Avicorp has a $14.3 million debt issue outstanding with a 6.1% coupon rate. The debt has semi-annual coupons. The next coupon is due in six months and the debt matures in five years it is currently priced at 95% of par value
a) What is Avicorp's pre-tax cost of debt? Note: compute the effective annual return
b)If Avicorp faces a 40% tax rate, what is its after-tax cost of debt?
For some reason I cannot begin to figure out the YTM? Please Help, Thank You!
3.60
Avicorp has a $10 million debt issue outstanding, with a 6% coupon rate. The debt has semi-annual coupons, the next coupon is due in 6 months, and the debt matures on 5 years. It is currently prices at 95% of its $1,000 face value. What is Avicorp’s cost of debt?
6.33%
To calculate the Yield to Maturity (YTM), we need to use the present value formula and solve for the discount rate (YTM) that makes the present value of the future cash flows equal to the current price.
In this case, we have a bond with a face value of $14.3 million, a coupon rate of 6.1%, semi-annual coupons, a maturity of 5 years, and is currently priced at 95% of par value.
To calculate the YTM, follow these steps:
Step 1: Calculate the semi-annual coupon payment
The coupon payment can be calculated as the coupon rate multiplied by the face value divided by the number of coupons per year:
Coupon payment = (Coupon rate * Face value) / Number of coupons per year
Coupon payment = (6.1% * $14.3 million) / 2
Coupon payment = $439,150
Step 2: Calculate the number of periods
Since the coupons are paid semi-annually and the bond has a maturity of 5 years, the total number of periods is 2 * 5 = 10.
Step 3: Calculate the present value of the coupons
We need to discount each coupon payment back to its present value using the YTM:
Present value of the coupons = Coupon payment / (1 + YTM/2) + Coupon payment / (1 + YTM/2)^2 + ... + Coupon payment / (1 + YTM/2)^10
Step 4: Calculate the present value of the face value
We also need to discount the face value back to its present value using the YTM:
Present value of the face value = Face value / (1 + YTM/2)^10
Step 5: Calculate the current price
The current price is given as 95% of the face value, so:
Current price = 0.95 * Face value
Step 6: Set up the YTM equation
We want the sum of the present value of the coupons and the present value of the face value to equal the current price:
Present value of the coupons + Present value of the face value = Current price
Step 7: Solve for YTM
We need to solve the YTM equation from Step 6 to find the YTM that satisfies the equation. This requires an iterative process or a financial calculator, solver, or spreadsheet software. You can use the Newton-Raphson method or built-in functions like Excel's RATE().
Once you calculate the YTM, you can use it to answer parts (a) and (b) of the question.
(a) What is Avicorp's pre-tax cost of debt?
The pre-tax cost of debt is equal to the YTM, which represents the effective annual return.
(b) If Avicorp faces a 40% tax rate, what is its after-tax cost of debt?
To calculate the after-tax cost of debt, you need to multiply the pre-tax cost of debt by (1 - tax rate).
I hope this helps you figure out how to calculate the YTM and the subsequent cost of debt.