In: Finance
Problem 9-12
Valuation of a constant growth stock
Investors require a 18% rate of return on Levine Company's stock (i.e., rs = 18%).
(a) Given, Rate of return required = r = 18%
D0 = 3
Growth rate = g
Hence, D1 = D0(1+g)
1. when g = -5%,
Price of Stock P0 = D1/(r - g) = 3(1-0.05)/(0.18 + 0.05) = 12.39
2. when g = 0%,
Price of Stock P0 = D1/(r - g) = 3(1+0.0)/(0.18 - 0.0) = 16.67
3. when g = 3%,
Price of Stock P0 = D1/(r - g) = 3(1+0.03)/(0.18 - 0.03) = 20.6
4. when g = 11%,
Price of Stock P0 = D1/(r - g) = 3(1+0.11)/(0.18 - 0.11) = 47.57
(b)
when g = 15%,
Price of Stock P0 = D1/(r - g) = 3(1+0.15)/(0.18 - 0.15) = 117
when g = 20%,
Price of Stock P0 = D1/(r - g) = 3(1+0.20)/(0.18 - 0.20) = -180
The price of the stock when g>r is -ve
Hence, (III)The results show that the formula does not make sense if the required rate of return is equal to or less than the expected growth rate.
(c) It is not possible for the company to grow at rate greater than the rate of return indefinetely
(IV) It is not reasonable for a firm to grow indefinitely at a rate higher than its required return.