Metallica Bearings Inc is a young startup company No dividen

Metallica Bearings, Inc., is a young start-up company. No dividends will be paid on the stock over the next nine years because the firm needs to plow back its earnings to fuel growth. The company will pay a $20 per share annual dividend 10 years from today and will increase the dividend by 4 percent per year thereafter. If the required annual return on this stock is 10 percent, what is the current share price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Solution

Here, we have a stock that pays no dividends for nine years. Once the stock begins paying dividends, it will have a constant growth rate of dividends. We can use the constant growth model at that point. It is important to remember the general growth constant dividend growth formula is:

P_t= [D_t*(1+g)]/(R-g)

This means that since we will use the dividend in year 10, we will be finding the stock price in year 11. The dividend growth model is similar to the present value of an annuity and the present value of a perpetuity. The equation gives you the present value of one period before the first payment. So, the price of the stock in year 9 will be

P₉=D₁₀/(R-g)

P₉=$20/ (0.10-.04)

P₉=$333.33

The price of the stock today is simply the PV of the stock price in the future. We simply discount the future stock price at the required return. The price of the stock today will be:

P₀=P₉/ (1+R)⁹

P₀=$333.33/ (1.10)⁹

P₀= $141.36

Hence, current price of the stock is $141.36.