Question

Kahn Inc. has a target capital structure of 55% common equity and 45% debt to fund its $12 billion in operating assets. Furthermore, Kahn Inc. has a WACC of 14%, a before-tax cost of debt of 12%, and a tax rate of 25%. The company's retained earnings are adequate to provide the common equity portion of its capital budget. Its expected dividend next year (D1) is $3, and the current stock price is $32. a. What is the company's expected growth rate? Do not round intermediate calculations. Round your answer to two decimal places. % b. If the firm's net income is expected to be $1.3 billion, what portion of its net income is the firm expected to pay out as dividends? Do not round intermediate calculations. Round your answer to two decimal places. (Hint: Refer to Equation below.) Growth rate = (1 - Payout ratio) ROE

Answer 1

Given:

Target Capital Structure

Common Equity

55%

Debt

45%

Weighted average cost of capital (WACC)

14%

Before tax cost of debt(kd)

12%

Tax rate (t)

25%

Expected dividend next year (D1)

$3

Current stock price (P0)

$32

Solution:

a.

8.72%

b.

55.74%

a) Growth rate (g)

To find growht rate, first find cost of equity from WACC

WACC = We*Ke + Wd*Kd(1-t)

Where,

WACC (Weighted average cost of capital) = 14%

We (Weight of equity)            = 55%

Ke   (Cost of equity)

Wd (Weight of debt)                = 45%

Kd (Before tax cost of debt) = 12%

t    (Tax rate)                                = 25%

Now solve the above equation

WACC = We*Ke + Wd*Kd(1-t)

or, 14% = (55%)(Ke ) + (45%)(12%)(1-25%)

or, 0.14 = (0.55)(Ke ) + (0.45)(0.12)(1-0.25)

or, 0.14 = (0.55)(Ke ) + (0.45)(0.12)(0.75)

or, 0.14 = (0.55)(Ke ) + 0.0405

or, 0.14 - 0.0405 = (0.55)(Ke )

or, 0.0995 = (0.55)(Ke )

or, 0.0995/0.55 = Ke

or, Ke = 0.1809

or, Ke = 18.09%

Now that we have the cost of equity, we can solve the growth by using the Gordon Growth Model.

g = Ke - D1/P0

Where:

Ke = Required return or cost of common equity

D1 = Expected dividend next year

P0 = Current Price per share

g = Constant growth rate

Now

g = Ke - D1/P0

g = 0.1809 - $3/$32

g = 0.1809 - 0.09375

g = 0.08715

g = 8.72%

b) Dividend payout ratio

Growth rate(g) = (1 - Payout ratio)ROE

Where,

ROE = Net income / Common equity

ROE = Net income / Common equity

ROE = {$1,300,000,000/($12,000,000,000*55%)}

ROE = 0.19696969

ROE = 19.70%

Now solving for dividend payout ratio

Growth rate(g) = (1 - Payout ratio)ROE

or,   8.72% = (1 - Payout ratio)19.70%

or,   8.72% / 19.70% = (1 - Payout ratio)

or,   0.4426 = (1 - Payout ratio)

or,   Payout ratio = 1 - 0.4426

or,   Payout ratio = 0.5574

or,   Payout ratio = 55.74%