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? RTE Inc. 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 $1,160.35. However, RTE Inc. 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 RTE Inc.’s bonds?
If interest rates are expected to remain constant, what is the best estimate of the remaining life left for RTE Inc.’s bonds?
If RTE Inc. issued new bonds today, what coupon rate must the bonds have to be issued at par?

What are the YTM and the yield to call (YTC) on RTE Inc.’s bonds?

RTE annual 9% coupon with 18 years to maturity

par value $1,000

current market price $1,160.35

callable in 8 years at $1,060

YTM = {coupon + [(face value - market value) / years to maturity]} / [(face value + market value) / 2

YTM = {90 + [(1,000 - 1,160.35) / 18]} / [(1,000 + 1,160.35) / 2

YTM = (90 - 8.91) / 1,080.18 = 7.51%

YTC = {coupon + [(face value - call value) / years to call]} / [(face value + call value) / 2

YTC = {90 + [(1,000 - 1,060) / 8]} / [(1,000 + 1,060) / 2

YTC = (90 - 7.50) / 1,030 = 8.01%

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

Since the market rate is lower than the coupon rate, the company will probably call the bonds in 8 eight years.

If RTE Inc. issued new bonds today, what coupon rate must the bonds have to be issued at par?

If RTE was to issue new bonds, then they would probably need to issue them with a 8.01% coupon rate (equal to the yield to call). Under the current circumstances, no investor will believe that RTE will not call the bonds, so the YTC is a more accurate measure of the market interest rate.