Question

1. An investor requires a return of 12 percent. A stock sells for $18, it pays a dividend of $1, and the dividends compound annually at 6 percent. What should the price of the stock be?

2. You are considering a stock A that pays a dividend of $1. The beta coefficient of A is 1.3. The risk free return is 6%, while the market average return is 13%.

a. What is the required return for Stock A?

b. If A is selling for $10 a share, is it a good buy if you expect earnings and dividends to grow at 6%?

3. Lawrence Industries’ most recent annual dividend was $1.80 per share (D0$1.80), and the firm’s required return is 11%. Find the market value of Lawrence’s shares when:

a. Dividends are expected to grow at 8% annually for 3 years, followed by a 5% constant annual growth rate in years 4 to infinity.

b. Dividends are expected to grow at 8% annually for 3 years, followed by a 0% constant annual growth rate in years 4 to infinity.

c. Dividends are expected to grow at 8% annually for 3 years, followed by a 10% constant annual growth rate in years 4 to infinity.

Answer 1

Answer : 1 . Calculation of Stock Price

Stock Price = [Dividend * (1 + growth rate)] / (Required Return - growth rate)

= [1 * (1 + 0.06)] / (0.12 - 0.06)

= 1.06 / 0.06

= $17.67

If the price is $18,stock is overvalued, & investor should not buy.

Answer : 2 (a.) Calculation of Required Return

Required Return = Risk free rate + Beta * (Expected Return from market - Risk free Rate)

= 6% + 1.3 (13% - 6%)

= 6% + (1.3 * 7%)

= 15.1%

(b.) Stock Price = [Dividend * (1 + growth rate)] / (Required Return - growth rate)

= [1 * (1 + 0.06)] / (0.151 - 0.06)

= 1.06 / 0.091

= 11.65

As Stock is selling at $10, it is underpriced and can be purchased.

Answer :3 Calculation of Market Value

(a.) Market Value is shown the table below :

Year	Dividend / Horizon Value	PVF @11%	Present Value of Dividend / Horizon Value
0	1.8	1
1	1.944 [1.8*(1 + 0.08)]	0.900900901	1.751351351
2	2.09952 [1.944*(1 + 0.08)]	0.811622433	1.704017531
3	2.2674816 [2.09952*(1 + 0.08)]	0.731191381	1.657963003
3 (Horizon Value)	39.680928 (Working Note)	0.731191381	29.01435256
		Market Value	34.12768444

Working Note :

Calculation of Horizon Value:

Horizon Value (P3) = [Dividend 3 * (1 + growth rate)] / (Required Return - growth rate)

= [2.2674816 * (1 + 0.05)] / (0.11 - 0.05)

= 2.38085568 / 0.06

= 39.680928

Market Value = Present value of Dividend and horizon value (calculated in table above)

= 34.13

(b.) Market Value is shown the table below :

Year	Dividend / Horizon Value	PVF @11%	Present Value of Dividend / Horizon Value
0	1.8	1
1	1.944	0.900900901	1.751351351
2	2.09952	0.811622433	1.704017531
3	2.2674816	0.731191381	1.657963003
3 (Horizon Value)	20.61346909	0.731191381	15.07239094
		P0	20.18572282

Calculation of Horizon Value:

Horizon Value (P3) = [Dividend 3 * (1 + growth rate)] / (Required Return - growth rate)

= [2.2674816 * (1 + 0)] / (0.11 - 0)

= 2.2674816 / 0.11

= 20.6134690909

Market Value = Present value of Dividend and horizon value (calculated in table above)

= 20.19

(c.) Market Value is shown the table below :

Year	Dividend / Horizon Value	PVF @11%	Present Value of Dividend / Horizon Value
0	1.8	1
1	1.944	0.900900901	1.751351351
2	2.09952	0.811622433	1.704017531
3	2.2674816	0.731191381	1.657963003
3 (Horizon Value)	249.422976	0.731191381	182.3759303
		P0	187.4892622

Calculation of Horizon Value:

Horizon Value (P3) = [Dividend 3 * (1 + growth rate)] / (Required Return - growth rate)

= [2.2674816 * (1 + 0.10)] / (0.11 - 0.10)

= 2.49422976 / 0.01

= 249.422976

Market Value = Present value of Dividend and horizon value (calculated in table above)

= 187.49