Question

A $1,000 par bond with a 12.25% coupon has 10 years to maturity. If the yield to maturity is 12.25%, what is the price of the bond?

		$1,138.25
		$1,047.92
		$1,000.00
		$889.20

Answer 1

The correct answer is $1000.00

Price of Bond = Cupon Amount * Present Value of Annuity Factor (r,n) + Redemption Amount * Present Value of Interest Factor (r,n)

Where Cupon Amount = Face value of bond * Cupon Rate

= $1000 * 12.25%

= $122.5

Redemption Amount = $1000

r or Yield to maturity = 12.25%

n or number of years to maturity = 10 years

Present Value of Annuity Factor (12.25%, 10) = 5.59287

Present Value of Interest Factor (12.25%, 10) = 0.31487

Therefore

Bond Price = $122.5 * 5.59287 + $1000 * 0.31487

Bond Price =$685.1266 + $314.87

Bond Price = $999.9966

Rounding to two decimal places

Bond Price = $1000

Notes

Why did we use Present Value of Annuity Factor for Cupon Amounts

The cupon amounts would be received every year till maturity of the bond. This means for 10 years there will be 10 cupon payments from the bond.

Why did we use Present Value of Interest Factor for Redemption amount

The Redemption amount would be received only once and that is at the 10th year or the year of maturity of the bond.

How did we calculate the discounting factors @ 12.25%

Year 1 = 1/1.1225

= 0.89087

Year 2 = 0.89087/1.1225

= 0.79365

Year 3 = 0.79365 /1.1225

= 0.70704

Year 4 = 0.70704/1.1225

= 0.62988

Year 5 = 0.62988/ 1.1225

= 0.56114

Year 6 = 0.56114/ 1.1225

= 0.49990

Year 7 = 0.49990 / 1.1225

= 0.44534

Year 8 = 0.44534 / 1.1225

= 0.39674

Year 9 = 0.39674/ 1.1225

= 0.35345

Year 10 = 0.35354/ 1.1225

= 0.31487

Now if we add all these discounting factors we will get the Present Value of Annuity Factor (12.25%, 10) = 5.59287

For Present Value of Interest Factor we will take discounting factor of Year 10 i.e. 0.31487 since we will receive the redemption amount at year 10.