Heww Inc., issued a $50,000, 10 year bond with a stated interest rate of 6%. Assume interest payments are made semi-annually. What is the selling price of the bond if the market rate of interest is 5%? (Round to the nearest dollar.)
To calculate the selling price of the bond, we need to use the present value formula for a bond. The formula is:
Present Value = (C/r) × (1 - (1/(1+r)^n)) + (M/(1+r)^n)
Where:
C = Coupon payment
r = Market interest rate
n = Number of periods (in this case, number of semi-annual periods)
M = Face value of the bond
In this case:
C = ($50,000 × 6%) / 2
r = 5% / 2
n = 10 years × 2
First, let's calculate the coupon payment:
C = ($50,000 × 6%) / 2 = $1,500 per period
Next, let's calculate the number of periods:
n = 10 years × 2 = 20 periods
Now, let's calculate the present value:
PV = ($1,500 / (5% / 2)) × (1 - (1/(1+(5%/2))^20)) + ($50,000 / (1+(5%/2))^20)
To calculate this, you'll need to use a financial calculator or a spreadsheet program like Microsoft Excel. Alternatively, you can use an online present value calculator.
Inputting the values in the formula and performing the calculations, the selling price of the bond is approximately $45,786 (rounded to the nearest dollar).