Question

On January 1, 2019, Lightfoot Corporation issues 10%, 5-year bonds with a face value of $275,000 when the effective interest rate is 9%. Interest is to be paid semiannually on June 30 and December 31. Prepare calculations to prove that the selling price of the bonds is $285,880.07. Click here to access the tables to use with this exercise. Round your answers to two decimal places, if necessary.

Answer 1

Value of bond = Present value of coupon payments + Present value of maturity or par value

Present value of coupon payments:

Coupon is semi annual = 275,000 * 10% * 1/2

= $13,750

Interest = 9%/ 2 = 4.5%

Duration = 5 * 2 = 10 semi annual periods

Present value will be that of an annuity as this cash flow is fixed:

= 13,750 * (1 - (1 + 4.5%)⁻¹⁰) / 4.5%

= $108,799.87

Present value of par value:

= 275,000 / ( 1 + 4.5%)¹⁰

= 177,080.11

Value of bond:

= 108,799.87 + 177,080.11

= $285,879.98

= $285,880

Proven.

Difference due to rounding errors.