Question

On January 1, 2020, Smith 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 40% 11.652


a. The present value of the interest is:_________
b. The present value of the principal is:_________
c. The price of bond is:_________

Answer 1

a. The present value of the interest is:_________

PV of coupon payments = coupon x PV annuity factor, 4%, 16 periods = $180,000 x 11.652 = $2,097,360

b. The present value of the principal is:_________

PV of face value = face value x PV 4%, 16 periods = $6,000,000 x 0.534 = $3,204,000

c. The price of bond is:_________

market price of the bonds = $2,097,360 + $3,204,000 = $5,301,360

since the market rate is higher than the coupon rate, the bonds will always be sold at a discount