Question

Note: If not otherwise stated, assume that:

• Firms make annual dividend payments

• Stock prices are the present value of all future dividends and don’t include dividends that were just paid.

Micro Inc. (MI) just paid a dividend of $2.00/share. MI has a new technology that is expected to go on the market this year, and their dividend is expected to grow at 10% per year for the next five years (i.e., the growth rate applies only to the next five dividend payments). After that, the dividend is not expected to increase for the foreseeable future (i.e., forever). The next dividend will be paid exactly in one year. Assume investors require a 10% rate of return (EAR) for MI’s stock.

a) What is MI’s stock price today?

Select one:

$20.0

$32.0

$30.0

$27.3

$28.2

$2.0

$100.0

No solution; growth rate is equal to the discount rate

b) What is MI’s stock price in three years from now (right after the dividend payment)?

Select one:

$32.2

$20.0

$13.0

$31.9

$29.3

$29.0

The same as today (P₀)

No solution; growth rate is equal to the discount rate

c) What is MI’s stock price in twenty years from now (right after the dividend payment)?

Select one:

$30.0

$32.2

$35.4

$29.3

$20.0

$22.0

$4.8

No solution; growth rate is equal to the discount rate

NOTE: Please show all the work, without using excel, unless necessary. (step by step with equations) Thanks!

Answer 1

A1	B	C	D	E	F	G	H	I	J	K	L	M
2		a)
3		Growth rate for 5 years	10%
4		Terminal growth rate (gL)	0%
5		Required return (rs)	10%
6		D0	$2.00
7
8		As per dividend growth model, Price of share is the present value of all future dividends.
9		Future dividends can be calculated as follows:
10		Year	0	1	2	3	4	5	6	…
11		Dividend	$2.00	$2.20	$2.42	$2.66	$2.93	$3.22	$3.22	…
12		Calculation Price of the share at Year 0:
13		Required return	10.00%
14		Year	0	1	2	3	4	5	6	…
15		Dividend	$2.00	$2.20	$2.42	$2.66	$2.93	$3.22	$3.22	…
16		Terminal value = DIV6/(rs-gL)						32.2102	=J15/(D5-D4)
17		Present value of dividends		$2.00	$2.00	$2.00	$2.00	$22.00	=(I15+I16)/((1+$D$13)^I14)
18		Price of share at Year 0	$30.00	=SUM(E17:I17)
19
20		Hence the current price is	$30.00
21		Thus the third option is correct.
22
23		b)
24
25		Calculation Price of the share at Year 3:
26		Required return	10.00%
27		Year	0	1	2	3	4	5	6	…
28		Dividend	$2.00	$2.20	$2.42	$2.66	$2.93	$3.22	$3.22	…
29		Terminal value = DIV6/(rs-gL)						32.2102	=J28/($D$5-$D$4)
30		Present value of dividends at year 3					$2.66	$29.28	=(I28+I29)/((1+$D$13)^(I27-$G$27))
31		Price of share at Year 3	$31.9	=SUM(E30:I30)
32
33		Hence the price at year 3 is	$31.9
34		Thus the fourth option is correct.
35
36		c)
37		After 20 Years, Dividends will be constant at $3.22.
38		Constant Dividend (D)	$3.22
39		Required rate of return (r)	10%
40
41		MI Price after 20 Years	=Present Value of future dividends i.e. constant perpetuity
42			=$3.22 / 10%
43			$32.20	=D38/D39
44
45		Hence MI Price after 20 Years	$32.20
46		Thus the second option is correct.
47