Capital Part 2

1. Capital
Part 2

2. Statement of Cash Flows
2

3. Cash Flows
3
Net cash from
operating activities
Net cash from
investing activities
Net cash from
financing activities
∆CE = CFO + CFI + CFF
Liabilities
Non-interest bearing
Debt
Deferred tax
Equity
Retained Earnings
Common stock
Assets
Cash &
equiv

4. 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 & equiv
FCF
*Modified to remove effects of non-
operating cash flows
Cash flow available to capital
providers after all investments (DIC)
are made with roi > k

5. 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

6. 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

7. 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.
8

9. Balance Sheet For Simple
Corp
9
Net Operating
Assets
Invested
Capital
Capital

10. Balance Sheet For
LeanTech
10
Net Operating
Assets
Invested
Capital
Capital

11. Harvard VC Case “LeanTech”
11

12. Harvard VC Case “LeanTech”
12

13. Fair Value of Simple Corp
13
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
V= D+E
=
FCFi
(1+k)i
i=1
N
å
Fair value, V, of
capital
(debt, D, and
equity, E)

14. (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 debt
o E = market value of equity
o V = market value of net operating asserts
= market value of capital
14
k = kD ×(1 - t) ×
D
V
+ kE ×
E
V
V= D+E
=
FCFi
(1+k)i
i=1
N
å

15. (Rate) Cost of Equity
o 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 rate
15
kE =E rE[ ]

16. (Rate) Cost of Equity
o 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
E rE[ ]= rF + b ×E[rM-rF ]
E rE -rF[ ]= b ×E[rM -rF ]
b =
E rE -rF[ ]
E[rM -rF ]

17. Example
17
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
18
rMk
- rFk
, rEk
-rFk
( )

19. S&P500 v. Total US Market
19

20. CAPM
20
rMk
-rFk
, rEk
-rFk
( )
k is the index for historical
excess rate pairs

21. CAPM
21
yk
=b × xk
+ a + ek
rEk
-rFk
é
ë
ù
û= b × rMk
-rFk
é
ë
ù
û+ a+ ek
rMk
-rFk
, rEk
-rFk
( )

22. CAPM
22
yk
=b × xk
+ a + ek
rEk
-rFk
é
ë
ù
û= b × rMk
-rFk
é
ë
ù
û+ a+ ek
rMk
-rFk
, rEk
-rFk
( )

23. CAPM LM Summary
23
b
a
R2

24. Calibrate CAPM
• This linear model estimates the monthly b and a
o These are ‘raw’ parameters
o Financial information services may adjust parameters
• CAPM assumes a is zero looking forward
o 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
24
kE
= E rE
é
ë
ù
û=rF
+b ×E[rM
-rF
]

25. WMT Example
• Monthly cost of equity capital
• Using the current ten year Treasury rate, ^TNX, 2.238% annual
• And kE annual
25
kE
=rF
+b ×E[rM
-rF
]
kE
=
2.238
100×12
+ 1.0216×.00796
= .00999
kE
» .00999×12=11.98%

26. Risk and Return
26
E[rM - rF]
kE
E[rE]
rF
b
kE =E rE[ ]= rF + b ×E[rM-rF ]

27. Risk and Return
27
E[sE]
E[rE ]
rF
SE
E[rE
-rF
]=SE
×E[sE
]
E[rE
]=rF
+SE
×E[sE
]
SE
=
E[rE
-rF
]
E[sE
]
SE = Sharpe Ratio
Note:
Sharpe ratio computed with historical data, then annualized mean
and standard deviations

28. WMT Example
28
E[sE]
E[rE ]
rF
S
SE
=
mean[rE
-rF
]×12
[sE
]×12.5
=
.00796×12
.07204×12.5
=
0.09552
0.24955
=.383
S = Sharpe Ratio

29. Approximation
29
r rE
,rM( )≈r rE
-rF
é
ë
ù
û, rM
-rF
é
ë
ù
û( )
b rates( )≈b excessrates( )
s rates( )≈s excessrates( )
bE
» rE,M
×
sE
sM

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 data
o Use ^TNX (10 year Treasury rates) for the risk free rate of return and SPY for the market rate of return
o 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
30