Question

McGaha Enterprises expects earnings and dividends to grow at a rate of 40% for the next 4 years, after the growth rate in earnings and dividends will fall to zero, i.e., g = 0. The company's last dividend, D0, was $1.25, its beta is 1.20, the market risk premium is 5.50%, and the risk-free rate is 3.00%. What is the current price of the common stock? Select the correct answer. a. $44.24 b. $44.98 c. $45.72 d. $43.50 e. $46.46

Answer 1

Step-1, Required Rate of Return

As per Capital Asset Pricing Model [CAPM], the Required Rate of Return is computed by using the following equation

Required Rate of Return = Risk-free Rate + [Beta x Market risk premium]

= 3.00% + [1.20 x 5.50%]

= 3.00% + 6.60%

= 9.60%

Step-2, Dividend for the next 4 years

Dividend in Year 0 (D0) = $1.25 per share

Dividend in Year 1 (D1) = $1.7500 per share [$1.25 x 140%]

Dividend in Year 2 (D2) = $2.4500 per share [$1.7500 x 140%]

Dividend in Year 3 (D3) = $3.4300 per share [$2.4500 x 140%]

Dividend in Year 4 (D4) = $4.8020 per share [$3.4300 x 140%]

Step-3, The Price of the stock in year 4 (P4)

Dividend Growth Rate after 4 years (g) = 0% per year

Required Rate of Return (Ke) = 9.60%

Therefore, the Share Price in year 4 (P4) = D4(1 + g) / (Ke – g)

= $4.8020(1 + 0.00) / (0.0960 / 0.00)

= $4.8020 / 0.0960

= $50.02 per share

Step-4, Current Price of common stock (P0)

As per Dividend Discount Model, the Current Price of common stock is the Present Value of the future dividend payments and the present value the share price in year 4

Year	Cash flow ($)	Present Value factor at 9.60%	Present Value of cash flows ($)
1	1.7500	0.91241	1.60
2	2.4500	0.83249	2.04
3	3.4300	0.75957	2.61
4	4.8020	0.69304	3.33
4	50.02	0.69304	34.66
TOTAL			44.24

“Therefore, the current price of the common stock will be (a). $44.24”

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.