A bond payable is dated January 1, 2016, and is issued on that date. The face va
ID: 1174626 • Letter: A
Question
A bond payable is dated January 1, 2016, and is issued on that date. The face value of the bond is $120,000, and the face rate of interest is 6%. The bond pays interest semiannually. The bond will mature in five years. Round your PV/FV factors to five decimal places and final answer to the nearest dollar.
1. What will be the issue price of the bond if the market rate of interest is 6% at the time of issuance?
$
2. What will be the issue price of the bond if the market rate of interest is 10% at the time of issuance?
$
Explanation / Answer
The face rate of Interest is also known as the Cupon rate.
1. Issue Price of the bond if the market rate of interest is 6%
Price of Bond = Cupon Amount * Present Value of Annuity Factor (r,n) + Redemption Amount * Present Value of Interest Factor (r,n)
Where Cupon Amount = $120,000 * 6% * 1/2
= $3600
Why did we multiply 1/2?
- Since compounding is Semi Annual
Redemption Amount = $120,000
r is the Yield to Maturity (YTM) or the market rate of interest
Yield for 6 months = 6/2
r = 3%
n is the remaining maturity
n = 5 * 2
n = 10
(Semi Annual Compounding)
Present Value of Annuity Factor (3% ,10) = 8.53020
Present Value of Interest Factor (3% ,10) = 0.74409
Therefore
Bond Price =$3,600* 8.53020 + $120,000 *0.74409
Bond Price = $30,708.72 + 89,290.8
Bond Price = 119,999.52
Rounding to nearest dollar
Bond Price = $120,000
2. Issue Price of the bond if the market rate of interest is 10%
Price of Bond = Cupon Amount * Present Value of Annuity Factor (r,n) + Redemption Amount * Present Value of Interest Factor (r,n)
Where Cupon Amount = $120,000 * 6% * 1/2
= $3600
Why did we multiply 1/2?
- Since compounding is Semi Annual
Redemption Amount = $120,000
r is the Yield to Maturity (YTM) or the market rate of interest
Yield for 6 months = 10/2
r = 5%
n is the remaining maturity
n = 5 * 2
n = 10
(Semi Annual Compounding)
Present Value of Annuity Factor (5% ,10) = 7.72173
Present Value of Interest Factor (5% ,10) = 0.61391
Therefore
Bond Price =$3,600* 7.72173 + $120,000 *0.61391
Bond Price =$27,798.228 +$73,669.2
Bond Price = 101,467.428
Rounding to nearest dollar
Bond Price = $101,467
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