Question

A stock just paid a dividend of $1, and is estimated to have a dividend growth rate of 25% and 10% in the next two years. The stock is estimated to settle down to a 4% constant dividend growth thereafter. The required return of investors is 12%. (Round your answer to two digits after the decimal point.) show your work

What is the dividend of year 1?

What is the dividend of year 2?

What is the dividend of year 3?

What is the stock price at year 2?

What is the stock price at year 1?

What is the stock price at year 0?

What is the dividend yield of year 1?

What is the capital gain yield of year 1?

What is the dividend yield of year 10?

What is the capital gain yield of year 10?

Answer 1

Div Calculation for Years 1, 2 and 3:

Year	Cash Flow / Div	Formula	Calculation
1	$                     1.25	D0 ( 1 + g)	1 ( 1 + 0.25 )
2	$                     1.38	D1 ( 1 + g)	1.25 * ( 1 + 0.1 )
3	$                     1.43	D2 ( 1 + g)	1.38 * ( 1 + 0.04 )

Price at the end of Year 2:

Price of Stock is nothing but PV of CFs from it.
P2 = D3 / [ Ke - g ]
= $ 1.43 / [ 12 % - 4 % ]
= $ 1.43 / [ 8 % ]
= $ 17.88
Price at the end of Year 1:

= [ $ 17.88 + $ 1.38 ] / [ 1 + 0.12 ]

= $ 19.26 / 1.12

= $ 17.20

P1 = [ P2 + D2 ] / [ 1 + ke ]

P1 = price at the end of Year 1

P2 = price at the end of Year 2

D2 = Div at the end of Year 2

Ke = required Ret

Price at Year 0:

PV of CFs from it.

Year	Particulars	Cash Flow	PVF @12 %	Disc CF
1	D1	$      1.25	0.8929	$              1.12
2	D2	$      1.38	0.7972	$              1.10
2	P2	$   17.88	0.7972	$           14.25
Price				$           16.47

DIv Yield at year1:

= D1 / P0

= $ 1.25 / $ 16.47

= 0.0759 i.e 7.59%

CG Yield at Year 1

= [ P1 - P0 ] / P0

= [ $ 17.20 - $ 16.47 ] / $ 16.47

= $ 0.73 / $ 16.47

= 0.0443 i.e 4.43%

DIv Yield for Year 10:

Year	Cash Flow / Div	Formula	Calculation
1	$                     1.25	D0 ( 1 + g)	1 ( 1 + 0.25 )
2	$                     1.38	D1 ( 1 + g)	1.25 * ( 1 + 0.1 )
3	$                     1.43	D2 ( 1 + g)	1.38 * ( 1 + 0.04 )
4	$                     1.49	D3 ( 1 + g)	1.43 * ( 1 + 0.04 )
5	$                     1.55	D4 ( 1 + g)	1.49 * ( 1 + 0.04 )
6	$                     1.61	D5 ( 1 + g)	1.55 * ( 1 + 0.04 )
7	$                     1.67	D6 ( 1 + g)	1.61 * ( 1 + 0.04 )
8	$                     1.74	D7 ( 1 + g)	1.67 * ( 1 + 0.04 )
9	$                     1.81	D8 ( 1 + g)	1.74 * ( 1 + 0.04 )
10	$                     1.88	D9 ( 1 + g)	1.81 * ( 1 + 0.04 )
11	$                     1.96	D10 ( 1 + g)	1.88 * ( 1 + 0.04 )

P9 = D10 / [ Ke - g ]
= $ 1.88 / [ 12 % - 4 % ]
= $ 1.88 / [ 8 % ]
= $ 23.52

P10 = D11 / [ Ke - g ]
= $ 1.96 / [ 12 % - 4 % ]
= $ 1.96 / [ 8 % ]
= $ 24.46

Div Yield for Year 10:

= D10 / P9

= $ 1.88 / $ 23.52

= 0.0799 i.e 7.99%

CG yield for Year 10:

= [ P 10 - P 9 ] / P 9

= [ $ 24.46 - $ 23.52 ] / $ 23.52

= $ 0.94 / $ 23.52

= 0.04 i.e 4.00%