Question

ABC Corp. has just paid a dividend of $3 per share. You—an experienced analyst—feel quite sure that the growth rate of the company ’ s dividends over the next 10 years will be 15% per year. After 10 years you think that the company ’ s dividend growth rate will slow to the industry average, which is about 5% per year. If the cost of equity for ABC is 12%, what is the value today of one share of the company?

Answer 1

The value today of one share of ABC Corp. is -$115.

Step-by-step explanation:

To determine the value today of one share of ABC Corp., we need to calculate the present value of the future dividends. Since the dividend growth rate is expected to be 15% for the next 10 years and 5% thereafter, we can use the dividend discount model (DDM) to calculate the present value.

The DDM formula is: Value = D0 * (1 + g) / (r - g), where D0 is the dividend just paid, g is the growth rate, and r is the required rate of return.

Using the given information, the value today of one share of ABC Corp. is:

1. Dividend just paid (D0) = $3
2. Growth rate (g) for the next 10 years = 15%
3. Growth rate (g) after 10 years = 5%
4. Required rate of return (r) = 12%

Substituting these values into the DDM formula:

Value = $3 * (1 + 0.15) / (0.12 - 0.15) = $3 * 1.15 / (-0.03) = -$3 * 38.333 = -$115

Therefore, the value today of one share of ABC Corp. is -$115.

Answer 2

Value of Share is $ 116.85

Step-by-step explanation:

The question relates to super normal growth rate. First the company grows at growth rate higher than industry rate and then growth rate slow down to stable rate. Under this Model, the stock price is calculated by discounting present value of all dividends and price of the stock at stable rate.

Do = 3

Growth rate = 15 %

Cost of Equity = 12 %

Present Value

D1 = 3 x 1.15^1 = 3.45 3.45/1.12 = 3.08

D2 = 3 x 1.15^2 = 3.97 3.97/1.12^2= 3.16

D3 = 3 x 1.15^3 = 4.56 4.56/1.12^3 = 3.25

D4 = 3 x 1.15^4 = 5.25 5.25/1.12^4 = 3.33

D5 = 3 x 1.15^5 = 6.03 6.03/1.12^5= 3.42

D6 = 3 x 1.15^6 = 6.94 6.94/1.12^6= 3.52

D7 = 3 x 1.15^7 = 7.98 7.98/1.12^7= 3.61

D8 = 3 x 1.15^8 = 9.18 9.18/1.12^8= 3.71

D9 = 3 x 1.15^9 = 10.55 10.55/1.12^9 = 3.81

D10 = 3 x 1.15^10 = 12.14 12.14/1.12^10= 3.91

Present value of all dividends = 3.08+3.16+3.25+3.33+3.42+3.52+3.61+3.71+3.81+3.91 = 34.79 --- (a)

Price of Stock after 10 years when growth rate is stable = D11 / (Cost of equity - Stable growth rate)

Stable growth rate = 5 %

D11 = D10 x 1.05 = 12.14 x 1.05 = 12.74

Price of Stock = 12.74 / ( 12 % - 5 %) = 254.87

Present value = 254.87 / 1.12^10 = 82.06 --- (b)

By adding (a) & (b), we'll get value of one share of the company.

Value of one share of company = 34.79+82.06 = 116. 85