Question

Flora​ Co.'s bonds, maturing in 7 ​years, pay 9 percent interest on a $ 1 comma 000 face value.​ However, interest is paid semiannually. If your required rate of return is 6 ​percent, what is the value of the​ bond? How would your answer change if the interest were paid​ annually?

Answer 1

Value of the Bond if the interest is paid semi-annually

Face Value of the bond = $1,000

Semi-annual Coupon Amount = $45 [$1,000 x 9% x ½]

Semi-annual Yield to Maturity = 3% [6% x ½]

Maturity Period = 14 Years [7 Years x 2]

Value of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $45[PVIFA 3%, 14 Years] + $1,000[PVIF 3%, 14 Years]

= [$45 x 11.29607] + [$1,000 x 0.66112]

= $508.32 + $661.12

= $1,169.44

“Value of the Bond = $1,169.44”

Value of the Bond if the interest is paid annually

Face Value of the bond = $1,000

Annual Coupon Amount = $90 [$1,000 x 9%]

Annual Yield to Maturity = 6%

Maturity Period = 7 Years

Value of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $90[PVIFA 6%, 7 Years] + $1,000[PVIF 6%, 7 Years]

= [$90 x 5.58238] + [$1,000 x 0.66506]

= $502.41 + $665.06

= $1,167.47

“Value of the Bond = 1,167.47”

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.