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# International Business Machines Corp. (IBM)

## Dividend Discount Model (DDM)

Difficulty: Intermediate

In discounted cash flow (DCF) valuation techniques the value of the stock is estimated based upon present value of some measure of cash flow. Dividends are the cleanest and most straightforward measure of cash flow because these are clearly cash flows that go directly to the investor.

### Intrinsic Stock Value (Valuation Summary)

International Business Machines Corp., dividends per share (DPS) forecast

USD \$

Year Value DPSt or Terminal value (TVt) Calculation Present value at %
0 DPS01
1 DPS1 = × (1 + %)
2 DPS2 = × (1 + %)
3 DPS3 = × (1 + %)
4 DPS4 = × (1 + %)
5 DPS5 = × (1 + %)
5 Terminal value (TV5) = × (1 + %) ÷ (% – %)
Intrinsic value of IBM's common stock (per share) \$
Current share price \$

1 DPS0 = Sum of last year dividends per share of IBM's common stock. See details »

Disclaimer!
Valuation is based on standard assumptions. There may exist specific factors relevant to stock value and omitted here. In such a case, the real stock value may differ significantly form the estimated. If you want to use the estimated intrinsic stock value in investment decision making process, do so at your own risk.

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### Required Rate of Return (r)

 Assumptions Rate of return on LT Treasury Composite1 RF % Expected rate of return on market portfolio2 E(RM) % Systematic risk (β) of IBM's common stock βIBM Required rate of return on IBM's common stock3 rIBM %

1 Unweighted average of bid yields on all outstanding fixed-coupon U.S. Treasury bonds neither due or callable in less than 10 years (risk-free rate of return proxy).

Calculations

3 rIBM = RF + βIBM [E(RM) – RF]
= % + [% – %]
= %

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### Dividend Growth Rate (g)

#### Dividend growth rate (g) implied by PRAT model

International Business Machines Corp., PRAT model

Average Dec 31, 2016 Dec 31, 2015 Dec 31, 2014 Dec 31, 2013 Dec 31, 2012
Selected Financial Data (USD \$ in millions)
Cash dividends paid, common stock
Net income attributable to IBM
Revenue
Total assets
Total IBM stockholders' equity
Ratios
Retention rate1
Profit margin2 % % % % %
Asset turnover3
Financial leverage4
Averages
Retention rate
Profit margin %
Asset turnover
Financial leverage
Dividend growth rate (g)5 %

2016 Calculations

1 Retention rate = (Net income attributable to IBM – Cash dividends paid, common stock) ÷ Net income attributable to IBM
= () ÷ =

2 Profit margin = 100 × Net income attributable to IBM ÷ Revenue
= 100 × ÷ = %

3 Asset turnover = Revenue ÷ Total assets
= ÷ =

4 Financial leverage = Total assets ÷ Total IBM stockholders' equity
= ÷ =

5 g = Retention rate × Profit margin × Asset turnover × Financial leverage
= × % × × = %

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#### Dividend growth rate (g) implied by Gordon growth model

g = 100 × (P0 × rD0) ÷ (P0 + D0)
= 100 × (\$ × % – \$) ÷ (\$ + \$) = %

where:
P0 = current price of share of IBM's common stock
D0 = last year dividends per share of IBM's common stock
r = required rate of return on IBM's common stock

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#### Dividend growth rate (g) forecast

Year Value gt
1 g1 %
2 g2 %
3 g3 %
4 g4 %
5 and thereafter g5 %

where:
g1 is implied by PRAT model
g5 is implied by Gordon growth model
g2, g3 and g4 are calculated using linear interpoltion between g1 and g5

Calculations

g2 = g1 + (g5g1) × (2 – 1) ÷ (5 – 1)
= % + (% – %) × (2 – 1) ÷ (5 – 1) = %

g3 = g1 + (g5g1) × (3 – 1) ÷ (5 – 1)
= % + (% – %) × (3 – 1) ÷ (5 – 1) = %

g4 = g1 + (g5g1) × (4 – 1) ÷ (5 – 1)
= % + (% – %) × (4 – 1) ÷ (5 – 1) = %

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