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1. You purchase a bond with an invoice price of $1,043. The bond has a coupon ra

ID: 2739825 • Letter: 1

Question

1. You purchase a bond with an invoice price of $1,043. The bond has a coupon rate of 6.8 percent, semiannual coupons, and there are five months to the next coupon date.

a) What is the clean price of the bond?

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2. Bond P is a premium bond with a coupon rate of 9 percent. Bond D is a discount bond with a coupon rate of 5 percent. Both bonds make annual payments, have a YTM of 7 percent, and have five years to maturity.

a: What is the current yield for bond P? _%
b What is the current yield for bond D? _%
c. If interest rates remain unchanged, what is the expected capital gains yield over the next year for bond P?
d) If interest rates remain unchanged, what is the expected capital gains yield over the next year for bond D?

Explanation / Answer

1. You purchase a bond with an invoice price of $1,043. The bond has a coupon rate of 6.8 percent, semiannual coupons, and there are five months to the next coupon date.

a) What is the clean price of the bond?

Solution: Clean price = Dirty price – Accrued interest = $1,043 – 5.67 = $1,037.33

Calculation of accrued interest: Accrued interest is the coupon payment for the period times the fraction of the period that has passed since the last coupon payment.

Since we have a semiannual coupon bond, the coupon payment per six months is one-half of the annual coupon payment. There are five months until the next coupon payment, so one months have passed since the last coupon payment.

The accrued interest for the bond is = Using 30 days per month, 360 per year, 6.8% on 1,000 = $68 per yr

= 68 / 2 for semiannual = $34 * 1 / 6 = $5.67 is the accrued interest.

2. Bond P is a premium bond with a coupon rate of 9 percent. Bond D is a discount bond with a coupon rate of 5 percent. Both bonds make annual payments, have a YTM of 7 percent, and have five years to maturity.

a: What is the current yield for bond P? _%

Answer: P0= $90(PVIFA7%,5) + $1,000(PVIF7%,5) = 90*4.10 + 1000 * 0.731 = $1,082

Current yield = $90 / $1,082 = .0832 or 8.32%

b What is the current yield for bond D? _%

Answer: P0= $50(PVIFA7%,5) + $1,000(PVIF7%,5) = 50*4.10 + 1000 * 0.731 = $918

Current yield = $50 / $918 = .0545 or 5.45%

c. If interest rates remain unchanged, what is the expected capital gains yield over the next year for bond P?

Answer: The capital gains yield is:Capital gains yield = (New price – Original price) / Original price

we need to calculate new price, P1= $90(PVIFA7%,4) + $1,000(PVIF7%,4) = 90*3.387 + 1000 * 0.763 = $1,067.83

Capital gains yield = ($1,067.83 - $1,082) / $1,082 = –0.0131 or –1.31%

d) If interest rates remain unchanged, what is the expected capital gains yield over the next year for bond D?

Answer: The capital gains yield is:Capital gains yield = (New price – Original price) / Original price

we need to calculate new price, P1= $50(PVIFA7%,4) + $1,000(PVIF7%,4) = 50*3.387 + 1000 * 0.763 = $932.35

Capital gains yield = ($932.35 - $918) / $918 = 0.0156 or 1.56%