Problem $3$

Yield to maturity in year $013\%$

Bond $1$ Bond $2$ Bond $3$

Coupon rate $12\mathrm{.}0\%13\mathrm{.}6\%15\mathrm{.}5\%$

Maturity $91125$

Face value $1,0001,0001,000$

Bond price $$949$ $$1,034$ $$1,183$

Face value equal to $$1,000$ of market value $$2,658$ $$2,658$ $$2,658$

Duration $5\mathrm{.}896\mathrm{.}378\mathrm{.}15$

Yield to maturity in year $813\%$

Bond $1$ Bond $2$ Bond $3$

Bond price $($in year $8),$ assume YTM$=13\%$ $$991\mathrm{.}15$ $$1,014\mathrm{.}17$ $$1,168\mathrm{.}23$

Value of Reinvested coupons $($in year $8)$ $$1,410\mathrm{.}87$ $$1,598\mathrm{.}99$ $$1,822\mathrm{.}38$

Total $2,402\mathrm{.}022,613\mathrm{.}152,990\mathrm{.}60$

Multiply by percent of face value bought

Product $($Terminal Value$)$ $$312\mathrm{.}26$ $$339\mathrm{.}71$ $$388\mathrm{.}78$

Bond $1$ Bond $2$ Bond $3$

$3\%$ $$1,087\mathrm{.}38$ $$1,299\mathrm{.}83$ $$2,645\mathrm{.}76$

$4\%$ $$933\mathrm{.}33$ $$865\mathrm{.}19$ $$785\mathrm{.}14$

$5\%$

$6\%$

$7\%$

YTM $($yr$8)8\%$

$9\%$

$($e$)$ Assume year $8$ YTM could be different from $13\%.10\%$

Which bond is best suited to meet the obligation? $11\%$

Explain $(5$ pts$)12\%$

$13\%$

$14\%$

$15\%$

$16\%$

$17\%$

$18\%$

$19\%$

$20\%$ $$933\mathrm{.}33$ $$865\mathrm{.}19$ $$785\mathrm{.}14$