Learn how to find the value of an equity which pays dividend consistently. This is more relevant to dividend kings who have the history of paying dividends for a minimum of 50 years.

1. Dividends
Shiva Indukoori

2. Learning Objectives
LO4.2-1 Calculate the intrinsic value of a firm using either a constant-growth or multistage
dividend discount model.
LO4.2-2 Calculate the intrinsic value of a firm using growth and perpetual dividend discount
model.
Shiva Indukoori 2

3. Shiva Indukoori 3
Equity Value
• Market Value: Market price times number of shares.
• Book Value: Net worth common equity on balance sheet.
• Liquidation Value: Selling the assets in times of
bankruptcy.
• Replacement Value: Cost to replace firm’s assets.
• Tobin’s Q: Ratio of firm’s market value to replacement cost.
• Intrinsic value: Present value of net earnings.

4. Dividend Discount Model
(DDM)
1. Period model: Single period and multiple period.
2. Growth model: single growth and multiple growth.
3. Perpetual model: with growth and without growth.
4. Growth and Perpetual Model.

5. Shiva Indukoori
DDM– Single Period Model
𝐼𝑉 =
𝐷1
(1+𝑘)
+
𝑃1
(1+𝑘)
5

6. 𝐼𝑉 =
$3.50
(1+0.25)
+
$45
(1+0.25)
¿
$3.50
1.25
+
$45
1.25
An investor expects to get $ 3.50 as dividend from a share next year and hopes to sell of off the share at
$ 45 after holding it for one year and if his required rate of return is 25% calculate intrinsic value of this
share.
¿ $ 2.80+$ 36.00=$ 38.80
6
Shiva Indukoori
DDM – Single Period Model Example

7. Shiva Indukoori
𝐼𝑉 =
𝐷1
(1+𝑘)1
+
𝐷2
(1+𝑘)2
+
𝐷3
(1+𝑘)3
+.............
𝐷𝑛
(1+𝑘)𝑛
+
𝑃𝑛
(1+𝑘)𝑛
𝐼𝑉 =∑
𝑡 =1
𝑛
𝐷𝑡
(1+𝑘)𝑡
+
𝑃𝑛
(1+𝑘)𝑛
7
DDM– Multiple Period

8. 𝐼𝑉 =
$3.50
(1+0.25)1
+
$ 4.00
(1+0.25)2
+
$ 4.50
(1+0.25)3
+.....+
$75
(1+0.25)3
If an investor expects to get $3.50, $4, and $4.50 as dividend from a share during the next three years
and hopes to sell it off at $75 at the end of the third year and if his required rate of return is 25 percent
calculate the intrinsic value.
¿ $2.80+$ 2.56+$2.30+$ 38.80=$ 46.06
8
Shiva Indukoori
DDM – Multiple Period Example

9. Shiva Indukoori
𝐼𝑉 =
𝐷
𝑘
9
𝑉 0=
𝐷1
1+𝑘
+
𝐷2
¿ ¿
DDM – Constant Perpetual Model

10. Shiva Indukoori
𝐼𝑉 =
$3.50
0.25 ¿ $14
If an investor expects to get $3.50 dividend for ever with a required rate of return of 25 percent calculate
the intrinsic value.
10
DDM – Perpetual Model Example

11. Dividend Growth Model

12. Shiva Indukoori
𝐼𝑉 =
𝐷0 (1+𝑔)
(1+𝑘)1
+
𝑃1
(1+𝑘)
¿
𝐷1
(1+𝑘)1
+
𝑃1
(1+𝑘)1
12
DDM - 1 Year Growth Model
Dividends are expected to grow at a certain rate.

13. ¿
$26+$220
1.20
¿
$ 246
1.20
𝐼𝑉 =
$20 (1+0.30)
(1+0.20)
+
$ 220
(1+0.20)
Calculate intrinsic value of a stock which paid $20 as dividend and expected to reach $220 with a
dividend growth rate of 30% and required rate of return is 20%.
¿ $ 205
13
Shiva Indukoori
DDM - 1 Year Growth Model Example

14. Shiva Indukoori
𝐼𝑉 =
𝐷0 (1+𝑔)1
(1+𝑘)1
+
𝐷0 (1+𝑔)2
(1+𝑘)2
+
𝐷0 (1+𝑔)3
(1+𝑘)3
+.....+
𝐷0 (1+𝑔)𝑛
(1+𝑘)𝑛
𝐼𝑉 =
𝐷0 (1+𝑔)
(1+𝑘)1
+
𝐷1 (1+𝑔)
(1+𝑘)2
+
𝐷2 (1+𝑔)
(1+𝑘)3
+.....+
𝐷𝑛−1(1+𝑔)
(1+𝑘)𝑛
¿∑
𝑡=1
𝑛
𝐷𝑡 −1 (1+𝑔)
(1+𝑘)𝑡
¿∑
𝑡=1
𝑛
𝐷0(1+𝑔)𝑡
(1+𝑘)𝑡
14
DDM – Multiple Years Growth Model

15. 𝐼𝑉 =
20(1.30)1
(1.20)
1
+
20(1.30)2
(1.20)
2
+
20(1.30)3
(1.20)
3
+
20(1.30)4
(1.20)
4
+
20(1.30)5
(1.20)
5
¿
$20(1.30)
1.20
+
$20(1.69)
1.44
+
$20(2.197)
1.728
+
$20(2.8561)
2.0736
+
$20(3.7129)
2.4883
Calculate intrinsic value of a stock which paid a current dividend $20 and expected to grow @ 30% for
five years with a required rate of return is 20%.
¿
$26
1.20
+
$33.80
1.44
+
$ 43.94
1.728
+
$57.12
2.0736
+
$ 74.26
2.4883
𝐼𝑉 =$ 21.67+$ 23.47+$25.43+$ 27.55+$29.84
𝐼𝑉 =$ 127.96
15
Shiva Indukoori
DDM – Multiple Years Growth Model Example

16. Shiva Indukoori 16
Life Cycles and Multistage Growth Models
• Two-stage DDM : DDM in which dividend growth assumed to level off only at future date.
• Multistage Growth Models : Allow dividends per share to grow at different rates as firm
matures.
DDM – Multistage Growth Model
𝑃0 =
𝐷0 ×(1+ 𝑔)
(1+𝑘)
+ ...+ 𝐷0 ׿ ¿

17. Shiva Indukoori 17
Consider the following information:
• The firm’s dividends are expected to grow at g = 20% until t = 3 yrs.
• At the start of year four, growth slows to gs= 5%.
• The stock just paid a dividend Div0 = $1.00
• Assume a market capitalization rate of k = 12%
What is the expected price (P0) of this stock after 4 years?
DDM – Multistage Growth Model Example

18. Shiva Indukoori 18
• Form of DDM that assumes dividends will grow at constant rate
• Implies stock’s value greater if:
• Larger dividend per share
• Lower market capitalization rate, k
• Higher expected growth rate of dividends
DDM – Perpetual Growth Model

19. Shiva Indukoori
𝐼𝑉 =
𝐷0 (1+𝑔)1
(1+𝑘)1
+
𝐷0 (1+𝑔)2
(1+𝑘)2
+
𝐷0 (1+𝑔)3
(1+𝑘)3
+.....+
𝐷0 (1+𝑔)∞
(1+𝑘)∞ ¿
𝐷1
𝑘− 𝑔
¿
𝐷0 (1+𝑔)1
𝑘−𝑔
19
DDM – Perpetual Growth Model (Gordon)
• Form of DDM that assumes dividends will grow at constant rate
• Implies stock’s value greater if:
• Larger dividend per share
• Lower market capitalization rate, k
• Higher expected growth rate of dividends

20. Shiva Indukoori
¿
$ 2.75
0.05
=$ 55
𝐼𝑉 =
$2.50 (1+0.10)
0.15− 0.10
A company has declared a dividend of $2.50 per share for the current year. The company has been
following a policy of enhancing its dividends by 10 percent every year and is expected to continue this
policy in the future also. An investor who is considering the purchase of the shares of this company has
a required rate of return of 15 percent. Calculate intrinsic value of the company’s share. Also advise the
investor if CMP is $40.
20
DDM – Perpetual Growth Model (Gordon)

21. Shiva Indukoori
¿
𝐷1
(1+𝑘)1
+
𝐷2
(1+𝑘)2
+
𝐷3
(1+𝑘)3
+.........+
𝐷𝑛
(1+𝑘)𝑛
+
𝐷𝑛 (1+𝑔)
(𝑘 −𝑔)(1+𝑘)𝑛
¿∑
𝑡 =1
𝑛
𝐷𝑡
(1+𝑘)𝑡
+
𝐷𝑛 (1+𝑔)
(𝑘− 𝑔)(1+𝑘)𝑛
21
IV=Value with Growth + Value with Growth Perpetual
DDM – Multiple Growth and Perpetual Model

22. 𝐼𝑉 =
2.00
(1.20)1
+
3.00
(1.20)2
+
3.50
(1.20)3
+
3.50(1.10)
(0.20−0.10)(1.20)3
¿
2.00
(1.20)
+
3.00
(1.44)
+
3.50
(1.728)
+
3.85
(0.10)(1.728)
¿ $1.67+$ 2.08+$2.03+$ 22.28
A company paid a dividend of $1.75 per share during the current year. It is expected to pay a dividend
of $2 per share during the next year. Investors forecast a dividend of $3 per share and $3.50 per share
respectively during the two subsequent years. After that it is expected that annual dividends will grow at
10 percent per year into an indefinite future. If the investor’s required rate of return is 20 percent, what
would be the intrinsic value of the stock.
¿ $ 28.06
22
Shiva Indukoori
DDM – Multiple Growth and Perpetual Model Example

23. Shiva Indukoori 23
• Stock Prices and Investment Opportunities
• Dividend payout ratio: Percentage of earnings paid as dividends
• Plowback ratio/earnings retention ratio: Proportion of firm’s earnings
reinvested in business
• Present value of growth opportunities (PVGO)
𝑃0=No−Growth Value per Share+PVGO
DDM – No Growth and Perpetual Model

24. Dividend
Discount
Models: Stock
Value
The Constant Growth Model states that a
stocks value will be greater
• The larger its expected dividend per
share.
• The lower the market capitalization rate,
k.
• The higher the expected growth rate of
dividends.
Shiva Indukoori 24

25. Shiva Indukoori 25
Dividend Growth and Reinvestment

26. Questions
Shiva Indukoori 26