Question

MC algo 8-24 Supernormal Growth

The Bell Weather Co. is a new firm in a rapidly growing industry. The company is planning on increasing its annual dividend by 20 percent a year for the next 4 years and then decreasing the growth rate to 3 percent per year. The company just paid its annual dividend in the amount of $3.40 per share. What is the current value of one share of this stock if the required rate of return is 8.90 percent?

Answer 1

Price of Stock is nothing but PV of CFs from it.

Year	Particulars	Cash Flow	PVF @8.9 %	Disc CF
1	D1	$        4.08	0.9183	$              3.75
2	D2	$        4.90	0.8432	$              4.13
3	D3	$        5.88	0.7743	$              4.55
4	D4	$        7.05	0.7110	$              5.01
4	P4	$    123.08	0.7110	$            87.51
Price				$          104.95

Value of the stock today is 104.95

Working Note 1

Dividents computation

Divident	Cash Flow / Div	Formula	Calculation
D1	$                      4.08	D0 ( 1 + g)	3.4 ( 1 + 0.2 )
D2	$                      4.90	D1 ( 1 + g)	4.08 * ( 1 + 0.2 )
D3	$                      5.88	D2 ( 1 + g)	4.9 * ( 1 + 0.2 )
D4	$                      7.05	D3 ( 1 + g)	5.88 * ( 1 + 0.2 )
D5	$                      7.26	D4 ( 1 + g)	7.05 * ( 1 + 0.03 )

Working Note 2

Computation of stock price after year 4

P4 = D5 / [ Ke - g ]
= $ 7.26 / [ 8.9 % - 3 % ]
= $ 7.26 / [ 5.9 % ]
= $ 123.08

Value of the stock after year 4 is $ 123.08

Value of the stock today is $ 104.95

Please let me know if you need any further clarification