Question

Simpkins Corporation does not pay any dividends because it is expanding rapidly and needs to retain all of its earnings. However, investors expect Simpkins to begin paying dividends, with the first dividend of $0.75 coming 3 years from today. The dividend should grow rapidly - at a rate of 70% per year - during Years 4 and 5. After Year 5, the company should grow at a constant rate of 6% per year. If the required return on the stock is 14%, what is the value of the stock today (assume the market is in equilibrium with the required return equal to the expected return)? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

Price of stock = PV of CFs from it.

Div calculation:

Year	Cash Flow / Div	Formula	Calculation
1	$          -	Given	Given
2	$          -	Given	Given
3	$ 0.7500	Given	Given
4	$ 1.2750	D3 ( 1 + g)	0.75*1.70
5	$ 2.1675	D4 ( 1 + g)	1.275 * 1.70
6	$ 2.2976	D5 ( 1 + g)	2.1675 * 1.06

Price after 5 Years:

P5 = D6 / [ Ke - g ]

= $ 2.2976 / [ 14% - 6% ]

= $ 2.2976 / 8%

= $ 28.72

Price Today:

Year	Cash Flow / Div	PVF @14%	PV of CFs
1	$            -	0.8772	$          -
2	$            -	0.7695	$          -
3	$   0.7500	0.6750	$      0.51
4	$   1.2750	0.5921	$      0.75
5	$   2.1675	0.5194	$      1.13
5	$ 28.7194	0.5194	$   14.92
Price of Stock			$   17.30

Price of stock today is $ 17.30