Question

A firm's bonds have a maturity of 10 years with a $1,000 face value, have an 11% semiannual coupon, are callable in 5 years at $1,172.87, and currently sell at a price of $1,309.24. 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?

A)Investors would not expect the bonds to be called and to earn the YTM because the YTM is less than the YTC.

B)Investors would expect the bonds to be called and to earn the YTC because the YTC is less than the YTM.

C)Investors would expect the bonds to be called and to earn the YTC because the YTC is greater than the YTM.

D)Investors would not expect the bonds to be called and to earn the YTM because the YTM is greater than the YTC.

Answer 1

Yield to maturity is the annualized rate of return on the investment that the investor expect (on the date of Investment) to earn from the date of investment to the date of maturity. It is also referred to as the required rate of return.

Given Face value 1000

Coupon Rate 11% semiannually

Maturity Year = 10 year or 10x2 = 20 Periods

Present Value = 1309.24

PMT = 1000x11/100x2 = 55

Using IRR method we can calculate I% = 3.3530% or YTM(Annually) = 3.3530x2 = 6.705991%

	Period	Amount
	Period 0	-1309.24
	Period 1	55
	Period 2	55
	Period 3	55
	Period 4	55
	Period 5	55
	Period 6	55
	Period 7	55
	Period 8	55
	Period 9	55
	Period 10	55
	Period 11	55
	Period 12	55
	Period 13	55
	Period 14	55
	Period 15	55
	Period 16	55
	Period 17	55
	Period 18	55
	Period 19	55
	Period 20	1055
IRR	3.3530%	*irr(value,guess)
YTM	6.705991

Sometimes the terms of issue of bonds contain a provision for call option i.e issuer has the option of calling the bonds for redemption before the date of maturity of the bonds. Yield to call refers to the annualized rate of return on the investment that the investor expect to earn from the date of investment to the date of call.

Call price 1172.87 Periods = 5x2 = 10 Periods

= I% = 3.305 or YTC = 3.305x2 = 6.610015 i.e calculated as follows

Period	Amount
Period 0	-1309.24
Period 1	55
Period 2	55
Period 3	55
Period 4	55
Period 5	55
Period 6	55
Period 7	55
Period 8	55
Period 9	55
Period 10	1227.87
IRR	3.305%
YTC	6.610015

Note that at 10th period end total realization would be 1172.87+55 and IRR calculation formula shall be same.

Since YTC is less than YTM the investor would like to bonds to be called because the bonds are selling at a premium which tell us that the interest rate have declined and are very likely to be called when the interest rate are lower than the coupon rate.