Question

There is a firm which reinvests its profits back in itself. Consequently, it does not distribute any of its profit to the owners for the first 5 years. Afterward, it begins paying $6 per share for the 6th year.

That rises by 200% for the 7^th year and by 100% for the 8^th. Beyond the 8^th year, it grows perpetually at a constant rate. Its dividend payout ratio is .6

Its D/E (debt-to-equity) is 50/50

its tax rate is .2

and its unlevered beta is 1

The net profit margin is .05

The asset turnover ratio is 2

The market premium is .04, and the risk free rate is .02

If the information for the last three sentences is applying to year 9,

compute the price of the company. (show your work)

Answer 1

Dividends in the 6^th year = $6

Dividends in the 7^th year = $6*(100%+200%) = $18 (jumps by 200%, so impact is thrice from the normal)

Dividends in the 8^th year = $18*(100% + 100%) = $36 (jumps by 100%, so impact is double from the normal)

Dividends / Earnings = Dividend Payout Ratio

Or, Earnings = $36/0.6 = $60

Net Profit Margin = Net Earnings/ Sales*100

Or, 0.05 = $60/sales

Or, Sales = $1200

Asset Turnover = Sales/ Net Assets

Net Assets = $1200/2= $600

Return on Equity = Net Earnings/ Total Equity

Again (Debt: Equity) is (50:50) so if Total Assets is $600, then equity is $600*50% = $300

Return on Equity = $60/$300*100= 20%

Again Growth for the perpetual years = Return on equity* retention ratio

Or, Retention Ratio = 1- Dividend Payout Ratio = 1-0.6= 0.40

Growth for the perpetual years = 0.2*0.40= 0.08= 8%

Again Cost of Equity = Risk free rate + Beta (Levered)* Market Risk Premium

Beta Levered = Beta Unlevered * [1+ Debt/ Equity* (1-tax)]

Beta Unlevered= 1

Debt/ Equity = 50/50

Tax= 0.20

Beta Levered = 1* [1+1*0.8] = 1.80

Cost of Equity = 0.02 + 1.80*0.04= 0.092= 9.2%

Price of the share = Dividends in the 6^th year/ (1+ cost of equity) ^ 6 + Dividends in the 7^th year/ (1+ cost of equity) ^ 7 + = Dividends in the 8^th year/ (1+ cost of equity) ^ 8 + Dividends in the 8^th year/ (cost of equity – perpetual growth) * 1/ (1+cost of equity) ^8

Or, Price = $6/ (1.092) ^ 6 + $18/ (1.092) ^7 + $36/ (1.092) ^ 8 + $36/ (0.092-0.08)* 1/ (1.092) ^8

Or, Price = $3.538 + $9.721 + $17.804 + $1483.70= $1514.75

Price of the Company is $1514.75