Question

The YTM on a bond is the interest rate you earn on your investment if interest rates donâ t change. If you actually sell the bond before it matures, your realized return is known as the holding period yield (HPY). Suppose that two years ago, you bought a bond with an annual coupon rate of 7 percent, priced at $1,160 with 15 years to maturity, and $1000 par value. Since then the YTM of the bond has declined by 1 percent, and you decide to sell. What price will your bond sell for now? What is the HPY on this investment?

		$1,251; 9.8%
		$1,354; 10.2%
		$1,233; 11.2%
		$1,254; 10.5%

Answer 1

Face Value = $1000

Coupon Rate = 7%

Coupon = 7% *1000 = $70

Bond price = $1,160

Bond Maturity = 15 years

Yield to maturity can be calculated using the RATE function in spreadsheet

RATE(number of periods, payment per period, present value, future value, when-due, rate guess)

Where, number of periods = Bond Maturity = 15 years

payment per period = coupon = $70

present value = price of bond = $1,160

future value = face value = $1000

when-due = when is the payment made each year = end = 0

rate guess = A guess value of yield to maturity = 0.1

Yield to maturity = RATE(15, 70, -1160, 1000, 0, 0.1) = 5.4150%

Yield to maturity has dropped by 1%

new yield to maturity = old yield to maturity - 1% = 5.4150% - 1% = 4.4150%

new bond maturity = bond maturity -2 = 15-2 = 13 years

New price of the bond can be calculated using PV function in spreadsheet

PV(rate, number of periods, payment amount, future value, when-due)

Where, rate = yield to maturity = 4.4150%

number of periods = bond maturity = 13 years

payment amount = coupon = $70

future value = face value = $1000

when-due = when is the payment made each year = end = 0

New price of the bond = PV(4.4150%, 13, 70, 1000, 0) = $1,251.61

The cash flows for the bond are as given below

Year 0 -$1,160 Price at which bond is bought

Year 1 $70 Coupon payment

Year 2 $70 + $1,251.61 Coupon Payment + Price at which bond is sold

HPY is calculated using the IRR function in spreadsheet

IRR(cash flow amounts, rate guess)

HPY = 9.80%

Hence the correct answer is option 1, bond price = $1251 and HPY = 9.8%