Question

This​ year, Midland Light and Gas​ (ML&G) paid its stockholders an annual dividend of

​$2.50

a share. A major brokerage firm recently put out a report on​ ML&G predicting that the​ company's annual dividends should grow at the rate of

6​%

per year for each of the next seven years and then level off and grow at the rate of

3​%

a year thereafter.

​(Note​:

Use four decimal places for all numbers in your intermediate​ calculations.)

a. Use the​ variable-growth DVM and a required rate of return of

12.00​%

to find the maximum price you should be willing to pay for this stock.

b. Redo the​ ML&G problem in part ​a, this time assuming that after year​ 7, dividends stop growing altogether​ (for year 8 and​ beyond,

g=0​).

Use all the other information given to find the​ stock's intrinsic value.

c. Contrast your two answers and comment on your findings. How important is growth to this valuation​ model?

Answer 1

Answer Part-a

Recent Dividend paid (D0) = $2.50

Growth rate (g) = 6% for next 7 year and then 3%

Required rate of return(Ke) = 12% or 0.12

P0 = Current intrinsic value of share

D1 = Next dividend

D1 = D0*(1+g)

First lets calculate the future dividends-

Year	Growth	Dividend
0		$2.5000
1	6%	$2.6500
2	6%	$2.8090
3	6%	$2.9775
4	6%	$3.1562
5	6%	$3.3456
6	6%	$3.5463
7	6%	$3.7591
8	3%	$3.8718

P7 = Price or intrinsic value at the end of 7 th year

D8 = Dividend of 8th year

Hence Price or Intrinsic value at the end of 7th year =

As per the variable Growth Model,

P0 or Intrinsic Value of the share = Present value of dividend receivable till the end of abnormal growth+ Present value of the intrinsic value of the share at the end of the Abnormal Growth.

=> P0 = PV of the dididends till 7 th year + PV of the intrinsic at the end of 7 th year.

	A		B		A*B
Year		Nature	Present value discount factor@12%		Present value
1	$2.6500	Dividend	0.8928571429	1/(1.12)^1	$2.3661
2	$2.8090	Dividend	0.7971938776	1/(1.12)^2	$2.2393
3	$2.9775	Dividend	0.7117802478	1/(1.12)^3	$2.1194
4	$3.1562	Dividend	0.6355180784	1/(1.12)^4	$2.0058
5	$3.3456	Dividend	0.5674268557	1/(1.12)^5	$1.8984
6	$3.5463	Dividend	0.5066311212	1/(1.12)^6	$1.7967
7	$3.7591	Dividend	0.4523492153	1/(1.12)^7	$1.7004
7	$43.02	Intrinsic value	0.4523492153	1/(1.12)^7	$19.4601
				Total	$33.5861

hence Current Intrinsic value per share = $33.5861.

maximum price you should be willing to pay for this stock= intrinsic value = $33.5861.

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Answer-(b)

Here the growth rate after 7th year = 0%

First lets calculate the future dividends-

Year	Growth	Dividend
0		$2.5000
1	6%	$2.6500
2	6%	$2.8090
3	6%	$2.9775
4	6%	$3.1562
5	6%	$3.3456
6	6%	$3.5463
7	6%	$3.7591
8	0%	$3.7591

P7 = Price or intrinsic value at the end of 7 th year

D8 = Dividend of 8th year

Hence Price or Intrinsic value at the end of 7th year =

P0 = PV of the dididends till 7 th year + PV of the intrinsic at the end of 7 th year.

	A		B		A*B
Year		Nature	Present value discount factor@12%		Present value
1	$2.6500	Dividend	0.8928571429	1/(1.12)^1	$2.3661
2	$2.8090	Dividend	0.7971938776	1/(1.12)^2	$2.2393
3	$2.9775	Dividend	0.7117802478	1/(1.12)^3	$2.1194
4	$3.1562	Dividend	0.6355180784	1/(1.12)^4	$2.0058
5	$3.3456	Dividend	0.5674268557	1/(1.12)^5	$1.8984
6	$3.5463	Dividend	0.5066311212	1/(1.12)^6	$1.7967
7	$3.7591	Dividend	0.4523492153	1/(1.12)^7	$1.7004
7	$31.3258	Intrinsic value	0.4523492153	1/(1.12)^7	$14.1702
				Total	$28.2962

Hence stock sintrinsic value = $28.2962.

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Answer-c

Situation	Intrinsic value
If g=3% after 7th year	$33.5861
if g=0% after 7th year	$28.2962

we can conncluse that growth rate plays an important in deciding the value of the share.

The more the growth rate, the more the Dividend.

The more the dividend , the more the value of the share.

Because the share holders are mainly focused on the cashflow(Dividend) from the share.

If dividend is less then the value of the share will be less.