Question

You intend to purchase a 10-year, $1,000 face value bond that pays interest of $40 every year.  If your annual required rate of return is 10 percent with, how much should you be willing to pay for this bond?

Answer 1

Price of the Bond

Price of the Bond is the Present Value of the Coupon Payments plus the Present Value of the Face Value

Face Value of the bond = $1,000

Annual Coupon Amount = $40 per year

Annual Yield to Maturity = 10.00%

Maturity Period = 10 Years

Therefore, The Price of the Bond = Present Value of the Coupon Payments + Present Value of the Face Value

= $40[PVIFA 10%, 10 Years] + $1,000[PVIF 10%, 10 Years]

= [$40 x 6.14457] + [$1,000 x 0.38554]

= $245.79 + $385.54

= $631.33

“The Price that would be willing to pay for the Bond is $631.33”

NOTE

-The formula for calculating the Present Value Annuity Inflow Factor (PVIFA) is [{1 - (1 / (1 + r)ⁿ} / r], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.  

-The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.