Question

You bought a bond today that has a $1,000 par value and makes semiannual coupon payments. The bond has a coupon rate of 8%, a YTM of 6%, and has 15 years to maturity.
What is the price of this bond today?
Six months later, the YTM goes up to 7%. If you sell the bond in 6 months after receiving a coupon payment, what do you expect the selling price of this bond?
What will be your total dollar return on this bond investment over the 6-month holding period? What is the rate of return over the 6-month holding period?

Answer 1

Given

Par value of bond	$1000
Coupon rate	8%
YTM	6%
Maturity Period	15 years

Since coupon payments are made semiannually we need to adjust the coupon rate, YTM & maturity period accordingly.

Revised Coupon rate = 8% /2 = 4%

Interest amount = $1000*4% = $40

Revised YTM = 6%/2 = 3%

Revised Maturity Period = 15 *2 = 30

a) Calculation of price of bond

where YTM = yield to maturity
n = nos of years to maturity

Bo = 40* PVAF(3%,30) + 1000 * PVF(3%,30)

Bo = 40* 19.6004413 + 1000 * 0.4119868

Bo = 784.01 + 411.99

Bo = $1,196.00

Price of bond = $1,196.00

b) Value of bond after six months

After six months YTM = 7%

Revised YTM = 7%/2 = 3.5%

Remaining period to maturity = 30 -1 = 29  

Calculation of Price of bond after 6 months

where YTM = yield to maturity
n = nos of years to maturity

Bo = 40* PVAF(3.5%,29) + 1000 * PVF(3.5%,29)

Bo = 40* 18.035767 + 1000 * 0.368748

Bo = 721.43 + 368.75

Bo = $1090.18

Expected Selling Price of bond after 6 months = $1,090.18

c) Calculation of Total dollar return

Total return in dollars = Interest received + Selling Price of bond - Purchase cost of bond

Total return in dollars = $40 + $1090.18 -  $1,196.00

Total return in dollars = $40 - $105.82

Total return in dollars = ($65.82)

d) Calculation of Holding period rate of return

Holding period rate of return = (Interest received + Selling Price - Purchase cost )/ Purchase cost

Holding period rate of return = ($40 + $1090.18 -  $1,196.00) /  $1,196.00

Holding period rate of return = ($65.82) /  $1,196.00

Holding period rate of return = -0.05503 or (5.50%)