Question
In: Accounting
On January 1, 2018, bonds with a face value of $ 79,000 were sold. The bonds...
On January 1, 2018, bonds with a face value of $ 79,000 were sold.
The bonds mature on January 1, 2028. The face interest rate is
8%. The bonds pay interest semiannually on July 1 and January 1.
The market rate of interest is 12%. What is the market price of
the bonds on January 1, 2018? The present value of $1 for 20
periods at 6% is 0.312. The present value of an ordinary annuity
of $1 for 20 periods at 6% is 11.47. The present value of $1 for
20 periods at 4% is 0.456. The present value of an ordinary
annuity of $1 for 20 periods at 4% is 13.59. (Round your final
answer to the nearest dollar.)
A.79,000
B.82,160
C.60,893
D.78,968
Solutions
Expert Solution
Correct answer-----------(C) $60,893
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 | $ 79,000 | ||
| Market Rate | 12.00% | 6.00% | Term (in years) | 10 | |
| Coupon Rate | 8.00% | 4.00% | Total no. of interest payments | 20 |
| Calculation of Issue price of Bond | ||||||||
| Bond Face Value | Market Interest rate (applicable for period/term) | |||||||
| PV of | $ 79,000 | at | 6.00% | Interest rate for | 20 | term payments | ||
| PV of $1 | 0.31180 | |||||||
| PV of | $ 79,000 | = | $ 79,000 | x | 0.31200 | = | $ 24,648 | A |
| Interest payable per term | at | 4.00% | on | $ 79,000 | ||||
| Interest payable per term | $ 3,160 | |||||||
| PVAF of 1$ | for | 6.00% | Interest rate for | 20 | term payments | |||
| PVAF of 1$ | 11.46992 | |||||||
| PV of Interest payments | = | $ 3,160.00 | x | 11.47000 | = | $ 36,245 | B | |
| Bond Value (A+B) | $ 60,893 |
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