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 $10 per share dividend in 10 years and will increase the dividend by 6 percent per year thereafter. If the required return on this stock is 13 percent, what is the current share price?

We know that as per dividend discount model the price of share is the present value of all the dividends discounted using the required rate of return'

Now no dividends are paid till year -9

Now, we will estimate the price of share at the end of year -9

That is as per DDM the price of share

IV9 = D10/( Re - g)

Where IV9 is the intrinsic value at the end of year-9 at D10 is the dividend in the year 10

Re is the required rate of return and g is the growth rate

Now, Stock price at the end of year-9 is

IV9 = 10/(0.13 - 0.06)

IV9 = 10/0.07

IV9 = 142.8571

( The formula for present value of future cash flow is A/(1+r)ⁿ where A is the future cash flow r is the rate of return and n is the number of periods)

Now, The present stock value 142.8571/(1+0.13)⁹

142.8571/3.004042

= 142.8571 * 0.332885

= 47.55498

Hence the current share price is 47.555