1. What is the market interest rate on XYZ’s debt and its component cost of debt?
Coupon rate 12%
Coupons per year 2
Years to maturity 15
Price $1,153.72
Face value $1,000
Tax rate 40%
Market Interest Rate =
Cost of Debt =
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. What is the market interest rate on XYZ’s debt and its component cost of debt?
Coupon rate
12%
Coupons per year
2
Years to maturity
15
Price
$1,153.72
Face value
$1,000
Tax rate
40%
Market Interest Rate =
Cost of Debt =
To determine the market interest rate on XYZ's debt, you can use the formula for the present value of a bond:
PV = C * (1 - (1/ (1+r)^t))/r + F / (1+r)^t
Where:
PV = Present value of the bond (Price in this case)
C = Coupon payment (Coupon rate * Face value)
r = Market interest rate (also known as the required return or yield to maturity)
t = Years to maturity
F = Face value of the bond
Given the following values:
Coupon rate = 12%
Coupons per year = 2
Years to maturity = 15
Price = $1,153.72
Face value = $1,000
We can calculate the coupon payment (C) as follows:
C = Coupon rate * Face value
C = 12% * $1,000
C = $120
Now, substituting the values into the present value formula, we can solve for the market interest rate (r):
$1,153.72 = $120 * (1 - (1/(1+r)^15))/r + $1,000 / (1+r)^15
To solve this equation, you can use numerical methods or financial calculators/software to find the value of r that satisfies the equation. This will give you the market interest rate on XYZ's debt.
The cost of debt is calculated as the effective interest rate that XYZ pays on its debt after considering the tax advantage of interest expense. To find the cost of debt, you need to use the after-tax cost of debt formula:
Cost of Debt = Market Interest Rate * (1 - Tax Rate)
Given that the tax rate is 40% (0.40), you can substitute the market interest rate you calculated earlier into the formula to find the cost of debt.