Question

Mano Home Investment Company (MHIC) is presently in a stage of abnormally high growth because of a surge in the demand for motor homes. The company expects earnings and dividends to grow at a rate of 20 percent for the next 4 years, after which time there will be no growth (g = 0) in earnings and dividends. The company's last dividend was $1.50. MHIC's beta is 1.6, the return on the market is currently 12.75 percent, and the risk-free rate is 4 percent. What should be the current common stock price?

Answer 1

Step 1:

Risk Free Rate = Rf = 4%

Return on Market = Rm = 12.75%

Beta = β = 1.6

Required rate of Return using CAPM formula = Rf + β (Rm - Rf)

                                                                 = 4% + 1.6 (12.75% - 4%)

                                                                 = 4% + 14%

                                                                 = 18%

Required Rate of Return is 18%

Step 2:

Last Dividend = D0 = $1.5

Dividend in Year 1 = D1 = D0 * (1+g) = $1.5 * (1+20%) = $1.8

Dividend in Year 2 = D2 = D1 * (1+g) = $1.8 * (1+20%) = $2.16

Dividend in Year 3 = D3 = D2 * (1+g) = $2.16 * (1+20%) = $2.592

Dividend in Year 4 = D4 = D3 * (1+g) = $2.592 * (1+20%) = $3.1104

Dividend in Year 5 = D5 = D4 * (1+g) = $3.1104 * (1+0) = $3.1104

Value of Dividend at year 4 for years 5 to forever =H = D5 / Required rate of return = $3.1104 /18% = $17.28

Step 3:

Current Common Stock Price = Present value of all dividends

= [D1 / (1+r)^1] + [D2 / (1+r)^2] + [D3 / (1+r)^3] + [D4 / (1+r)^4] + [H / (1+r)^4]\

= [$1.8 / (1+18%)^1] + [$2.16 / (1+18%)^2] + [$2.592 / (1+18%)^3] +[$3.1104 / (1+18%)^1] + [$17.28 / (1+18%)^4]

= [$1.8 / 1.18] + [$2.16 / 1.3924] + [$2.592 / 1.643032] + [$3.1104 / 1.93877776] + [$17.28 / 1.93877776]

= $1.52542373 + $1.55127837 + $1.57757122 + $1.60430972 + $8.91283176

= $15.1714148

Therefore, Current Common Stock Price is $15.17