Question

Metallica Bearings, Inc., is a young start-up 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 pay a $13 per share dividend in 8 years and will increase the dividend by 6 percent per year thereafter.

   

Required:

If the required return on this stock is 12 percent, what is the current share price? (Do not round your intermediate calculations.)

$102.91

$100.95

$93.11

$87.51

$98.01

Answer 1

E. $98.01

Here, we have a stock that pays no dividends for seven 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 constant dividend growth formula is:

P_t = [D_t × (1 + g)] / (R − g)

This means that since we will use the dividend in Year 8, we will be finding the stock price in Year 7. 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 one period before the first payment. So, the price of the stock in Year 7 will be:

P₇ = D₈ / (R – g)

P₇ = $13 / (.12 – .06)

P₇ = $216.67

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 = $216.67 / 1.12⁷

P₀ = $98.01