Question

ABC private limited as given the dividend of $5 last year and has promised to increase the dividend by 8% each year for the next four years.

1. Find out the dividend of each of the next four years. [2 marks]

2. If the stocks are selling at $120 at the end of fourth year, find out the price of stock today, assuming expected return as 12%. [2 marks]

3. Write a detailed comment on what will happen to the today’s selling price of the stock if the expected return is increased from 12% to 16%. [3 marks]

4. If the stocks are selling at $90 today, find out the price of stock at the end of fourth year, assuming expected return as 12%. [2 marks]        

5. Write a detailed comment on what will happen to the selling price of the stock at the end of fourth year if the expected return is decreased from 12% to 8%. [3 marks]

Answer 1

Stock Value today = PV of CFs from it.

Part A:

Year	Cash Flow / Div	Formula	Calculation
1	$                     5.40	D0 ( 1 + g)	5 ( 1 + 0.08 )
2	$                     5.83	D1 ( 1 + g)	5.4 * ( 1 + 0.08 )
3	$                     6.30	D2 ( 1 + g)	5.83 * ( 1 + 0.08 )
4	$                     6.80	D3 ( 1 + g)	6.3 * ( 1 + 0.08 )

Part B:

Price Today = PVof CFs from it.

Year	Particulars	Cash Flow	PVF @12 %	Disc CF
1	D1	$      5.40	0.8929	$              4.82
2	D2	$      5.83	0.7972	$              4.65
3	D3	$      6.30	0.7118	$              4.48
4	D4	$      6.80	0.6355	$              4.32
4	P4	$ 120.00	0.6355	$           76.26
Price				$           94.54

PVF(r%, n) = 1 / ( +r )^n

r = Disc Rate

n = Time gap

Part C:

If the disc Rate increases, PVF will decrease. Hence Stock price today will also decrease.

Year	Particulars	Cash Flow	PVF @16 %	Disc CF
1	D1	$      5.40	0.8621	$              4.66
2	D2	$      5.83	0.7432	$              4.33
3	D3	$      6.30	0.6407	$              4.04
4	D4	$      6.80	0.5523	$              3.76
4	P4	$ 120.00	0.5523	$           66.27
Price				$           83.06

Part D:

Let X be the price of Stock after 4 Years:

Year	Particulars	Cash Flow	PVF @12 %	Disc CF
1	D1	$      5.40	0.8929	$              4.82
2	D2	$      5.83	0.7972	$              4.65
3	D3	$      6.30	0.7118	$              4.48
4	D4	$      6.80	0.6355	$              4.32
4	P4	X	0.6355	0.6355X
Price				$ 18.28 + 0.6355X

Thus 0.6355X + 18.28 = 90

0.6355X = 90 -18.28

X = 71.72/0.6355

=$ 112.86

Part E:

Year	Particulars	Cash Flow	PVF @8 %	Disc CF
1	D1	$      5.40	0.9259	$              5.00
2	D2	$      5.83	0.8573	$              5.00
3	D3	$      6.30	0.7938	$              5.00
4	D4	$      6.80	0.7350	$              5.00
4	P4	X	0.7350	0.7350 X
Price				$ 20.00 + 0.7350X

Thus 0.7350X + 20 = 90

X = 70 / 0.7350

= $ 95.24