Metallica Bearings, Incorporated, is a young startup company. No dividends will be paid on the stock over the next 7 years because the firm needs to plow back its earnings to fuel growth. The company will then pay a dividend of \( \$ 16.75 \) per share 8 years from today and will increase the dividend by 6 percent per year, thereafter. If the required return on this stock is 14 percent, what is the current share price?
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To determine the current share price of Metallica Bearings, we can follow these steps: First, we need to find the price of the stock at the end of year 7, which is when the first dividend of \( \$16.75 \) will be paid. This dividend will increase at a constant rate of 6% thereafter, so we calculate the price using the Gordon Growth Model (also known as the Dividend Discount Model): \[ P_7 = \frac{D_8}{r - g} = \frac{16.75}{0.14 - 0.06} = \frac{16.75}{0.08} = 209.375 \] Now, we need to discount this price back to its present value (PV) at time 0 (today). Since the stock price at year 7 is \( 209.375 \), we can discount it back using the required return of 14%: \[ PV_0 = \frac{P_7}{(1 + r)^7} = \frac{209.375}{(1 + 0.14)^7} \approx \frac{209.375}{2.5023} \approx 83.694 \] Therefore, the current share price of Metallica Bearings, Incorporated, is approximately \( \text{USD } 83.69 \).
