Problem 10-15 WACC and Cost of Common Equity Kahn Inc. has a target capital stru

Question

Problem 10-15
WACC and Cost of Common Equity

Kahn Inc. has a target capital structure of 45% common equity and 55% debt to fund its $10 billion in operating assets. Furthermore, Kahn Inc. has a WACC of 14%, a before-tax cost of debt of 9%, and a tax rate of 40%. The company's retained earnings are adequate to provide the common equity portion of its capital budget. Its expected dividend next year (D1) is $4 and the current stock price is $28.

What is the company's expected growth rate? Round your answer to two decimal places at the end of the calculations.

If the firm's net income is expected to be $1.6 billion, what portion of its net income is the firm expected to pay out as dividends? (Hint: Refer to Equation below.)

Growth rate = (1 - Payout ratio)ROE

Round your answer to two decimal places at the end of the calculations.

Explanation / Answer

Part A)

Step 1: Calculate the Cost of Equity:

The cost of equity can be calculated with the use of information provided for WACC, cost of debt, weight of debt and weight of equity. We will use the formula for WACC to arrive at the cost of equity. The formula for WACC is given below:

WACC = After-Tax Cost of Debt*Weight of Debt + Cost of Equity*Weight of Equity

Here, WACC = 14%, After-Tax Cost of Debt = 9%*(1-40%) = 5.40%, Weight of Debt = 55% and Weight of Equity = 45%

Substituting these values in the above formula, we can calculate the cost of equity

14% = 5.40%*55% + Cost of Equity*45%

Rearranging Values, we get,

Cost of Equity = (14% - 2.97%)/45% = 24.51%

_________

Step 2: Calculate the Growth Rate:

The growth rate will be calculated with the use of information for d1, current stock price and cost of equity from step 1. The formula that can be used to arrive at the growth rate is given below:

Growth Rate = Cost of Equity - D1/Current Stock Price

or

Growth Rate = 24.51% - 4/28 = 10.23%

__________

Part B)

To calculate the dividend payout ratio, we will have to calculate the ROE first with the use of following formula:

ROE = Net Income/Equity = 1.6/(10*45%) = 35.56%

Using this value of ROE and Growth Rate calculated above in the formula provided in the question, we get,

10.23% = (1-Payout Ratio)*35.56%

Payout Ratio =10.23% - 35.56 - 1 = 71.24%

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