Question

(a)       Consider a stock that pays annual dividends. It just paid $4.50 dividends per share, and the next dividend will be paid in 1 year. The dividends are expected to remain constant at $4.50 per share for the next 10 years, after which the dividends are expected to decrease at a rate of 0.5% per year. The annual cost-of-capital is 15.50%. Find the fair value of the stock today.

(b)       Consider the same stock as described in part (a), except that the stock will not pay any dividend in at the end of year 8, i.e., it will skip the year 8 dividend. All other dividends and timing of dividends are exactly the same as described in part (a). The cost-of-capital is also the same. Compute the fair value of the stock today.

Answer 1

Part A:

Price = PV of CFs from it.

P10 = D11 / [ Ke - g ]

D11 = D10 ( 1+g)

= $ 4.50 ( 1 -0.005 )

= $ 4.50 * 0.995

= $ 4.4775

P10 = D11 / [ Ke - g ]

= $ 4.4775 / [ 15.5% - ( -0.5%) ]

= $ 4.4775 / [ 15.5% + 0.5% ]

= $ 4.4775 / 16%

= $ 27.98

Price today :

Year	Particulars	CF	PVF @15.50%	Disc CF
1	Div	$      4.50	0.8658	$      3.90
2	Div	$      4.50	0.7496	$      3.37
3	Div	$      4.50	0.6490	$      2.92
4	Div	$      4.50	0.5619	$      2.53
5	Div	$      4.50	0.4865	$      2.19
6	Div	$      4.50	0.4212	$      1.90
7	Div	$      4.50	0.3647	$      1.64
8	Div	$      4.50	0.3158	$      1.42
9	Div	$      4.50	0.2734	$      1.23
10	Div	$      4.50	0.2367	$      1.07
10	P10	$   27.98	0.2367	$      6.62
Price Today	$   28.78

Part B:

If Year 8 div is skipped, Price will be reduced by PV of Year 8 div.

PV of Year div = Div* PVF(r%, n)

= $ 4.5 * PVF ( 15.5%, 8)

= $ 4.5 * 0.3158

= $ 1.42

Price = Price in Part A - PV of DIv

= $ 28.78 - $ 1.42

= $ 27.36