the yield to maturity if the bonds paid interest​ semiannually? Explain the difference.

a. The​ bond's yield to maturity if the bond pays interest annually is

​(Round to three decimal​ places.)

b.  The​ bond's yield to maturity if the bond paid interest semiannually would be

(Round to three decimal​ places.)

c.  Based on the findings in parts a and b​, which of the following statements is​ correct?  ​(Select the best choice​ below.)

A.

Other things being​ equal, the YTM is the same for both an annual bond and a semiannual bond if the bond is selling at a discount.

B.

Other things being​ equal, the YTM is the same for both an annual bond and a semiannual bond if the bond is selling at a premium.

C.

Other things being​ equal, the YTM is higher for an annual bond than a semiannual bond if the bond is selling at a discount.

D.

Other things being​ equal, the YTM is higher for a semiannual bond than an annual bond if the bond is selling at a discount.

Answer 1

Par Value = 1000
PV = -845
Coupon = 6%*1000 = 60
Number of Years = 25

a) Using Financial Calculator
N = 25; PMT = 60; PV = -845; FV = 1000; CPT I/Y
YTM = 7.375%

b) Semi Annual Compounding
Par Value = 1000
PV = -845
Coupon = 6%*1000/2 = 30
Number of Years = 25*2 = 50

Using Financial Calculator
N = 50; PMT = 30; PV = -845; FV = 1000; CPT I/Y
I/Y = 3.683%
Rate = 3.683%*2 = 7.366%

c) Option c is correct .
Other things being​ equal, the YTM is higher for an annual bond than a semiannual bond if the bond is selling at a discount.

Please Discuss in case of Doubt

Best of Luck. God Bless
Please Rate Well