Question

A stock has a \beta of 1, and the expected market return this year is 2.93%, and the current risk-free rate is 1.14%. The firm just recently released a dividend for $1.94 per share, and it expects that dividends will continue to grow at the sustainable growth rate for the future. Given that firm equity was $508,500.00 last year, and that the firm had Net Income of $7,876.63 and dividends were $6,222.53. What is the price per share of the stock? (tolerance is 0.1, round to 2 decimals, do not enter $ symbol)

Answer 1

Return on Equity = Net Income / Equity
Return on Equity = $7,876.63 / $508,500.00
Return on Equity = 0.0155 or 1.55%

Retention Ratio = (Net Income - Dividends) / Net Income
Retention Ratio = ($7,876.63 - $6,222.53) / $7,876.63
Retention Ratio = 0.21

Sustainable Growth Rate = [Return on Equity * Retention Ratio] / [1 - Return on Equity * Retention Ratio]
Sustainable Growth Rate = [0.0155 * 0.21] / [1 - 0.0155 * 0.21]
Sustainable Growth Rate = 0.003255 / 0.996745
Sustainable Growth Rate = 0.0033 or 0.33%

Required Return = Risk-free Rate + Beta * (Market Return - Risk-free Rate)
Required Return = 1.14% + 1.00 * (2.93% - 1.14%)
Required Return = 2.93%

Last Dividend = $1.94

Expected Dividend = Last Dividend * (1 + Growth Rate)
Expected Dividend = $1.94 * 1.0033
Expected Dividend = $1.946402

Current Price = Expected Dividend / (Required Return - Growth Rate)
Current Price = $1.946402 / (0.0293 - 0.0033)
Current Price = $1.946402 / 0.0260
Current Price = $74.86

So, price per share of the stock is $74.86