Capital

Part 2

Statement of Cash Flows

2

Cash Flows

3

Net cash from operating activities

Net cash frominvesting activities

Net cash from financing activities

CFO

CFI

CFF

∆CE = CFO + CFI + CFF

Liabilities

Non-interest bearing

Debt

Deferred tax

Equity

Retained Earnings

Common stock

Assets

Cash & equiv

Cash Flows

4

Net cash from operating activities

Net cash used by investing activities

Net cash from financing activities

Liabilities

Non-interest bearing

Debt

Deferred tax

Equity

Retained Earnings

Common stock

Dividends paid out

Interest paid out

Assets

Cash & equivFCF

CFO *

CFI*

*Modified to remove effects of non-operating cash flows

Cash flow available to capital providers after all investments (DIC) are made with roi > k

Free Cash Flow FCF = CFO* + CFI*

CFO = NP + DX + ∆T –DNOWC* - DG

CFO* = CFO - IDI∙(1-t) + IX∙(1-t) -DOCE = NP + DX + ∆T –DNOWC – DG -

IDI∙(1-t) + IX∙(1-t)

= EBIT ·(1 – t) – IX·(1 – t) + DX + ∆T - ∆NOWC – DG

-IDI∙(1-t) + IX∙(1-t) -

= (EBIT – IDI)·(1 – t) + ∆T + DX - ∆NOWC – DG

= NOPAT + DX - ∆NOWC – DG

5

At Fairway Corp• All IDI and IX income/ expenses

are in cash • Investment securities, IS, are

non-operating assets Note• DNOWC = DNOWC* +DOCE

CFI = -CX + DIS + CS

CFI* = CFI – DIS= -CX + DIS + CS – DIS = - CX + CS

Free Cash Flow FCF = CFO* + CFI*

FCF = NOPAT + DX - ∆NOWC – DG - CX + CS

-DG = -CS + CC (from part 1, slide 10)

FCF = NOPAT – DNOWC – CX + DX + CC

-DNFA = -CX + DX + CC (from part 1, slide 11)

FCF = NOPAT – DNOWC - DNFA = NOPAT – DIC

6

Free Cash Flow: Summary

7

FCF = NOPAT – DIC = NOPAT – DNFA – DNOWC

NOPAT = EBIT·(1 – t) +DT

DNFA = CX – DX - CC

DNOWC = DAR + DINV + DOCE – DAP – DITP

If DT = 0 and CC = 0 (no change in deferred taxes and sell only fully depreciated assets)

FCF = EBIT·(1 – t) + DX – CX – DNOWC

If DX = CX and DNOWC = 0 (steady state)

FCF = EBIT·(1 – t)

8

Homework 17• Determine the free cash flow for Fairway Corp for

the year ending Dec. 2015.

9

Balance Sheet For Simple Corp

Net Operating

Assets

Invested Capital

Capital

10

Balance Sheet For LeanTech

Net Operating

Assets

Invested Capital

Capital

11

Harvard VC Case “LeanTech”

12

Harvard VC Case “LeanTech”

13

Fair Value of Simple Corp

Book value of invested capital, IC

(net operating assets)

NWC + NFC

Fair value, V, of invested

capital, IC (net operating

assets)

$

From balance sheet

From present value of future free cash flows discounted at cost of capital

Fair value, V, of capital

(debt, D, and equity, E)

(Rate) Cost of Capital• A firm’s cost of capital is equal to the capital

provider’s expected return on the market value of her investment o k = weighted average cost of capital o kE = cost of equity o kD = cost of debt o D = market value of debto E = market value of equityo V = market value of net operating asserts

= market value of capital

14

(Rate) Cost of Equityo The rate cost of equity capital, kE, is equal to the expected

return rate on the market value of the firm’s equity capital, E[rE]

o For LeanTech, the expected cost and return rate were negotiated. Remember that it was 50% annually in the first scenario.

o For a publically traded stock, we need a model

• The most common model is the CAPM model

E[rE] = rF + additional expected return for a risky investment in a firm’s equity

rF = risk free rate15

(Rate) Cost of Equityo The CAPM model was developed with a number of

assumptions, but is presented intuitively here

E[rM - rF] = expected value of the equity market risk premium or the equity market excess return rate (over the risk free rate)

b = a measure of expected risk in the stock’s excess return rate relative to the expected excess return

rate of the

16

17

Example

SPY MSFT 10 Years, monthly sampling Dec 2005 to Dec 2015

18

Calibrate CAPM• Determine b from a linear regression on historical excess return

pairs

o M is the total equity market • Typical proxy is S&P 500 total return with its typical proxy SPY

(1993)• or VFINX (1980)

o F is the risk free asset• Typical proxy is zero coupon treasuries of some ‘duration’

o E is the equity for which the cost of capital, kE, is sought, e.g., WMT• Typical historical sampling frequency is a week or a month• Balance between too much (noisy) and too little data • Typical backtest periods are 3, 5 or 10 years

19

S&P500 v. Total US Market

20

CAPM

k is the index for historical excess rate pairs

21

CAPM

22

CAPM

23

CAPM LM Summary

b

a

R2

24

Calibrate CAPM• This linear model estimates the monthly b and a

o These are ‘raw’ parameterso Financial information services may adjust parameters

• CAPM assumes a is zero looking forwardo No excess return without taking b risk

• Thus far, this is a monthly cost of equity, kE, or a monthly expected rate of return on equity, E[rE]

• Approximate the annual rates by multiplying by 12

25

WMT Example • Monthly cost of equity capital

• Using the current ten year Treasury rate, ^TNX, 2.238% annual

• And kE annual

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Risk and Return

E[rM - rF]

kEE[rE]

rF

b

27

Risk and Return

E[sE]

E[rE ]

rF

SE

SE = Sharpe Ratio

Note: Sharpe ratio computed with historical data, then annualized mean and standard deviations

28

WMT Example

E[sE]

E[rE ]

rF

S

S = Sharpe Ratio

29

Approximation

30

Final Exam Part 1 (~HW18)• Determine the a and b for Microsoft, MSFT, using R’s linear model

o Use 10 years of monthly datao Use ^TNX (10 year Treasury rates) for the risk free rate of return and SPY for the market rate of

returno Summarize the quality of the regression

• Plot the scatter diagram of historical excess rate pairs and the regression line

• Compute the mean and the standard deviation of the simple and excess rates for MSFT and for SPY

• Compute the monthly and then the annualized rate cost of equity, kE, for MSFT

• Compute the annualized market risk premium

• Compute the annualized Sharpe ratios for MSFT and SPY from the annualized mean excess rates of return and the annualized standard deviation of rates of return