Final answer:
Using the Dividend Discount Model and given a required rate of return of 15%, the current stock price of Mack Industries should be approximately $53.21, considering initial dividends and a perpetual growth rate.
Step-by-step explanation:
The current stock price of Mack Industries can be determined using the Dividend Discount Model (DDM), which takes into account the expected dividends and their growth rates. Given that the company just paid a dividend (D0) of $5, analysts expect a growth of 7% this year, which gives us a dividend (D1) of $5.35. The dividend is expected to grow by 5% next year and continue to grow at a constant rate of 5% thereafter.
The next step is to calculate the present value of the expected dividends for the first two years and then use the Gordon Growth Model to calculate the present value of all subsequent dividends, also known as the terminal value. The required rate of return is 15%. The formula for the stock price (P0) is:
- P0 = (D1 / (1 + r)) + (D2 / (1 + r)^2) + (D2 * (1 + g) / (r - g)) / (1 + r)^2
Here, D1 is the dividend in year 1, D2 is the dividend in year 2, r is the required rate of return, and g is the growth rate after year 2. By plugging in the numbers given:
- D1 = $5.35
- D2 = D1 * 1.05 = $5.35 * 1.05 = $5.6175
- r = 0.15
- g = 0.05
The terminal value at the end of year 2, which represents the present value of all future dividends, is calculated as:
- Terminal Value = D2 * (1 + g) / (r - g) = $5.6175 * 1.05 / (0.15 - 0.05) = $58.98375
Finally, we can determine the current stock price as follows:
P0 = ($5.35 / (1 + 0.15)) + ($5.6175 / (1 + 0.15)^2) + ($58.98375 / (1 + 0.15)^2)
Calculating these, we get:
- P0 = $4.65217 + $4.23368 + $44.3222
- P0 = $53.20805
Thus, the current stock price should be approximately $53.21.