Question

 Lawrence​ Industries' most recent annual dividend was ​$1.44 per share ​(D0equals$ 1.44​), and the​ firm's required return is 10​%. Find the market value of​ Lawrence's shares when dividends are expected to grow at 20​% annually for 3​ years, followed by a 4​% constant annual growth rate in years 4 to infinity. The market value of​ Lawrence's shares is ​$ nothing. ​(Round to the nearest​ cent.)

Answer 1

Step-1, Dividend per share for the next 3 years

Dividend in Year 0 (D0) = $1.44 per share

Dividend in Year 1 (D1) = $1.7280 per share [$1.44 x 120%]

Dividend in Year 2 (D2) = 2.0736 per share [$1.7280 x 120%]

Dividend in Year 3 (D3) = $2.4883 per share [$2.0736 x 120%]

Step-2, Calculation of Stock Price for the Year 3(P3)

Dividend Growth Rate after 3^rd year (g) = 4.00%

Required Rate of Return (Ke) = 10.00%

Stock Price for the Year 3 = D3(1 + g) / (Ke – g)

= $2.4883(1 + 0.04) / (0.10 – 0.04)

= $2.5879 / 0.06

= $43.13 per share

Step-3, The market value of​ Lawrence's share

The Current Stock Price is the aggregate of the Present Value of the future dividend payments and the present value the stock price for the year 3

Year	Cash flow ($)	Present Value factor at 10.00%	Present Value of cash flows ($)
1	1.7280	0.909091	1.57
2	2.0736	0.826446	1.71
3	2.4883	0.751315	1.87
3	43.13	0.751315	32.40
TOTAL			37.56

“Hence, the market value of Lawrence's share will be $37.56”

NOTE

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.