C . We have a common stock which has a dividend which grows at 100%for the first

Question

C. 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. Second, what are the capital gains yield and dividend yield for the first and the second years? PLEASE SHOW WORK AND FORMULAS STEP BY STEP

Explanation / Answer

The question is not that clear ,i just managed to get the answer

Return on equity=ROE=(Net Income/Sales)*(Sales/Assets)*(Assets/Equity)

ROE=(profit margin)*(ATO )*(financial leverage)

as profit margin=Net Income/Sales,ATO =Sales/Assets,financial leverage=Assets/Equity

Thus ROE=.02*3*2=.12

After year 2 the growth rate=ROE*(1- dividend payout ratio)

After year 2 the growth rate=.12*(1-.4)=0.072

During first two years the Debt/Equity=1 as Assets/Equity=2

Thus levered Beta during first two years=2.5*(1+(1-.20)*Debt/Equity)=2.5*(1+(1-.20)*1)

levered Beta during first two years=4.5

Thus cost of equity for first two years=.04+4.5*(.12-.04)=0.4 or 40%

levered Beta after first two years=2.5*(1+(1-.20)*Debt/Equity)=2.5*(1+(1-.20)*(4/16))=3

Thus cost of equity after first two years=.04+3*(.12-.04)=0.28 or 28%

ROE in yr 1=growth rate/(1-.4)=100/.6=166.67%

Dividend in year 1=dividend payout ratio*ROE in yr 1*Equity=.4*1.667*16=10.6688 million

ROE in yr 2=growth rate/(1-.4)=200/.6=333.33%

Dividend in year 2=dividend payout ratio*ROE in yr 2*Equity=.4*3.333*16=21.3312 million

Terminal value in year 2=Dividend in year 2*(1+After year 2 the growth rate)/(cost of equity after first two years-After year 2 the growth rate)=21.3312 million*(1+.072)/(.28-.072)=109.94 million

Stock price in millions=Dividend in year 1/(1+cost of equity first two years)1+Dividend in year 2/(1+cost of equity first two years)2+Terminal value in year 2/(1+cost of equity first two years)2

Stock price in millions=(10.6688 /1.40)+(21.3312 /1.402)+(109.94 /1.402)

Stock price in millions=7.62+66.975=74.595 millions

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