Question

XYZ company presently pays a dividend of $ 1.50 per share on its common
stock. The company expects to increase the dividend at a 20% annual rate the
first four years and at the rate of 13% at the next four years then the growth on
the dividend at a 7% thereafter. This phased growth patterns is in keeping with
the expected life cycle of earnings. You are required a 16% return to invest in
this stock. What value should you place on a share of this Stock?

Answer 1

Stock Price :
The price is a reflection of the company's value – what the public is willing to pay for a piece of the company. It is nothing but present value of cash flows ( Div & Sale Price of Stock at future date) from it.

Div Calculation:

Year	Cash Flow / Div	Formula	Calculation
1	$                     1.50	Given	Given
2	$                     1.70	D1 ( 1 + g)	1.5 * ( 1 + 0.13 )
3	$                     1.92	D2 ( 1 + g)	1.7 * ( 1 + 0.13 )
4	$                     2.16	D3 ( 1 + g)	1.92 * ( 1 + 0.13 )
5	$                     2.45	D4 ( 1 + g)	2.16 * ( 1 + 0.13 )
6	$                     2.62	D5 ( 1 + g)	2.45 * ( 1 + 0.07 )
7	$                     2.80	D6 ( 1 + g)	2.62 * ( 1 + 0.07 )
8	$                     3.00	D7 ( 1 + g)	2.8 * ( 1 + 0.07 )
9	$                     3.21	D8 ( 1 + g)	3 * ( 1 + 0.07 )

Price after 8 Years:

Price of Stock is nothing but PV of CFs from it.
P8 = D9 / [ Ke - g ]
= $ 3.21 / [ 16 % - 7 % ]
= $ 3.21 / [ 9 % ]
= $ 35.62

P8 - Price after 8 years
D9 - Div after 9 years
Ke - Required Ret
g - Growth Rate

Price today:

Year	Particulars	Cash Flow	PVF @16 %	Disc CF
1	D1	$      1.50	0.8621	$              1.29
2	D2	$      1.70	0.7432	$              1.26
3	D3	$      1.92	0.6407	$              1.23
4	D4	$      2.16	0.5523	$              1.20
5	D5	$      2.45	0.4761	$              1.16
6	D6	$      2.62	0.4104	$              1.07
7	D7	$      2.80	0.3538	$              0.99
8	D8	$      3.00	0.3050	$              0.91
8	P8	$   35.62	0.3050	$           10.87
Price				$           19.98

Value of stock is $ 19.98