Constant Growth Model with CAPM

Question

Constant Growth Model with CAPM. A firm expects to generate earnings over the next year of ​$2.94 per share. In one​ year, the firm will pay out ​45% of its earnings as its annual cash dividend and retain the rest to reinvest in new projects. The firm intends to indefinitely maintain its divided payout​ rate, retention​ rate, and its shares outstanding. The​ risk-free rate is ​2.2%, the market risk premium is ​8.2%, and this​ firm's beta is 2.1. If the​ firm's cost of equity capital​ (according to​ CAPM) and its return on new investments are the same​ value, then what is this​ firm's stock price under the constant growth​ model?

The answer is $15.14

what are the steps to this answer

Answer 1

Hello!

This question requires application of three key financial models/formulas: 1. CAPM 2. Sustainable growth rate 3. Constant Growth Model (also know as Gordon Growth Model). Formulas and calcs are below. Slight differences are due to rounding.

The question states that the ROE equals the cost of equity ("​ firm's cost of equity capital​ (according to​ CAPM) and its return on new investments are the same​ value"), so we know that 1. Using CAPM, the cost of equity (required return on equity) is 19.42% 2. Dividend payout rate is 45% --> Retention rate is 1-.45% or 55% 3. Growth rate (for use in constant growth model) is 10.68%

CAPM = rf + beta (market risk premium)

Cost of Equity/Required Return r --> 19.4200% =0.022+2.1*(0.082)

Growth Rate g 10.6810% =0.55*0.1942 Sustainable growth rate = retention rate (inverse of dividend payout rate) x ROE

Dividends in Year 1 D1 $1.32 = 2.94*0.45

$15.14 = 1.32/(0.1942-0.10681) Constant Growth Model: (Dividend in next Period D1) / (r-g)