Question

Hamilton, Inc. bonds have a coupon rate of 15 percent. The interest is paid semiannually, and the bonds mature in 14 years. Their par value is $1,000. If your required rate of return is 14 percent, what is the value of the bond? What is the value if the interest is paid annually?

Answer 1

Coupon rate of the bond = 15%

Tenure of the Bond = 14 years

Par value of the Bond = $1000

Interest for semi annual period = par value X Interest rate X 0.5

= 1000 x 15% x 0.5

= $75

Required rate of return = 14%

Total semi annual payments =14 x 2 =28

Required rate of return for 6 months = 14/2 = 7%

Formula for present value cash flows = Cash flow / (1+R)

^{PV Cash flow =} ? C_n / (1+R)ⁿ

PV annuity factor for =  ? 1 / (1+.07)²⁸  

^{= 12.14}

^{PV value of coupon payments = 12.14 x 75}

^{= $ 910.28}

PV value of Bond payable after 14 years = 1000 x 1/(1+.14)¹⁴

^{= $ 150.4}

^{PV value of Bond = $ 150.4 + $ 910.28}

^{= $ 1060.69}

^{If Interest is payable annually then the present value factor for 14 years = 6.00}

Interest payable per annum = 1000 x 15% = 150

PV value of coupon payment = 150 x 6 = $ 900

PV value Bond repayable after 14 years = $ 150.4 ( Calculated above)

PV value of Bond is = 150.4 + 900

= $ 1050.4