We have a common stock which has a dividend which grows at 100%for the first 1 y

Question

We have a common stock which has a dividend which grows at 100%for the first 1 year and 200% for the next 1 year. After that it rises more reasonably, but we only know it indirectly. Net profit margin, ATO and financial leverage are .02, 3 and 2 respectively. The dividend payout ratio is .4. The risk free rate, market rate and bheta unlevered is .04, .12 and 2.5 respectively. The tax rate debt and equity are 20%, $4 million and $16 million respectively. First, compute the price of the stock.

PLEASE SHOW IN DETAIL AND SHOW FORMULAS

Explanation / Answer

Beta levered=beta unlevered*(1+(1-t)*D/E)=2.5*(1+(1-20%)*4/16)=3

Required return or cost of equity=risk free+beta*(market return-risk free)=4%+3*(12%-4%)=28%

Assuming here Financial Leverage means Equity Multiplier or Total Assets/Equity

Return on Equity=Net profit margin*Asset Turonver*Financial Leverage=2%*3*2=12%

Growth rate=Return on Equity*(1-Dividend Payout Ratio)=12%*(1-40%)=7.2%

Return on Equity=Net Profit/Equity

hence, 12%=Net Profit/16

So, Net Profit=1.92 million

Dividends=1.92*40%=0.768 million

Market Cap=0.768*(1+100%)/1.28+0.768*(1+200%)/1.28^2+Horizon Value/1.28^2

Horizon Value=0.768*(1+200%)*(1+7.2%)/(28%-7.2%)=11.8744

Hence, Market Cap=0.768*(1+100%)/1.28+0.768*(1+200%)/1.28^2+11.8744/1.28^2=9.853 million

So, Price=Market Cap/Number of shares outstanding

Plug in the shares outstanding and you will get the price of the stock

ALTERNATIVELY, we can use the following method if number of shares is not known

Equity=16
Return on Equity=Net profit margin*ATO*Financial Levergae=2%*3*2=12%
Net Income=Equity*Return on Equity

Hence, Net Income=12%*16=1.92
Current Dividend=Net Income*Dividend Payout Ratio=0.4*1.92=0.768
Growth rate=Return on Equity*(1-dividend payout)=12%*(1-0.4)=7.2%

Beta levered=beta unlevered*(1+(1-t)*D/E)=2.5*(1+(1-20%)*4/16)=3
Hence, required return=4%+3*(12%-4%)=28%

So, Price of stock=0.768*(1+100%)/1.28+0.768*(1+100%)*(1+200%)/1.28^2+0.768*(1+100%)*(1+200%)*(1+7.2%)/((28%-7.2%)*1.28^2)
=18.50769

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