Question

A firm is currently paying $2.75 each year in dividends. Recently sales have declined and the board of directors has recommended reducing their dividends in the next few years. Shareholders have agreed to a 10% reduction in dividends each year, over the next 4 years. After this four-year period, the firm’s prospects are expected to improve. Starting in year 5, the firm will increase dividends by 5% each year, forever. If shareholders require a 12% return on this stock and the stock is currently selling for $20.00, would you be interested in purchasing this stock? Why or why not?

Answer 1

Answer:

Yes, you would be interested in buying the stock at $20 because it's underpriced. It's actual intrinsic value is $23.76

Explanation:

Use dividend discount model to solve this question;

D1 = 2.75(1-0.10) = 2.475

D2 = 2.475 (1-0.10) = 2.228

D3 =2.228 (1-0.10) = 2.005

D4 = 2.005(1-0.10) = 1.805

D5 =  1.805(1+0.05) = 1.895

Next, find the Present values of each dividend;

PV (D1) = 2.475 /1.12 = 2.2098

PV (D2) =  2.228/1.12² = 1.7761

PV (D3) =  2.005/1.12³ = 1.4271

PV (D4) =  1.805/1.12^4 = 1.1471

Next find PV of  constant growing dividends

PV (D5 onwards) = $\frac{\frac{ 1.895}{0.12-0.05} }{1.12^{4} }$

PV (D5 onwards) = 17.2044

Next, sum up these PVs to find the price of the stock;

2.2098 + 1.7761 + 1.4271 + 1.1471 + 17.2044 = $23.76

Yes, you would be interested in buying the stock at $20 because it's underpriced. It's actual intrinsic value is $23.76