Chapter $6$ Valuing Bonds

$169$

$6\mathrm{.}1$ Self$-$Test

The following table shows a small sample of prices of Treasury bonds in $2020$:

$\backslash$table$[[$Coupon $(\%),$Maturity,Price, $\%$ of face value$],[2\mathrm{.}875,$April $2025,112\mathrm{.}069],[4\mathrm{.}5,$February $2036,151\mathrm{.}091],[3\mathrm{.}0,$November $2045,133\mathrm{.}270]]$

a$.$ How much would you need to pay to buy the bond maturing in $2036?$

b$.$ How much interest would you receive each year if you own the bond maturing in $2025?$

c$.$ What payment would you receive when the $3\mathrm{.}0\%$ bond matures in $2045?$

$$1,075$

Did you notice that your bond is like a package of two investments? The first provides a level stream of coupon payments of $$75$ a year for each of four years. The second consists of the final repayment of the $$1,000$ face value. Therefore, you can use the annuity formula to value the coupon payments and then add on the present value of the inal payment of face value:

$PV=PV($ coupons $)+PV($ face value $)$

$=($ coupon $$ annuity factor $)+($ face value $+$ discount factor $)$

$=$$$75[\frac{1}{\mathrm{.}03}-\frac{1}{\mathrm{.}03(1\mathrm{.}03{)}^4}]+$$$1,000\frac{1}{{1\mathrm{.}03}^4}$