Question

Kahn Inc. has a target capital structure of 55% common equity and 45% debt to fund its $11 billion in operating assets. Furthermore, Kahn Inc. has a WACC of 15%, a before-tax cost of debt of 8%, 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 $4, and the current stock price is $34. 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 $1.8 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

SOLUTION:

THE VALUES PROVIDED IN THE QUESTION ARE AS FOLLOWS :

WACC =15 % or 0.15

Operating Assets = $ 11 billion

Net income = $ 1.8 billion

( We )Common Equity = 55 % or 0.55

(Wd )Debt = 45 % or 0.45

(Kd )Before tax cost of debt = 8 % or 0.08

Tax Rate =25 % or 0.25

Expected dividend (D1 )= $ 4

Current stock price ( Po ) = $ 34

( a )The formula to calculate growth rate is as follows

As Per Gorden growth model ,

Current stock price ( Po ) = Expected dividend (D1 )/ cost of equity (Ke)- growth rate ( g )

The formula to calculate cost of equity (Ke)

As per WACC,

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

Putting the values in the WACC formula provided in the question,

0.15 =0.45 *0.08 (1- 0.25 ) + 0.55 * ( Ke)

0.15 = 0.45 *0.06 +0.55 *( Ke)

0.15 =0.027 +0.55 *( Ke)

0.15 -0.027 =0.55 *( Ke)

0.123 =0.55 *( Ke)

Cost of equity ( Ke) =0.123/0.55

Cost of equity ( Ke) =0.2236 or 22.36 %

Putting the values in the Gorden growth Model,

Current stock price ( Po ) = Expected dividend (D1 )/ cost of equity (Ke)- growth rate ( g )

$ 34 = $4 /0.2236 –g

$34 (0.2236 – g ) = $ 4

$7.6024 - $ 34 g = $ 4

$7.6024- $ 4 = $ 34 g

$ 3.6024 = $ 34 g

Growth rate ( g ) =0.1060 or 10.60 %

(a ) Hence , Required Answer i.e Growth Rate is 10.60 %

(b ) The formula to calculate common equity is as follows :

Common equity = ( We )Common Equity * Operating Assets

Common equity =0.55 *$ 11 billion

Common equity = $ 6.05 billion

The formula to calculate the return on equity is as follows :

Return on equity = Net Income / common equity

Return on equity = $ 1.8 billion /$ 6.05 billion

Return on equity =0.2975 or 29.75 %

The Formula to calculate dividend pay out Ratio ia as follows :

Growth Rate = ROE * ( 1 – Dividend pay out ratio )

0.1060 = 0.2975 * ( 1- Dividend Pay out ratio )

0.1060/0.2975 = 1- Dividend pay out ratio

0.3563= 1- Dividend pay out ratio

Dividend pay out ratio =1-0.3563

Dividend pay out ratio =0.6437 or 64.37 %

(a ) Hence , Required Answer i.e Growth Rate is 10.60 %

(b) Hence , Required Answer i.e Dividend pay out ratio =0.6437 or 64.37 %