Question

A firm's bonds have a maturity of 10 years with a $1,000 face value, have an 8% semiannual coupon, are callable in 5 years at $1,048.55, and currently sell at a price of $1,094.26. What are their nominal yield to maturity and their nominal yield to call? Do not round intermediate calculations. Round your answers to two decimal places.

YTM% =

YTC%=

What return should investors expect to earn on these bonds?

1. Investors would not expect the bonds to be called and to earn the YTM because the YTM is greater than the YTC.
2. Investors would not expect the bonds to be called and to earn the YTM because the YTM is less than the YTC.
3. Investors would expect the bonds to be called and to earn the YTC because the YTC is less than the YTM.
4. Investors would expect the bonds to be called and to earn the YTC because the YTC is greater than the YTM.

Answer 1

We can calculate ytm and ytc in excel,

YTM
Face value	1000
Coupon rate	8%
Coupon (semi annual)	40
Years	10
Number of periods	20
Current Price	1094.26
YTM(Semi annual)	3.35%	(=RATE(20,-40,1094.26,-1000))
YTM(Annual)	6.69%

Hence Ytm is 6.69%.

Ytm via financial calculator,

YTM = 6.69% (FV 1,000, PMT 40, N 20, PV 1,094.26)

YTC
Present Value	1,094.26
pmt	40
no periods	10
Future Value	1,048.55
YTC(Semi annual)	3.30%	(=Rate(10,40,1094.26,-1048.55,0)
YTC(Annual)	6.59%

Hence YTC is 6.59%.

Ytc via financial calculator,

Yield to Call = 6.59% (FV 1,048.55, PMT 40, N 10, PV 1,094.26)

What return should investors expect to earn on these bonds?

since ytc < ytm , investor would expect the bond to be called and earn ytc.

Hence the answer is option iii) Investors would expect the bonds to be called and to earn the YTC because the YTC is less than the YTM.

If you have any doubts please let me know in the comments. Please give a positive rating if the answer is helpful to you. Thanks.