Assume the following for a growth company: Today’s Share price P 0 = $125 Expect

Question

Assume the following for a growth company:

Today’s Share price

P0 =

$125

Expected Dividends per share

D1 =

$1

Expected Earnings per share

EPS1 =

$5

Shareholders’ Expected Growth

g =

15%

Steady state cost of equity for similar company

Ke(ss) =

10%.

Using the Gordon growth model determine the firm’s cost of equity, ke:

Demonstrate the company is a growth company:

Present Value of Growth Opportunities

Step 1: Calculate steady state P/E

P/E = 1/Ke(ss) (above)

Step 2: Multiply steady state P/E by EPS (above), which equals the share price at Steady State

Steady state P/E x EPS = steady state share price

Step 3: Compare current share price to steady state share price

Current share price – steady state share price = growth opportunity

Steady-state P/E

Step 1: Compare current P/E to Steady-state P/E

Current P/E = Price per share/earnings per share

Steady state P/E = 1/Ke(ss)

Differential = growth opportunity

Today’s Share price

P0 =

$125

Expected Dividends per share

D1 =

$1

Expected Earnings per share

EPS1 =

$5

Shareholders’ Expected Growth

g =

15%

Steady state cost of equity for similar company

Ke(ss) =

10%.

Explanation / Answer

Cost of Equity =R Growth rate=g=15%=0.15 P0=Current Price=D1/(R-g) R=(D1/P0)+g D1=$1, P0=$125 R=(1/125)+0.15= 0.158 Using Gordon growth model, Cost of Equity 15.80% P/E=1/0.1=10 Earning per share=$5 P=(P/E)*E=10*$5=$50 Steady state share price=$50 Current Share Price=P0=$125 Growth Opportunity=P0-P=125-50=$75 Current P/E=125/5=25 Steady State P/E=1/0.1=10 Growth Opportunity=25-10=5

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