Determining the present value of bonds payable Interest rates determine the pres
ID: 2461925 • Letter: D
Question
Determining the present value of bonds payable Interest rates determine the present value of future amounts. (Round all the numbers to the nearest whole dollar.) Requirements 1. Determine the present value of seven-year bonds payable with face value if $91,000 and stated interest of 14% paid semiannually. The matter rate of interest is 14% at issuance. 2. Same bonds payable as in Requirement 1, but the market interest rate is 16%. 3. Same bonds payable as in Requirement 1, but the market interest rate is 12%.Explanation / Answer
Solution:
Some basic rules which should be remembered with regard to bonds are:
Requirement 1: Determine the present value of seven-year bonds payable with face value if $91,000 and stated interest of 14% paid semi-annually. The market rate of interest is 14% at issuance.
Answer:
In this case Market rate of interest (i.e. Required Rate of Return) equals to coupon rate, the bond sells at par value.
It means Present Value of Bonds = Par Value of Bond = $91,000
We can also calculated by using following formula:
Coupon Rate = 14% p.a.
Semi-Annual Coupon Interest = $91,000 x 14% x ½ = $6,370
Number of interest payment = 7 years x 2 = 14
Market Rate of Return = 14% p.a. or 7% semi-annually
Present Value of Bond = Coupon Interest x PVIFA(7%, 14) + Maturity Value x PVIF (7%, 14)
= ($6,370 x 8.745468) + ($91,000 x 0.387817)
= $55,709 + $35,291
= $91,000
2. Same bonds payable as in Requirement 1, but the market interest rate is 16%.
Solution
Market Rate of Return = 16% p.a. or 8% semi-annually
Present Value of Bond = Coupon Interest x PVIFA (8%, 14) + Maturity Value x PVIF (8%, 14)
= ($6,370 x 8.2442) + ($91,000 x 0.34046)
= $52,516 + $30,982
= $83,498
3. Same bonds payable as in Requirement 1, but the market interest rate is 12%.
Market Rate of Return = 12% p.a. or 6% semi-annually
Present Value of Bond = Coupon Interest x PVIFA (6%, 14) + Maturity Value x PVIF (6%, 14)
= ($6,370 x 9.29498) + ($91,000 x 0.4423)
= $59,209 + $40,249
= $99,458
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