Nahanni Treasures Corporation is planning a new common stock issue of five million shares to fund a new project. The increase in shares will bring to 25 million the number of shares outstanding. Nahanni's long-term growth rate is 6%, and its current required rate of return is 12.6%. The firm just paid a $1.00 dividend and the stock sells for $16.06 in the market. On the announcement of the new equity issue, the firm's stock price dropped. Nahanni estimates that the company's growth rate will increase to 6.5% with the new project, but since the project is riskier than average, the firm's cost of capital will increase to 13.5%.
Using the DDM constant growth model, what is the change in the equilibrium stock price?
Constant Growth Dividend Discount Model:
This problem requires utilization of the constant growth dividend discount model, also known as the Gordon Growth Model. This commonly used stock valuation model establishes the fair value of a stock by discounting and summing its future dividends, assuming a constant growth rate.
Answer and Explanation:
The answer is -$0.85 or -5.3%.
The formula for the DDM is provided below.
P0 = D1/(r-g)
P0 = intrinsic value of stock
D1 = dividend payment one year from today
r = discount rate
g = growth rate
To solve for P0, we must be cognizant of the fact D1 = D0(1+g). Armed with this knowledge, we can structure and solve the problem, using known information, as follows:
P0 = $1.00(1+.065) / (.135-.065)
P0 = $1.065 / .07
P0 = $15.21
Therefore the change in the equilibrium stock price is -$0.85 ($15.21-$16.06) or -5.3% (-$0.85/$16.06).
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from Finance 101: Principles of FinanceChapter 14 / Lesson 3