Question

Coupon payments are fixed, but the percentage return that investors receive varies based on market conditions. This percentage return is referred to as the bond’s yield.

Yield to maturity (YTM) is the rate of return expected from a bond held until its maturity date. However, the YTM equals the expected rate of return under certain assumptions. Which of the following is one of those assumptions?

The bond is callable.

The probability of default is zero.

Consider the case of Swing Co.:

Swing Co. has 9% annual coupon bonds that are callable and have 18 years left until maturity. The bonds have a par value of $1,000, and their current market price is $1,070.35. However, Swing Co. may call the bonds in eight years at a call price of $1,060. What are the YTM and the yield to call (YTC) on Swing Co.’s bonds?

	Value
YTM	%
YTC	%

If interest rates are expected to remain constant, what is the best estimate of the remaining life left for Swing Co.’s bonds?

18 years

10 years

13 years

8 years

If Swing Co. issued new bonds today, what coupon rate must the bonds have to be issued at par? %

Answer 1

YTM is calculated using RATE function in Excel :

nper = 18 (years remaining until maturity with 1 annual coupon payment each year)

pmt = 1000 * 9% (annual coupon payment = face value * coupon rate)

pv = -1070.35 (Current price of bond. This is entered with a negative sign because it is a cash outflow to buy the bond today).

fv = 1000 (face value of bond receivable at maturity).

RATE is calculated to be 8.24%. This is the YTM.

А1 : х v f RATE(18,1000*9%,-1070.35,1000) B C D 1 8 A .24%!

YTC is calculated using RATE function in Excel with these inputs :

nper = 8 (8 years to call date with 1 annual coupon payment each year)

pmt = 1000 * 9% (annual coupon payment = face value * coupon rate)

pv = -1070.35 (Current price of bond. This is entered with a negative sign because it is a cash outflow to buy the bond today).

fv = 1060 (call price of the bond receivable on call date. This is a positive figure as it is an inflow to the bondholder)

The RATE is calculated to be 8.32%. This is the YTC.

A2 X foc =RATE(8,1000*9%,-1070.35,1060)

The YTM is lower than the coupon rate. So interest rates have declined since the bonds were issued. Therefore the bonds are likely to be called as Swing Co would likely call the bonds in order to refinance its debt at the lower interest rates. Swing Co. is likely to call the bonds in 8 years when they become callable.

Best estimate of the remaining life left for Swing Co.’s bonds is 8 years

A bond will be priced at par if its yield equals its coupon rate. The yield of the new bonds should equal the YTC of the old bonds because the bondholder of the old bonds is likely to earn the YTC by holding the bonds until they are called. The coupon rate the bonds must have is the YTC of the old bonds, which is 8.32%.