# Bond pricing, compute YTM … why t not = 2?

Consider a two-period corporate bond with the following characteristics. The bond was issued at $$t = 0$$ with face value $$FV = 100$$ at $$t = 2$$. In period $$t = 1$$ and $$t = 2$$ coupons of $$5$$ are paid out ($$c = 5$$). We are in $$t = 1$$ and the bond issuer has just paid the first coupon. The price of the bond is 101.942.

Suppose that the bond is callable at $$101$$. The bond issuer is informed by an investment bank that it can issue a new one period zero coupon bond worth $$101$$ today for a face value of $$104.030$$ in $$t = 2$$.What is the yield to maturity on this hypothetical bond?

The eqaution is given by: $$P_0 : \frac{c}{(1+r)} + \frac{C}{(1+r)^t} + \frac{FV}{(1+r)^t}$$

Where

$$c=0$$

$$FV= 104.03$$

$$P_0 = 101$$

$$t=2$$

And solve for $$r$$. But the right answer is all of this above, but $$t=1$$ .. Why? When they say that $$t=2$$?

• Hmmm.. someone? – soetirl13 Nov 18 '18 at 11:20

A better symbolism might be as follows.

T : periods to maturity from issuance, t : periods remaining to maturity, n : periods lapsed

Then t = T - n.

In your case, because the 1st coupon was paid the day in question, n = 1. T = 2. Thus, t = 2 - 1 = 1 period remaining to maturity.

You will only discount from the "current" time, in your example the end of year 1, across the remaining periods.

• how do we know that it's little t or big T - we're looking for? (or gonna use?) – soetirl13 Nov 20 '18 at 11:43
• Because the question wants you to determine the r from the "current" time. If you always use t, then you will always have the correct number of periods. Even if the question is dealing with the bond from the issuance date. In that case, n = 0, so t = T. – RJM Nov 20 '18 at 12:05
• The "t," which I am suggesting, is the biggest one in a calculation of Po. If you had more than one period for discounting, you would use Po = C/(1+r) + C/(1+r)^2 + ... + C/(1+r)^t + FV/(1+r)^t. In your question, t = 1. So Po = C/(1+r)+ FV/(1+r). – RJM Nov 20 '18 at 12:23