Question

Step by step of how to:

Calculate a $20 million of 10-year bond issuance price when the stated rate is 10% and the market rate is 12%

Answer 1

Calculate a $20 million of 10-year bond issuance price when the stated rate is 10% and the market rate is 12%

Issue price of bond = Present value of semi-annual coupon payments + Present value of face value of bond

Semi-annual coupon payment = $20,000,000 * 10% * ½ = $1,000,000

Number of semi-annual coupon payments in 10 years = 10 * 2 = 20

Semi-annual market rate = 12%/2 = 6% = 0.06

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

Present value of semi-annual coupon payments = $1,000,000*(1-1.06^-20)/0.06 = $11,469,921.22

Present value of face value of bond = $20,000,000/1.06²⁰ = $6,236,094.54

Issue price of bond = $11,469,921.22 + $6,236,094.54 = $17,706,015.76