Vaughn Corporation issues 570000 of 9 bonds due in 11 years

Vaughn Corporation issues $570,000 of 9% bonds, due in 11 years, with interest payable semiannually. At the time of issue, the market rate for such bonds is 10%.

Compute the issue price of the bonds. (Round present value factor calculations to 5 decimal places, e.g. 1.25124 and the final answer to 0 decimal places e.g. 58,971.)

Issue price of the bonds

$

Solution

Present Value of Ordinary Annuity Formula Bond Price = C/k * [ 1 - [ 1 ] ] (1 + i/k)nk i/k + P (1 + i/k)nk Plug In The Variables and Solve Bond Price = 51300/2 * [ 1 - [ 1 ] ] (1 + 0.1000/2)11*2 0.1000/2 + 570000 (1 + 0.1000/2)11*2 Bond Price = 25650.00 * [ 1 - [ 1 ] ] (1 + 0.0500)22 0.0500 + 570000 (1 + 0.0500)22 Bond Price = 25650.00 * [ 1 - [ 1 ] ] 2.925 0.0500 + 570000 2.925 Bond Price = 25650.00 * 1 - 0.3418 0.0500 + 570000 2.925 Bond Price = 25650.00 * 0.6582 0.0500 + 194854.43 Bond Price = 25650.00 * 13.16 + 194854.43 Bond Price = 337631.02 + 194854.43 Bond Price = $532,485.44 Variables C = coupon payment = $51,300.00 (Par Value * Coupon Rate) n = number of years = 11 i = market rate, or required yield = 10.000% = 0.10 k = number of coupon payments in 1 year = 2 P = value at maturity, or par value = 570000