Corporate Finance: Growth Opportunities 2

Growth Opportunities – Lewin Skis, Inc (today) expects to earn $6.25 per share for each of the future operating periods (beginning at time I) if the firm makes no new investments and returns the earnings as dividend as dividends to the shareholders. However, Clint Williams, president and CEO, has discovered an opportunity to retain and invest 20% of the earnings beginning three years from today. This opportunity to invest will continue for each period indefinitely. He expects to earn 11% on made. The firm’s equity discount rate is 13% throughout.

What is the price per share of Lewin Skies, Inc., stock without making the new investment?

P = Dividend/R

P = $6.25/0.13

P = $48.08

If the new investment is expected to be made, per the preceding information, what would the price of the stock be now?

The investment occurs every year in the growth opportunity, so the opportunity is a growing perpetuity. So we first need to find the growth rate. The growth rate is:

g = retention ratio x return on retain earnings

g = 0.20 x 0.11

g = 0.022 or 2.20%

next we need to calculate the NPV of the investment. During year 3, 20% of the earnings will be reinvested. Therefore, $1.25 is invested ($6.25 x 0.20). one year later, the shareholders receive an 11 percent return on the investment, or $0.138 ($1.25 x 0.11), in perpetuity.

The perpetuity formula values that streams as of year 3. Since the investment opportunity will continue indefinitely and growth at 2.2 %, apply the growing perpetuity formula to calculate the NPV of the investment as of year 2. Discount that value back two years to today.

NPVGO = ((investment + return) / R ) / (R – g) / (1+R)²

NPVGO = (-$1.25 + $0.138) / 0.13) / (0.13 – 0.022) / (1.13)²

NPVGO = -$1.39  

The value of the stock is the PV of the firm without making the investment plus the NPV of the investment, or:

P = PV (EPS) + NPVGO

P = $48.08 – 1.39

P = $46.68

Suppose the company could increase the investment in the project by whatever amount it chose. What would the retention ration need to be to make this project attractive?

Zero percent

Reference:  Chapter 9, Corporate Finance Book, Stephen A.Ross, Randolph W.Westerfield and Jeffrey Jaffe, Ninth Edition.

Corporate Finance: Growth Opportunities 1

Growth Opportunities – The Stambaugh Corporation currently has earnings per share of $8.25. The company has no growth and pays out all earnings as dividends. It has a new project which will require an investment of $1.60 per share in one year. The project is only a two – years following the investment by $2.10 and $2.45, respectively. Investors require a 12% return on Stambaugh stock.

what is the value per share of the company’s stock assuming the firm does not undertake the investment opportunity?

P = Dividend / R

P = $8.25 / 0.12

P = $68.75

if the company does undertake the investment, what is the value per share now?

The investment is a one – time investment that creates an increase in EPS for two years. To calculate the new stock price, we need the cash cow price plus the NPVGO.

NPVGO = C₁ / (1+R) + C₂/(1+R)² + C₃/(1+R)³

NPVGO = -$1.60/ 1.12 + $2.10/1.12² +$2.45/1.12³

NPVGO = $1.99

P = $68.75 + $1.99

P = $70.74

again, assume the company undertakes the investment. What will the price per share be four years from today?

 After the project is over, and the earning increase no longer exists, the price of the stock will revert back to $68.75, the value of the company as a cash cow.

Reference:  Chapter 9, Corporate Finance Book, Stephen A.Ross, Randolph W.Westerfield and Jeffrey Jaffe, Ninth Edition.

Corporate Finance: Essay Quiz Finding the Required Return

Finding the Required Return – Juggernaut Satellite Corporation earned $10 million for the fiscal year ending yesterday. The firm also paid out 20% of its earnings as dividend yesterday. The firm will continue to pay out 20% of its earnings as annual, end – of – year dividends. The remaining 80% of earnings is retained by the company for use in projects. The company has 2 million shares of common stock outstanding. The current stock price is $85. The historical return on equity (ROE) of 16% is expected to continue in the future. What is the required rate of return on the stock?

The required return of a stock consist of two components, the capital gains yield and the dividend yield.

R = D₁/P₀ + g

We can find the dividend growth rate by the growth rate equation, or:

g = ROE x b

g = 0.16 x 0.80

g = 0.1280 or 12.80%

This is also the growth rate in dividends. 

Dividend per share = (net income x payout ratio) / share outstanding

Dividend per share = ($10,000,000 x 0.20) / 2,000,000

Dividend per share = $1,00

R = D₁/P₀ + g

R = $1(1 + 0.1280) / $85 + 0.1280

R = 0.1413 or 14.13%

Reference:  Chapter 9, Corporate Finance Book, Stephen A.Ross, Randolph W.Westerfield and Jeffrey Jaffe, Ninth Edition.

Corporate Finance: Nonconstant Dividends & Differential Growth

Nonconstant Dividends – Bucksnort, Inc., has an odd dividend policy. The company has just paid a dividend of $10 per share and has announced that it will increase the dividend by $3 per share for each of the next five years, and then never pay  another dividend. If you require an 11 percent return on the company’s stock, how much will you pay for a share today?

P₀ = $13 /1.11 + $16/1.11² + $19/1.11³ + $22/1.11⁴ +$25/1.11⁵ = $67.92

Differential Growth – Hughes Co. is growing quickly. Dividends are expected to grow at a 25% rate for the next three years, with the growth rate falling off to a constant 7% thereafter. If the required return is 12% and the company just paid a $2.40 dividend, what is the current share price?

With differential dividends, we find the price of the stock when the dividend level off at a constant growth rate, and then find the PV of the future stock price, plus the PV of all dividends during the differential growth period.

The stock begin constant growth in year 4, so we can find the price of the stock in year 3, one year before the constant dividend growth begins as:

P₃ = D₃ (1+g) (R – g) = D₀ (1+g₁)³ (1+g₂)/ (R – g₂) = $2.40 (1.25)³(1.07) / (0.12 – 0.07) = $100.31

 

The price of the stock today is the PV of the first three dividends, plus the PV of the year 3 stock price. The price of stock today will be:

P₀ = $2.40 (1.25)/1.12 + $2.40 (1.25)²/1.12² +$2.40(1.25)³/1.12³ +$100.31/1.12³

P₀ = $80.40

Reference:  Chapter 9, Corporate Finance Book, Stephen A.Ross, Randolph W.Westerfield and Jeffrey Jaffe, Ninth Edition.