Question

Your grandfather wants to determine the value of his bond portfolio and asks you for help. Find the current market values of the components of your grandfather’s portfolio. (a) 80 bonds with a $1,000 face value and a coupon rate of 7.6%/year. These bonds have 11 years left to maturity and pay coupons on a semi‐annual basis. The YTM of these bonds is 8.8%/year. What is the total market value of these 80 bonds? (3 pts.) (b) 160 zero‐coupon bonds with a $1,000 face value, 9 years to maturity, and a YTM of 7.7%/year

Answer 1

a) $73,320.80

b) $82,068.80

Step-by-step explanation:

Current market value of bonds:

PV of face value = $1,000 / (1 + 4.4%)²² = $387.78

PV of coupon payments = $38 x 13.91402(PV annuity factor, 4.4%, 22 periods) = $528.73

Market price = $916.51

$916.51 x 80 = $73,320.80

Current market value of zero coupon bonds:

PV of face value = $1,000 / (1 + 7.7%)⁹ = $512.93

$512.93 x 160 = $82,068.80