Question

The current dividend on an equity share of a company is $3.the present growth rate is 50%. However, this will decline linearly over a period of 10 years and then stabilize at 12% . What is the intrinsic The value of that company if investors require a return of 16%.

Answer 1

The growth rate in year 1 is 50%. It has to decline to 12% in 10 years. Hence, decline in growth rate per year over next 10 years = (50% - 12%) / 10 = 3.80%

The dividend over next 10 years will be as shown below:

Time	Growth rate	Dividend
0		3.00
1	50.00%	4.50
2	46.20%	6.58
3	42.40%	9.37
4	38.60%	12.98
5	34.80%	17.50
6	31.00%	22.93
7	27.20%	29.17
8	23.40%	35.99
9	19.60%	43.05
10	15.80%	49.85
11	12.00%	55.83

Hence, horizon value of all the future dividend from year 11 onward, at the end of year 10 =D_HV,10 = D11 / (Ke - g) = 55.83 / ( 16% - 12%) =  1,395.71

Hence,  the intrinsic value of that company = PV of all the dividends over next 10 years + PV of D_HV,10 = D1 / (1 + Ke) + D2 / (1 + Ke)² + D3 / (1 + Ke)³ +.....+ D10 / (1 + Ke)¹⁰ + D_HV,10 / (1 + Ke)¹⁰ = 4.50 /(1 + 16%) + 6.58 / (1 + 16%)² + 9.37 / (1 + 16%)³ +.....+ 49.85 / (1 + 16%)¹⁰ + 1,395.71 / (1 + 16%)¹⁰ = $ 399.99 = $ 400 / share