Question

Consider the stock of SLB Inc., a growth stock that will pay no dividend the next year. Starting in year two, the company will pay a dividend of $3 and will increase it by 10% for the next three years. Afterwards, dividends will grow by 5% per year indefinitely. The stock has a required rate of return of 15%.

Answer the following questions. (SHOW YOUR WORK. Correct answers with no formulas/calculations receive no credit)

a) What is the value (price) of the stock today (i.e. P0)? Show your work and formulas.

b) What is the price of the stock at t=10, assuming the required rate of return (i.e. 15%) and the growth rate of dividends (i.e., 5%) do not change? Show your work and formulas.

c) What is the price of the stock at t=1, assuming the required rate of return (i.e. 15%) and the growth rate of dividends (i.e., 5%) do not change? Show your work and formulas.

Answer 1

Price of stock = PV of CFs from it.

Part A:

Div Calculation:

Year	Cash flow	Formula	Calculation
1	$          -	Given	Given
2	$      3.00	Given	Given
3	$      3.30	D2(1 + g )	3 * 1.1
4	$      3.63	D3(1 + g )	3.3*1.1
5	$      3.99	D4(1 + g )	3.63 *1.1
6	$      4.19	D5(1 + g )	3.99 * 1.05

Price after 5 Years:

P5 = D6 / [ Ke - g ]

= $ 4.19 / [ 15% - 5% ]

= $ 4.19 / 10%

= $ 41.90

Price Today:

Year	Cash flow	PVF @15%	PV of CFs
1	$          -	0.8696	$          -
2	$      3.00	0.7561	$      2.27
3	$      3.30	0.6575	$      2.17
4	$      3.63	0.5718	$      2.08
5	$      3.99	0.4972	$      1.99
5	$   41.90	0.4972	$   20.83
Price Today			$   29.33

Part B:

Price after 10 Years = D11 / [ Ke - g ]

D11 = D6 ( 1 + g )^5

= $ 4.19 ( 1 + 0.05 )^ 5

= $ 4.19 * ( 1.05^ 5 )

= $ 4.19 * 1.2763

= $ 5.35

Price after 10 Years = D11 / [ Ke - g ]

= $ 5.35 / [ 15% - 5% ]

= $ 5.35 / 10%

= $ 53.50

Part C:

Year	Cash flow	PVF @15%	PV of CFs
2	$      3.00	0.8696	$      2.61
3	$      3.30	0.7561	$      2.50
4	$      3.63	0.6575	$      2.39
5	$      3.99	0.5718	$      2.28
5	$   41.90	0.5718	$   23.96
Price after 1 year			$   33.73

P5 - Price after 5 Years

D6 - Div after 6 Years

P10 - Price after 10 Years

D11 - Div after 11 Years

Ke - Required Ret

g - Growth Rate.