Question

Determining the Proceeds from Bond IssuesMadison Corporation is authorized to issue $500,000 of 5-year bonds dated June 30, 2019, with a stated rate of interest of 11%. Interest on the bonds is payable semiannually, and the bonds are sold on June 30, 2019.Required:
Determine the proceeds that the company will receive if it sells the following: 1. The bonds to yield 12%. 2. The bonds to yield 10%.

Answer 1

Answer:

1.

Bond Price = $481599.8724 rounded off to $481599.78

2.

Bond Price = $519304.3373 rounded off to $519304.34

Explanation:

1.

To calculate the price of the bond today, we will use the formula for the price of the bond. We assume that the interest rate provided is stated in annual terms. As the bond is a semi annual bond, the coupon payment, number of periods and semi annual YTM will be,

Coupon Payment (C) = 500000 * 0.11 * 0.5 =  27500

Total periods (n)= 5 * 2 =10

r or YTM = 0.12 * 0.5 = 0.06

The formula to calculate the price of the bonds today is attached.

Bond Price = 27500 * [( 1 - (1+0.06)^-10) / 0.06]  +  500000 / (1+0.06)^10

Bond Price = $481599.8724 rounded off to $481599.78

2.

Coupon Payment (C) = 500000 * 0.11 * 0.5 =  27500

Total periods (n)= 5 * 2 =10

r or YTM = 0.10 * 0.5 = 0.05

The formula to calculate the price of the bonds today is attached.

Bond Price = 27500 * [( 1 - (1+0.05)^-10) / 0.05]  +  500000 / (1+0.05)^10

Bond Price = $519304.3373 rounded off to $519304.34