Asked by Leyla Jackson on Jun 18, 2024
Verified
The following information is available concerning a firm's capital: Debt : Bonds with a face value of $1000 and an initial 20-year term were issued five years ago with a coupon rate of 8% paying semiannually. Today these bonds are selling for $846.30.
Preferred stock : Preferred stock that pays an annual dividend of $9.50 is trading at $79.16.
Common equity : The stock is selling for $22.50 per share. An annual dividend of $1.70 was just paid and is expected to grow indefinitely at 6%.
Target capital structure : The firm's target capital structure is of 30% debt, 20% preferred stock, and 50% equity.
The firm can issue any type of security without paying floatation costs. The combined federal and state tax rate is 40%. Calculate the firm's WACC based on its target capital structure.
A) 9.4%
B) 11.2%
C) 8.2%
D) 12.4%
Target Capital Structure
The optimal mix of debt, equity, and other financing sources a company aims to achieve for financing its operations and growth.
Coupon Rate
The annual interest rate paid on a bond, expressed as a percentage of the face value, and received by the bondholders at specified intervals.
Flotation Costs
Expenses incurred by a company when it issues new securities, including underwriting fees, legal fees, and registration fees.
- Gain an understanding of the process involved in determining the weighted average cost of capital (WACC) and its constituent parts.
- Gain insight into how taxes influence the elements of cost of capital.
Verified Answer
DU
Daniella UghocJun 20, 2024
Final Answer :
B
Explanation :
1) Cost of debt:
Since the bonds are currently selling for $846.30 whereas they were issued at $1000, it is assumed that the market rate is now different from the coupon rate. Therefore, we need to calculate the current yield-to-maturity as the cost of debt.
PV = -$846.30, FV = $1000, PMT = $40 (8% coupon rate, semi-annual), n = 30-5=25*2 = 50 (semi-annual periods)
Solving for i (yield-to-maturity):
PV = FV / (1+i)^n + PMT * [(1 - 1 / (1+i)^n ) / i]
i = 4%
After considering the tax deductibility, the after-tax cost of debt is:
After-tax cost of debt = Yield-to-maturity * (1 - tax rate)
= 4% * (1 - 0.4)
= 2.4%
2) Cost of preferred stock:
Cost of preferred stock = Preferred dividend / Net issuing price
Net issuing price = $79.16 * (1 - 0.4) = $47.50 ($79.16 is before-tax price)
Cost of preferred stock = $9.50 / $47.50 = 20%
3) Cost of equity:
Cost of equity (using dividend growth model) = (Dividend / Current stock price) + Growth rate of dividend
Growth rate of dividend = 6%
Cost of equity = ($1.70 * (1+0.06)) / $22.50 + 0.06
= 13.2%
4) Weighted average cost of capital (WACC):
WACC = (Weight of debt * cost of debt) + (Weight of preferred stock * cost of preferred stock) + (Weight of equity * cost of equity)
= (0.3 * 2.4%) + (0.2 * 20%) + (0.5 * 13.2%)
= 11.2%
Since the bonds are currently selling for $846.30 whereas they were issued at $1000, it is assumed that the market rate is now different from the coupon rate. Therefore, we need to calculate the current yield-to-maturity as the cost of debt.
PV = -$846.30, FV = $1000, PMT = $40 (8% coupon rate, semi-annual), n = 30-5=25*2 = 50 (semi-annual periods)
Solving for i (yield-to-maturity):
PV = FV / (1+i)^n + PMT * [(1 - 1 / (1+i)^n ) / i]
i = 4%
After considering the tax deductibility, the after-tax cost of debt is:
After-tax cost of debt = Yield-to-maturity * (1 - tax rate)
= 4% * (1 - 0.4)
= 2.4%
2) Cost of preferred stock:
Cost of preferred stock = Preferred dividend / Net issuing price
Net issuing price = $79.16 * (1 - 0.4) = $47.50 ($79.16 is before-tax price)
Cost of preferred stock = $9.50 / $47.50 = 20%
3) Cost of equity:
Cost of equity (using dividend growth model) = (Dividend / Current stock price) + Growth rate of dividend
Growth rate of dividend = 6%
Cost of equity = ($1.70 * (1+0.06)) / $22.50 + 0.06
= 13.2%
4) Weighted average cost of capital (WACC):
WACC = (Weight of debt * cost of debt) + (Weight of preferred stock * cost of preferred stock) + (Weight of equity * cost of equity)
= (0.3 * 2.4%) + (0.2 * 20%) + (0.5 * 13.2%)
= 11.2%
Learning Objectives
- Gain an understanding of the process involved in determining the weighted average cost of capital (WACC) and its constituent parts.
- Gain insight into how taxes influence the elements of cost of capital.