# A firm currently pays no dividend but is expected to pay a dividend at the end of Year 6. Year 6...

A firm currently pays no dividend but is expected to pay a dividend at the end of Year 6. Year 6 earnings are expected to be $3.2, and the firm will maintain a payout ratio of 40%. Assuming a constant growth rate of 7% and a required rate of return of 12%, estimate the current value of this stock. ## Valuing a Stock using the Dividend Growth Model: It is important to know the intrinsic value of a stock for the company to determine its true worth and it is also important for investors to choose between various investments basing on the intrinsic value of the stock. The dividend growth model is one such stock valuation model that assumes that the present value of the future dividends from stock is the intrinsic value of the stock. The model assumes that the growth rate at which the future dividends are expected to grow remains constant to infinity. ## Answer and Explanation: Answer: The current value of the stock is$18.25.

Explanation:

As per the data:

• Expected earnings in year 6 = $3.20 • Dividend payout ratio = 40% • Expected dividend in year 6, D6 =$1.28 ($3.20 * 40%) • Constant growth rate, g = 7% • Required return, r = 12% • Current stock price, P0 =? Computation: The first step is to determine the stock price in year 5, i.e P5: Using the dividend growth model, • P5 = D6 / (r - g) • P5 =$1.28 / (12% - 7%)
• P5 = $25.60 The second step is to determine the current stock price, P0: • P5 = {eq}P0 * (1 + g)^5 {/eq} •$25.60 = {eq}P0 * (1 + 0.07)^5 {/eq}
• P0 = {eq}$25.60 / 1.4025517 {/eq} • P0 = {eq}$18.25 {/eq}