Question

10. You are considering the purchase of a common stock that just paid a dividend of $2.00. You expect this stock to have a growth rate of 30 percent for the next 3 years, then to have a long-run normal growth rate of 10 percent thereafter. If you require a 15 percent rate of retum, how much should you be willing to pay for this stock? a. $97.50 b. $62.68 c. $82.46 d. $79.15 e. $71.27

Answer 1

Rate Symbol G1 Given : Growth Rate (G) 1st Year 2nd Year 3rd Year Thereafter 30% 30% 30% 10% G3 Gn $ DO (Current Dividend) R (Discount Rate) 2 15% Solution:- Parta) As we know, that current value of stock is present vaule of future cash flow , . Current Price D1 1+R D2 (1+R)^2 - + D3 (1+r)^3 - + - P (1+r)^3 Where D1 = DO(1+G1) D2 = D1(1+G2) D3 = D1(1+G3) Dividend at end of 1st year Dividend at end of 2nd year Dividend at end of 3rd year D3(1+Gn) (R - Gn) P (Price of Stock) Hence Using above formula Current Price ($) - +- - +- - +- 2.6 =- 1.15 = 2.261 + = 71.27 3.38 1.3225 2.5558 + 4.394 96.668 1.52091.520875 2.8891 + 63.56078 Hence, amount willing to pay shall be 71.27 $ and option e is correct *Note: We are allowed to answer only one question