How do you calcualte Yield To Maturity, given only the coupon rate and current required rate of return?

Question

Suppose today a 10 per cent coupon bond sells at par. Two years from now, the required return on the same bond is 8 per cent. What is the YTM?

^That's a question I've been asked and have literally no clue about how to calculate the YTM.

My understanding is: YTM is the anticipated return on a bond if held to maturity. If I buy a fresh bond at say \$90 and the par value is \$100 at 10% coupon rate, the YTM will be 10/90 = 11.11%. So for this question, If I buy a bond on the secondary market at par value, the YTM should equal the coupon rate no? If so, how does rrr affect YTM?

I'm so confused, send help.

Answer 1

The yield-to-maturity is similar to an internal rate of return, so the calculations need to take into account the timing of cash flows. So your example calculation 10%/.90 = 11.11% does not work. (That is known as a simple interest convention, which I think is sometimes used in the Japanese bond market.)

The calculation form depends upon the coupon frequency of the bond. For an annual coupon, if we denote the yield as y, then the price of the bond equals (convention of \$100 equals par): $$p = \sum_{i=1}^8 \frac{10}{(1+y)^i} + \frac{100}{(1+y)^8}.$$

However, I do not know what “required return” in the question refers to (a true internal rate of return?). You would need to find the price of the bond using that “required return,” and then work from the price equation to get the yield.