Question

video equipmet. To hance its operations, Nnder Co. issued $25,000,000 of five-year, 7% bonds, with interest payable seminnally, at a market teeth") ๒terest rate of 9%. Determine the present value of the bonds payable, using the present value tables in Exhibit 8 and Exhibit 10. Round to the nearest dollar

Answer 1

Face value of bond = $25,000,000

Coupon rate = 7%

Semi annual coupon amount = $25,000,000 * 7% * ½ = $875,000

Effective interest rate = 9%

Semi-annual effective interest rate = r = 9%/2 = 4.5% = 0.045

Number of semi-annual coupon payments = n = 5 years * 2 = 10

Present value of annuity = Annuity amount*{1-(1+r)^-n}/r

Present value of semi-annual coupon payments = $875,000*(1-1.045^-10)/0.045 = $6,923,628.40

Present value of face value of bond = $25,000,000/1.045¹⁰ = $16,098,192.05

Present value of bond = Present value of coupon payments + Present value of face value

Present value of bond payable = $6,923,628.40 + $16,098,192.05 = $23,021,820.46 = $23,021,820