Question

Case 1.2: Time Value of Money and Firm Valuation Smokestack Technologies, Inc. (STI), is a company in a declining industry. The company is currently earning profits of $10 per share of common stock, but the company's profitability is expected to decline by 10% annually forever. The company intends to fully distribute whatever profits are earned to stockholders annually in the form of dividends, beginning with an immediate payment of $10 per share now and continuing payouts on this date each year from now. The relevant interest rate is 10% annually. A popular investors’ newsletter issues a recommendation to sell STI stock at its current price of $47 per share, based on the argument that the stock's value can only go down in the future as its profits decline. Do you agree with the recommendation to sell? Explain.

Answer 1

Formula sheet

A	B	C	D	E	F	G	H	I
2
3		1)
4
5		Growth Rate (g)	-0.1
6		Current Dividend	10
7		Relevant interest rate (r)	0.1
8
9		As per Dividend growth model the value of share is the present value of future dividends.
10		Since dividends is expected to deline at constant rate forever, therefore the
11		present value will be the present value of growing perpetuity.
12
13		Dividends can be represents as follows:
14		Year	0	1	2	3	…
15		Dividend	=D6	=D15*(1+$D$5)	=E15*(1+$D$5)	=F15*(1+$D$5)	=G15*(1+$D$5)
16
17		Present Value of Dividends	=Div1/ (r-g)
18			=E15/(D7-D5)	=E15/(D7-D5)
19
20		Hence the intrinsic value of the share is	=D18
21		Since intrinsic value of share is less than the current price of $47,
22		therefore recommendation to sell the share is correct.
23