he same pricing equation applies to this case as well. There are two differences: $1.$ The bond

no longer matures in $20$ years. There are only $16$ years left on the bond. $2.$ The interest rate is

now $3\%$ instead of $5\%.$

The price of the bond is:$()()$

$01\mathrm{.}379,1$$

$2/03\mathrm{.}01$

$000,1$

$2/03\mathrm{.}01$

$1$

$1$

$2/03\mathrm{.}0$

$30$

$)()($Pr

$216216$

$=$

$+$

$+$

$$

$$

$$

$$

$$

$$

$$

$+$

$=$

$+=$

$$

principalPVcouponsPVice

III$)$ How would you calculate the yield to maturity $($you only need to set up the problem.

No actual calculations are required$)?$ Compared to the coupon rate, do you think the

yield to maturity is a better or worse measure of the investors$$ annual rate of return?

Why?

Answer:

The yield to maturity is the discount rate that makes the cash flows of a bond equal to the bond

price:$()()$

$40402/1$

$000,1$

$2/1$

$1$

$1$

$2/$

$30$

$51\mathrm{.}125,1$:isYTMa$)$partFor YTMYTMYTM $+$

$+$

$$

$$

$$

$$

$$

$$

$$

$+$

$=()()$

$32322/1$

$000,1$

$2/1$

$1$

$1$

$2/$

$30$

$01/379,1$:isYTMb$)$partFor YTMYTMYTM $+$

$+$

$$

$$

$$

$$

$$

$$

$$

$+$

$=$

Compared to the coupon rate, the YTM is a better measure of investor$$s returns. Coupon rate is

predetermined and does not change throughout the life of the bond. In contrast, YTM measures

the rate of return to investors if they hold the bond till maturity. It takes coupon payments, face

value, and price of the bond into account.