Question

On January 1, 2017, Ellison Co. issued eight-year bonds with a face value of $6,000,000 and a stated interest rate of 6%, payable semiannually on June 30 and December 31. The bonds were sold to yield 8%.
Present value of 1 for 8 periods at 6% 0.627
Present value of 1 for 8 periods at 8% 0.540
Present value of 1 for 16 periods at 3% 0.623
Present value of 1 for 16 periods at 4% 0.534
Present value of annuity for 8 periods at 6% 6.210
Present value of annuity for 8 periods at 8% 5.747
Present value of annuity for 16 periods at 3% 12.561
Present value of annuity for 16 periods at 4% 11.652

The issue price of the bonds is:_________

a. $5,337,360.
b. $5,997,600.
c. $5,301,360.
d. $5,308,920.

Answer 1

Answer:

Bond Price = $5,300,862.264 rounded off to $5,300,862.26

Explanation:

To calculate the price of the bond today, we will use the formula for the price of the bond. Assuming the bond is an annual bond, the semi coupon payment, number of periods and semi annual YTM will be,

Coupon Payment (C) = 6,000,000 * 0.06 * 6/12 = 180 ,000

Total periods (n) = 8 * 2 = 16

r or YTM = 0.08 * 6/12 = 0.04 or 4%

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

Bond Price = 180000 * [( 1 - (1+0.04)^-16) / 0.04]  + 6000000 / (1+0.04)^16

Bond Price = $5,300,862.264 rounded off to $5,300,862.26