In: Accounting
On January 1, 2020, Bonita Industries issued eight-year bonds
with a face value of $5750000 and a stated interest rate of 10%,
payable semiannually on June 30 and December 31. The bonds were
sold to yield 12%. Table values are:
Present value of 1 for 8 periods at 10% | 0.467 | ||
Present value of 1 for 8 periods at 12% | 0.404 | ||
Present value of 1 for 16 periods at 5% | 0.458 | ||
Present value of 1 for 16 periods at 6% | 0.394 | ||
Present value of annuity for 8 periods at 10% | 5.335 | ||
Present value of annuity for 8 periods at 12% | 4.968 | ||
Present value of annuity for 16 periods at 5% | 10.838 | ||
Present value of annuity for 16 periods at 6% | 10.106 |
The issue price of the bonds is
Answer--------------The issue price of the bonds is $5,170,975
Working
Bonds issue price is calculated by ADDING the: |
Discounted face value of bonds payable at market rate of interest, and |
Discounted Interest payments amount (during the lifetime) at market rate of interest. |
.
Annual Rate | Applicable rate | Face Value | $ 5,750,000 | ||
Market Rate | 12.00% | 6.00% | Term (in years) | 8 | |
Coupon Rate | 10.00% | 5.00% | Total no. of interest payments | 16 |
.
Calculation of Issue price of Bond | ||||||||
Bond Face Value | Market Interest rate (applicable for period/term) | |||||||
PV of | $ 5,750,000 | at | 6.00% | Interest rate for | 16 | term payments | ||
PV of $1 | 0.39365 | |||||||
PV of | $ 5,750,000 | = | $ 5,750,000 | x | 0.394 | = | $ 2,265,500 | A |
Interest payable per term | at | 5.00% | on | $ 5,750,000 | ||||
Interest payable per term | $ 287,500 | |||||||
PVAF of 1$ | for | 6.00% | Interest rate for | 16 | term payments | |||
PVAF of 1$ | 10.10590 | |||||||
PV of Interest payments | = | $ 287,500 | x | 10.106 | = | $ 2,905,475 | B | |
Bond Value (A+B) | $ 5,170,975 |