Question

Suppose that it is 10:14 Monday morning, and the price of Microsoft stock is $17.80 per share, the company is currently paying a dividend of $0.50 per share this year, and its dividend is expected to grow at a rate of 7% per year. At 10:15, Microsoft releases new sales information that indicates that sales of its latest version of Windows have been much higher than expected, and the firm expects higher sales to continue into the future. This news causes you and other investors to revise upward your forecast of the growth rate of Microsoft’s annual dividend from 7% to 8%. At this higher growth rate, the present value of Microsoft’s future dividends rises from $17.80 to $27.

This was copied from a textbook, I want to know how they got to $27.

Answer 1

Step-1, Calculation of the Required Rate of Return (KE) using the Dividend Growth Model

Current Year Dividend (D0) = $0.50 per share

Current Dividend Growth Rate (g) = 7% per year

Current Share Price (P0) = $17.80 per share

Required Rate of Return (KE) using the Dividend Growth Model = [D1 / P0] + g

= [($0.50 x 1.07) / $17.80] + 0.07

= [$0.5350 / $17.80] + 0.07

= 0.0301 + 0.07

= 0.1001 or

= 10.01

Step-2, Calculation of the Present Value of the future dividends if the growth rate of Microsoft’s annual dividend increased from 7% to 8%

Current Year Dividend (D0) = $0.50 per share

Revised Dividend Growth Rate (g) = 8% per year

Required Rate of Return (KE) = 10.01%

As per the Dividend Discount Model, Present Value of the future dividend = D1 / (Ke – g)

= D0(1 + g) / (Ke – g)

= $0.50(1 + 0.08) / (0.1001 – 0.08)

= $0.5400 / 0.0201

= $27 per share

“Therefore, the Present Value of the future dividends would be $27 per share”