Question

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 dividend of $20 per share exactly 10 years from today and will Increase the dividend by 4 percent per year thereafter. If the required 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, ... 32.16.) Current share price

Answer 1

Here we need to use the dividend discount model.

we will receive 0 dividends for 9 years

we will receive our first dividend at the end of 10th year.

10th year dividend = $ 20

first, we find the value of share price at 10th year using Gordon Growth Model

V10 ={ D10 * (1+g) } / (r-g) = {$20* (1+0.04)} / (0.10- 0.04) = $20.8 / 0.06 = $346.66

where

V10 = share price at the end of 10t year

D10 = Dividend in 10th year

g = growth rate

r= require return

so total value at the end of 10th year = share price + 10th year dividend = $346.66 +$ 20 = $366.66

To find current share price find the present value of $366.66

Current share price (V0) = Value at end of 10th year / (1+r)ⁿ = $366.66 / (1+0.10)¹⁰ = $366.66 / 2.5937 =$141.36

where

r = discount rate

n = numer of year or dicounting period

Hence current share price is $141.36