# Chapter 19 Financing and Valuation by img20336

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```									               Chapter 19
Financing and Valuation
• Recall that there are three questions in
corporate finance.
• The first regards what long-term
investments the firm should make (the
capital budgeting question).
• The second regards the use of debt (the
capital structure question).
• This chapter is the nexus of these
questions.                        1
The 3 Methods for Valuation

1. After Tax WACC
2. Flow of Equity Method

2
Method 1
After Tax WACC

D        E
WACC  rD  (1  Tc )      rE  
V        V

3
After Tax WACC
Example - Sangria Corporation

The firm has a marginal tax rate of 35%. The cost of equity is 12.4% and
the pretax cost of debt is 6%. Given the book and market value balance
sheets, what is the tax adjusted WACC?

Balance Sheet (Book Value, millions)
Assets            1,000       500    Debt
500    Equity
Total assets      1,000      1,000 Total liabilities

Balance Sheet (Market Value, millions)
Assets            1,250       500      Debt
750      Equity
Total assets      1,250      1,250 Total liabilities

4
After Tax WACC
Example - Sangria Corporation - continued

The company would like to invest in a perpetual
crushing machine with cash flows of \$1.731
million per year pre-tax.
Given an initial investment of \$12.5 million, what
is the value of the machine?

5
Remember with WACC Approach !

• Since tax shield is accounted for in the
cost of capital, calculate cash flows as if
the company is all equity financed.
• WACC approach values the assets and
operations of the company. If you are
interested in equity value, do not forget to
subtract the value of the company’s debt.

6
Capital Budgeting
• The value of a business or Project is usually
computed as the discounted value of FCF out to
a valuation horizon (H).
• The valuation horizon is sometimes called the
terminal value.

FCF1       FCF2                 FCFH           PVH
PV                          ...               
(1  wacc) (1  wacc)
1           2
(1  wacc) H
(1  wacc) H

7
Example: Rio Corporation
Latest year                  Forecast
0      1      2       3         4          5          6
1   Sales                                  83.6    89.5   95.8   102.5     106.6      110.8      115.2
2   Cost of goods sold                      63.1   66.2   71.3    76.3      79.9       83.1         87
3   EBITDA (1-2)                            20.5   23.3   24.4    26.1      26.6       27.7       28.2
4   Depreciation                             3.3    9.9   10.6    11.3      11.8       12.3       12.7
5   Profit before tax (EBIT) (3-4)          17.2   13.4   13.8    14.8      14.9       15.4       15.5
6   Tax                                        6    4.7    4.8     5.2       5.2        5.4        5.4
7   Profit after tax (5-6)                  11.2    8.7      9     9.6       9.7         10       10.1
8   Investment in fixed assets                11   14.6   15.5    16.6        15       15.6       16.2
9   Investment in working capital              1    0.5    0.8     0.9       0.5        0.6        0.6
10   Free cash flow (7+4-8-9)                 2.5    3.5    3.2     3.4       5.9        6.1          6

PV Free cash flow, years 1-6          20.3                        113.4 (Horizon value in year 6)
PV Horizon value                      67.6
PV of company                         87.9     OCF=Profit After Tax + Depreciation

8
Example: Rio Corporation – continued - assumptions
Assumptions

Sales growth (percent)              6.7      7        7       7      4       4        4          3
75.5     74     74.5    74.5     75      75     75.5         76
13.3     13       13      13     13      13       13         13
79.2     79       79      79     79      79       79         79
5     14       14      14     14      14       14         14

Tax rate, percent                  35%
WACC                                9%
Long term growth forecast           3%

Fixed assets and working capital
Capital spending

Gross fixed assets                   95   109.6   125.1   141.8   156.8   172.4   188.6       204.5
Less accumulated depreciation        29    38.9    49.5    60.8    72.6    84.9    97.6       110.7
Net fixed assets                     66    70.7    75.6    80.9    84.2    87.5      91        93.8
Depreciation                        3.3     9.9    10.6    11.3    11.8    12.3    12.7        13.1
Working capital                    11.1    11.6    12.4    13.3    13.9    14.4      15        15.4

Investment in NWC
9
Example: Rio Corporation – continued

FCF = Profit after tax + depreciation - investment in fixed assets
- investment in working capital

FCF = 8.7 + 9.9 – (109.6 - 95.0) – (11.6 - 11.1) = \$3.5 million

PV (FCF) = 3.5/(1.09) + 3.2/(1.09^2) + 3.4/(1.09^3) + 5.9/(1.09^4) + 6.1/(1.09^5)
+ 6.0/(1.09^6) = 20.3

10
Example: Rio Corporation – continued

FCFH 1  6.8 
Horizon Value  PVH                         113.3
wacc  g  .09  .03 
1
PV(horizon value)           113.3  \$67.6
1.096

PV(busines s)  PV(FCF)  PV(horizon value)
 20.3  67.6
 \$87.9 million                       11
Things to Consider

1. Don’t value mechanically – for terminal
value it might be wise to use knowledge
about mature firms in the industry.
2. Liquidation value.

12
In Practice

How are costs of financing determined?
–   What is included in debt?
–   What if there are other securities?
–   How do we determine debt return?
–   How do we determine preferred stock return?
–   What if project has a different leverage ratio?
–   How do we determine equity return for a firm that
than what we observe in the stock market?

13
Project with Different Leverage
Perpetual Crusher project at 20% D/V
•    rD is constant at 6% (at all debt levels up to 40%)
•    At 40%: rE=12.4% ; Tc=35%  WACC = 9%

1.   Step 1: unlever the firm to find rA, the cost of capital
(WACC) in an all equity firm.
2.   Step 2: Find rE when Debt is 20% (note D/E =
0.2/0.8=25%)
3.   Step 3: Recalculate WACC

14
Example : Calculating WACC
• World-Wide Enterprises (WWE) is planning to enter
into a new line of business (widget industry)
• American Widgets (AW) is a firm in the widget industry
with an estimated beta of 1.5.
• WWE has a D/E of 1/3, AW has a D/E of 2/3.
• Borrowing rate for WWE is10 %
Borrowing rate for AW is 12 %
• Given: Market risk premium = 8.5 %, Rf = 8%, Tc= 40%
• What is the appropriate discount rate for WWE to use
for its widget venture?

15
Example : Calculating WACC

A four step procedure to calculate discount
rates:

1. Determining AW’s cost of Equity Capital (rE)
2. Determining AW’s Hypothetical All-Equity
Cost of Capital. (rA)
3. Determining rE for WWE’s Widget Venture
4. Determining rWACC for WWE’s Widget
Venture.
16
Beta and Leverage: No Corp.Taxes
• In a world without corporate taxes, and with riskless
corporate debt, it can be shown that the relationship
between the beta of the unlevered firm (beta of assets)
and the beta of levered equity is:
Equity
β Asset          β Equity
Asset

 In a world without corporate taxes, and with risky
corporate debt, it can be shown that the relationship
between the beta of the unlevered firm and the beta of
levered equity is:
Debt             Equity
β Asset         β Debt          β Equity
Asset            Asset                 17
Beta and Leverage: with Corp. Taxes
• In a world with corporate taxes, and riskless debt, it can
be shown that the relationship between the beta of the
unlevered firm and the beta of levered equity is:
    Debt            
 Equity  (1  TC )  β Asset
βEquity  1                  
                    

     Debt              
 Since 1  Equity  (1  TC )  must be more than 1 for a
                       
                       

levered firm, it follows that     βEquity  β Asset

18
Beta and Leverage: with Corp. Taxes

• If the beta of the debt is non-zero, then:
D
βEquity  β Asset  (1  TC )( β Asset  βDebt ) 
E

19
Method 2
Flow to Equity Approach
• Discount the cash flow from the project to the
equity holders of the levered firm at the cost of
levered equity capital, rE.

• There are three steps in the FTE Approach:
– Step One: Calculate the levered cash flows
– Step Two: Calculate rE.
– Step Three: Valuation of the levered cash
flows at rE.
20
Flow to Equity
Sangria Corporation - continued
The company would like to invest in a perpetual
crushing machine with cash flows of \$1.731
million per year pre-tax. Given an initial
investment of \$12.5 million, what is the value of
the machine?
Remember: rE = 12.4%, D=\$5million (40% of
project’s cost), rD = 6%, TC=35%.

21
Method 2
APV = Base Case NPV+ PV Impact
1. Base Case = All equity finance NPV –
Discount unlevered cashflow by
unlevered cost of equity (rA), assuming
not tax world.
2. PV Impact = all costs/benefits directly
resulting from project
- Discount all cost/benefits of financing
according to their particular risk.
22
Sangria Corporation - continued
The company would like to invest in a perpetual
crushing machine with cash flows of \$1.731
million per year pre-tax. Given an initial
investment of \$12.5 million, what is the value of
the machine?
Remember: rE = 12.4%, D=\$5million (40% of
project’s cost), rD = 6%, TC=35%.

23
Side Effects in APV – Easy to Add Up

Example:
Project A has an NPV of \$150,000. In
order to finance the project we must issue
stock, with a brokerage cost of \$200,000.
Project B has a NPV of -\$20,000. We can
issue debt at 8% to finance the project.
The new debt has a PV Tax Shield of
\$60,000.
Summary: APV, FTE, and WACC
APV      WACC      FTE
Initial Investment        All      All       Equity Portion
Cash Flows                Unlevered Unlevered Levered
Discount Rates            rA       rWACC     rE
PV of financing effects   Yes      No        No

Which approach is best?
Use APV when the level of debt is constant
Use WACC and FTE when the debt ratio is constant
– WACC is by far the most common
– FTE is a reasonable choice for a highly levered firm
25
A Comparison of the APV, FTE, and
WACC Approaches
• All three approaches attempt the same task: valuation in
the presence of debt financing.
• Guidelines:
– Use WACC or FTE if the firm’s target debt-to-value
ratio applies to the project over the life of the project.
– Use the APV if the project’s level of debt is known
over the life of the project.
• In the real world, the WACC is the most widely used
approach by far.

26
The Three Methods
1. The APV formula can be written as:

UCFt                        Initial
NPV                   effects of 
t 1 (1  rA )
t
investment
debt

2. The FTE formula can be written as:

LCFt        Initial       Amount 
NPV                    investment  borrowed 
                       
t 1 (1  rE )
t
                       
3. The WACC formula can be written as
                    Initial
UCFt
NPV                     
t 1 (1  r ACC )
t
W          investment             27
Some Practical Issues
1.   APV and NPV basically mean the same thing.
2.   The three approaches will most likely yield different
NPVs.
3.   The APV is useful when special financing
considerations are tied to the particular project.
4.   WACC most common – has an intuitive appeal, a
project should be accepted if its rate of return is
higher than the weighted average cost of capital.

28
WACC Approach

WACC approach is the most widely used because of its
relative simplicity.
WACC is only appropriate as a discount rate for a project
when:

1. The project has similar systematic business risk as the
firm.
2. The project and firm have the same debt capacity.
3. The debt to equity ratio is presumed to stay constant
throughout the life of the project.

29
Discounting Safe Cash Flows
(for APV Approach)
Safe (risk-free) cash flows are discounted by the
after tax borrowing rate rD(1-TC). This may be
applied for issues such as subsidized loans and
depreciation tax shields.
Example: The company is granted a one-year
subsidized loan of \$100k at 5%. The company’s
borrowing rate is 13% and its tax rate 35%.
What is the NPV of the loan?

30
PMM’s Project Valuation - APV

Suppose PMM Inc. has an investment that costs
\$10,000,000 with expected EBIT (cash flows from
operations) of \$3,030,303 per year forever. The
investment can be financed either with \$10,000,000 in
equity or with \$5,000,000 of 10% debt and \$5,000,000
of internally generated (equity) cash flows. The
discount rate on an all-equity-financed project with this
kind of risk is 20%. The firm's marginal tax rate is 34%.
1.   Using the APV approach – find whether the project
should be pursued if financed with equity only.
2.   Using the APV approach – find whether the project
should be pursued if financed with 50% debt.

31
PMM’s Project Valuation with Subsidy

Extension 1 : Subsidized (or below-market-rate)
financing
Suppose a municipal government decides that the
investment is socially (and politically) desirable and
agrees to raise the \$5,000,000 debt financing as a
municipal bond, or 'muni.' PPM Inc. can effectively
borrow \$5,000,000 at the municipality's borrowing rate,
rD = 7%. (Interest income on a muni is exempt from
Federal tax, so the muni rate is typically below the rate
on corporate debt.)
Using APV approach – find the effect of this subsidy on
APV.

32
PMM’s Project Valuation with Subsidy

Extension 2 : Flotation Costs
When a company raises funds through external debt or
equity, it must incur flotation costs. Assume that the
municipal government no longer sponsored the project
and PPM Inc. must obtain \$5,000,000 with new debt at
the market interest rate of 10%. Flotation costs are
12.5% of gross proceeds. Assume that the Canadian tax
code allows this expense to be amortized over five
years.
Using APV approach – find the effect of flotation costs
on APV.

33
PMM’s Project Valuation – Flow to Equity

Suppose PMM Inc. has an investment that costs
\$10,000,000 with expected EBIT (cash flows from
operations) of \$3,030,303 per year forever. The
investment can be financed with \$5,000,000 of 10%
debt and \$5,000,000 of internally generated (equity)
cash flows. The discount rate on an all-equity-financed
project with this kind of risk is 20%. The firm's marginal
tax rate is 34%. Assume D/E = 50/67.
Using the Flow to equity approach find whether the
project should be pursued if financed with 50% debt.

34
PMM’s Project Valuation – WACC

Suppose PMM Inc. has an investment that costs
\$10,000,000 with expected EBIT (cash flows from
operations) of \$3,030,303 per year forever. The
investment can be financed with \$5,000,000 of 10%
debt and \$5,000,000 of internally generated (equity)
cash flows. The discount rate on an all-equity-financed
project with this kind of risk is 20%. The firm's marginal
tax rate is 34%. Assume D/E = 50/67.
Using the WACC approach find whether the project
should be pursued if financed with 50% debt.

35
Pearson Company Project Valuation
Consider a project of the Pearson Company, the timing
and size of the incremental after-tax cash flows for an
all-equity firm are:
-\$1,000     \$125          \$250          \$375        \$500

0             1            2             3           4
The unlevered cost of equity of Pearson is rA = 10%.
The firm plans to finance the project with \$600 of debt
carrying an 8% interest. The overall debt to equity target
ratio of the firm is 1.5 and the corporate tax rate is
TC=40%. Calculate the NPV of the project according to
(1) APV, (2) Flow to equity, (3) WACC.
36
Pearson’s - Flows to Equity Approach

Switching from unlevered to levered cash flows.

CF3 = \$375 -28.80    CF4 = \$500 -28.80 -600
CF2 = \$250 -28.80
CF1 = \$125-28.80
-\$400        \$96.20     \$221.20      \$346.20    -\$128.80

0           1            2           3           4   37
Example: Worldwide Trousers
Worldwide Trousers, Inc. is considering a \$5 million
expansion of their existing business. The initial
expense will be depreciated straight-line over five
years to zero salvage value. The pretax salvage value
in year 5 will be \$500,000. The project will generate
pretax earnings (EBDIT) of \$1,500,000 per year, and
not change the risk level of the firm. The firm can
obtain a five-year \$3,000,000 loan at 12.5% to
partially finance the project. If the project were
financed with all equity, the cost of capital would be
18%. The corporate tax rate is 34%, and the risk-free
rate is 4%.
The project will require a \$100,000 investment in net
working capital. Calculate the NPV using the APV,
WACC, and flow to equity approaches.
38
Relative Valuation

Valuing a company relative to
another company

39
Relative vs. Fundamental Valuation
The DCF (WACC, FTE, APV) model of valuation is
a fundamental method.
• Value of firm (equity) is the PV of future cash
flows.
• Ignores the current level of the stock market
(industry).
• Appropriate for comparing investments across
different asset classes (stocks vs. bond vs. real
estate, etc).
• In the long run, fundamental is the correct way of
value any asset.

40
Relative vs. Fundamental Valuation
Relative valuation is based on P/E ratios and a host of
other “multiples”.
• Extremely popular with the press, CNBS, Stock brokers
• Used to value one stock against another.
• Can not compare value across different asset classes
(stocks vs. bond vs. real estate, etc).
• Can not answer the question is the “stock market over
valued?”
• Can answer the question, “I want to buy a tech stock,
• Can answer the question, “Which one of these
overpriced IPO’s is the best buy?”
41
Relative vs. Fundamental Valuation
You are investing for your retirement. You
are planning to take a buy and hold
strategy which involves picking some fairly
priced stocks and holding them for several
years. Which valuation approach should
you use?
Relative or fundamental?

42
Relative vs. Fundamental Valuation
You are a short term investor. You trade
account, and rarely hold a stock for more
than a month. Which valuation technique
should you use?
Relative or fundamental?

43
Relative Valuation
Prices can be standardized using a common variable such as earnings,
cashflows, book value, or revenues.
-     Earnings Multiples
•    Price/Earning ratio (PE) and variants
•    Value/EBIT
•    Value/EBDITA
•    Value/Cashflow
•    Enterprise value/EBDITA
-     Book Multiples
•    Price/Book Value (of equity) PBV
-     Revenues
•    Price/Sales per Share (PS)
•    Enterprise Value/Sales per Share (EVS)
-     Industry Specific Variables (Price/kwh, Price per ton of steel, Price per
click, Price per labor hour)

44
Multiples
Relative valuation relies on the use of multiples and a little
algebra.
For example: house prices.
House             Price            Sq ft           Price per sq ft
A                 \$ 110,000        1,700           \$ 64.71
B                 \$ 120,000        1,725           \$ 69.57
C                 \$ 96,000         1,500           \$ 64.00
D                 \$ 99,000         1,550           \$ 63.87
E                 \$ 105,000        1,605           \$ 65.42
Average     \$65.51
What is the price of a 1,650 sq ft house?
45
Answer: 1650 × 65.51 = \$108,092
To use a multiple intelegantly you must:
•    Know what are the fundamentals that determine the
multiple.
•    Know how changes in these fundamentals change the
multiple.
•    Know what the distribution of the multiple looks like.
•    Ensure that both the denominator and numerator
represent claims to the same group
•    - OK: P/E – Price  equityholders, EPS  equityholders
•    - Not OK: P/EBIT – Price equityholders, EBIT  All claimants
•    Ensure that firms are comparable.

46
Price Earnings Ratios
PE – Market price per share / Earnings per share
There are a number of variants of the basic PE ratio in use.
They are based on how the price and earnings are
defined.

•    Price
- current price
- or average price for the year
•    Earnings
- most recent financial year
- trailing 12 months (Trailing PE)
- forecasted eps (Forward PE)

47
PE Ratio: Understanding the Fundamentals

basic equity discounted cash flow model.

•   With the dividend discounted model
Div1
P0 
re  g

•   Dividing both sides by EPS
P0     Payout ratio  (1  g )

EPS 0          re  g
48
PE Ratio: Understanding the Fundamentals

Holding all else equal
• higher growth firms will have a higher PE ratio
than lower growth firms.
• higher risk firms will have a lower PE ratio
than low risk firms.
• Firms with lower reinvestment needs will have
a higher PE ratio than firms with higher
reinvestment needs.
Of course, other things are difficult to hold equal
since high growth firms, tend to have high risk
and high reinvestment rates.

49
150
100   Graph PE ratio (Amir Rubin)
VW_PE

50
0

1975q1   1980q1   1985q1      1990q1   1995q1   2000q1   2005q1
stata_qtr

50
Is low (high) PE cheap (expensive)?

• A market strategist argues that stocks are
over priced because the PE ratio today is
too high relative to the average PE ratio
across time. Do you agree?

• Yes
• No
• If you do not agree, what factor might
explain the high PE ratio today?
51
A Question

You are reading an equity research report on
Informix, and the analyst claims that the stock is
undervalued because its PE ratio is 9.71 while
the average of the sector PE ratio is 35.51.
Would you agree?
• Yes
• No
• Why or why not?

52
Example: Valuing a firm using P/E ratios

• In an industry we identify 4 stocks which are similar
to the stock we want to evaluate.
Stock A   PE=14
Stock B   PE=18
Stock C   PE=24
Stock D   PE=21

• The average PE = (14+18+24+21)/4=19.25
• Our firm has EPS of \$2.10
• P/2.25=19.25 P=19.25*2.25=\$40.425
• Note – do not include the stock to be valued in the
average
• Also do not include firm with negative P/E ratios
53
Value/Cashflow

• PE ratios are from equityholders, while cash flow
measures are the whole firm.
• Cash flow is from continuing operations before
capital expenditure.
• FCF is uncommitted freely available cash flow
after capital expenditure to maintain operations at
the same economic level.
• FCFF (cash flow from assets) is free cash flow to
total firm
Value MVequity  MVdebt

FCFF            FCFF

• In the US in 1999, the mean value was 24.             54
Value/FCFF

• For a firm with a constant growth rate

FCFF0 (1  g )
V0 
wacc  g
V0    (1  g )

FCFF0 wacc  g

• Therefore, the value/FCFF is a function of the
– The cost of capital
– The expected growth rate
55
Example: Valuing using value/FCFF

•   Industry average is 20
•   Firm has FCFF of \$2,500
•   Shares outstanding of 450
•   MV of debt = \$30,000

• Using Value/FCFF=20
 value = FCFF*20
 MV equity + MV debt = FCFF*20
 MV equity = FCFF*20 – MV debt
 Price = (FCFF*20-MV debt)/Shares
Price = (\$2,500*20-\$30,000)/450 = 44.44
56
Alternatives to FCFF : EBDITA and EBIT

• Most analysts find FCFF to complex or messy to
use in multiples. They use modified versions.

• After tax operating income: EBIT (1-t)
• Pre tax operating income or EBIT
• EBDITA, which is earnings before interest, tax,
depreciation and amortization.

Value   MVequity  MVdebt

EBDITA       EBDITA

57
Value/EBDITA multiple

• The no-cash version

Value   MVequity  MVdebt  cash

EBDITA          EBDITA

• When cash and marketable securities are netted
out of the value, none of the income from the cash
or securities should be reflected in the
denominator.
• The no-cash version is often called “Enterprise
Value”.

58
Enterprise Value
• EV = market value of equity + market value of debt – cash
and marketable securities
• Many companies who have just conducted an IPOs have
huge amount of cash – a “war chest”
• EV excludes this cash from value of the firm
• Cash +MV of non-cash assets = MV debt + MV equity
 MV of non-cash assets = MV debt + MV equity - Cash

For example: Nasdaq AWRE (did IPO in 1996)
Its 1996 cash was \$31.1 million, Total assets = \$40.1 million,
Debt=0  EV=\$9 million.

For young firms it is common to use EV instead of Value.
59
Reasons for increased use of Value/EBDITA

1. The multiple can be computed even for firms
that are reporting net losses, since EBDITA
are usually positive.
2. More appropriate than the PE ratio of high
growth firms.
3. Allows for comparison across firms with
different financial leverage.

60
Price to Book Value Ratio

The measure of market value of equity to book value of
equity.

P MV equity

B BVequity

61
Price Book Value Ratio: Stable Growth Firm
•     Going back to dividend discount model,         Div1
P0 
re  g
•     Defining the return on equity (ROE)=EPS0/BV0 and realizing that
div1=EPS0*payout ratio, the value of equity can be written as
BV0  ROE  payout ratio  (1  g )
P0 
re  g
P0         ROE  payout ratio  (1  g )
 PVB 
BV0                  re  g

•     If the return is based on expected earnings (next period)

P0         ROE  payout ratio
 PVB 
BV0               re  g
62
Price Sales Ratio
•   The ratio of market value of equity to the sales

P   MVequity

S Total Revenue

•   Though the third most popular ration it has a fundamental
problem.
- the ratio is internally inconsistent.

63
Price Sales Ratio
•   Using the dividend discount model, we have
Div1
P0 
re  g
•   Dividing both sides by sales per share and remembering that
Earnings per share
Profit margin 
Sales per share
•   We get

P0          Profit margin  payout ratio  (1  g )
 PS 
sales0                       re  g

64
Price Sales Ratio and Profit Margin
•       The key determinant of price-sales ratio is profit margin.
•       A decline in profit margin has a twofold effect
–      First, the reduction in profit margin reduces the price-sales ratio
directly
–      Second, the lower profit margin can lead to lower growth and
indirectly reduce price-sales ratio.

Expected growth rate = retention rate * ROE
 retention ratio *(Net profit/sales)*( sales/book value of equity)

 retention ratio * (profit margin) * (sales/ BV of equity)

65
Inconsistency in Price/Sales Ratio
•   Price is the value of equity
•   While sales accrue to the entire firm.
•   Enterprise to sales, however, is consistent.

EV0     MV equity  MV debt - Cash

sales0             re  g

•   To value a firm using EV/S
•   Compute the average EV/S for comparable firms
•   EV of subject firm = average EV/S time subject’s firm projected
sales
•   Market value = EV – market debt value + cash

66
Choosing between the Multiples
•    There are dozen of multiples
•    There are three choices
– Use a simple average of the valuations obtained
using a number of different multiples
– Use a weighted average of the valuations obtained
using a number of different multiples (one ratio may
be more important than another)
– Choose one of the multiples and base your
valuation based on that multiple (usually the best
way as you provide some insights why that multiple
is important – remember car industry video
segment)

67
Real Options – Chapter 22

4 types of “Real Options”
1 - The opportunity to expand and make follow-up
investments.
2 - The opportunity to “wait” and invest later.
3 - The opportunity to shrink or abandon a project.
4 - The opportunity to vary the mix of the firm’s
output or production methods.

Value “Real Option” = NPV with option
- NPV w/o option
68
Microcomputer Forecasts
Example – Mark I Microcomputer (\$ millions)

Year
1982     1983   1984      1985   1986    1987
After-tax operating cash flow (1)                 110    159       295     185       0
Capital investment (2)                     450      0       0        0       0       0
Increase in working capital (3)              0     50    100       100    -125    -125
Net cash flow (1)-(2)-(3)                 -450     60     59       195     310     125

NPV at 20% = - \$46.45, or about -\$46 million

69
Microcomputer Forecasts
Your comment – If we do not launch the Mark I, it
will probably be too expensive to enter the micro
market later, when Apple and IBM are firmly
established. In other words, we lose the option to
produce the Mark II Microcomputer.

Assumptions:
1) The decision on Mark II will take place 3 years from now, in
1985.
2) The investment in Mark II is double that of Mark I, i.e., \$900m.
3) Forecasted cash flows are also doubled, with PV of \$807m in
1985, and \$467m in 1982.
4) Assume standard deviation of 35% for cashflow uncertainty.
5) Annual riskfree rate is 10%.
70
Microcomputer Forecasts
Example – Mark II Microcomputer (\$ millions)
Forecasted cash flows from 1982
Year
1982   ……….   1985     1986   1987   1988   1989        1990
After-tax operating cash flow                                  220    318    590    370           0
Increase in working capital                                    100    200    200   -250        -250
Net cash flow                                                  120    118    390    620         250
Present Value @ 20%                     467          807
Investment, PV @ 10%                    676          900
Forecasted NPV in 1985                               -93

NPV(1982) =PV(inflows) -PV(investment)
= 467 – 676
= - \$209 million

71
Microcomputer Forecasts
Example – Mark II Microcomputer (1985)
Distribution of possible Present Values
Probability

Present value in 1985
Expected value        Required investment
(\$807)                 (\$900)                           72
Restaurant Investment
You have negotiated a deal with a major restaurant chain to open one
of its restaurants in your home town. The terms of the contract
specify that you must open the restaurant either immediately or in
exactly one year. If you do neither, you lose the right to open the
restaurant. It will cost you \$5 million to open the restaurant,
whether you open it now or in one year. If you open the restaurant
immediately, you expect to generate \$600,000 in free cash flow the
first year. While future cash flow vary with the consumer tastes,
they are expected to grow at a rate of 2% per year. The risk free
rate is 5% , the appropriate cost of capital for this investment is
12%, and the return volatility of publicly traded comparable firms is
40%.
a. What is the NPV of the project if you open today?
b. What is the NPV of the project if you delay the opening and wait the
year?

73
Option Valuation
There are two ways to calculate the value of an option.
1. Find the combination of stock and loan that replicates
an investment in the option. Since the two strategies
give identical payoffs in the future, they must sell for
the same price today. This is basically how one
derives the B&S formula.
2. Since option pricing does not depend on risk aversion
of investors, we can pretend that all investors are
indifferent to risk, work out the expected future value of
the option in such a world, and discount it back at the
risk-free rate to give the current value. This is called
risk-neutral pricing.

74
Growth Option
StartUp Incorporated is a new company whose only asset
is a patent on a new drug. If produced, the drug will
generate certain profits of \$1 million per year for the
life of the patent, which is 17 years (after then,
competition will drive profits to zero). It will cost \$10
million to produce the drug. Assume that the yield on a
17 year risk free annuity is currently 8% per year.
a. What is the value of the patent?
b. Now assume interest rates will change in exactly one
year. At that time, all risk-free interest rates in the
economy will be either 10% per year or 5% per year,
and then will remain at that level forever. What is the
value of the patent?
75
Option to Wait
Malted Herring Plant Valuation
The project costs \$180, either
200 (NPV = 200-180 = 20)
now or later. Waiting means
loss of first year’s cash flows.
Assume risk free rate is 5%.

Cash flow = 16         Cash flow = 25        Year 1 cash flows

Cash flow = 250      PV of Year 2 on
Cash flow = 160                                              cash flows
Option value = 0                 Option value = 250-80=70

76
Option to Wait

Real Estate Development
Suppose you own a slot of vacant land
that can be used for a hotel or an office
building, but not for both. To convert a
hotel to an office, or an office to a hotel
involves high costs. You may be reluctant
to invest, even if both investments have
positive NPVs.

77
Option to Wait

Example – Development option
Cash flow
Office Bldg

240
Office Bldg
NPV>0                   Wait

100

Cash flow
100           240
NPV<0                       from hotel
Hotel NPV>0

78
Option to Abandon
Example - Abandon
Mrs. Mulla gives you a non-retractable offer to buy your company for
\$150 mil at anytime within the next year. Given the following decision
tree of possible outcomes, what is the value of the offer (i.e. the put
option) and what is the most Mrs. Mulla could charge for the option?
Assume a discount rate of 10%
Year 0             Year 1            Year 2
120 (.6)
100 (.6)
90 (.4)
NPV = 145
70 (.6)
50 (.4)
40 (.4)
79
Option to Abandon
Example - Abandon
Mrs. Mulla gives you a non-retractable offer to buy your company for
\$150 mil at anytime within the next year. Given the following decision
tree of possible outcomes, what is the value of the offer (i.e. the put
option) and what is the most Mrs. Mulla could charge for the option?
Assume a 10% discount rate.

Year 0             Year 1            Year 2
120 (.6)
100 (.6)
90 (.4)
NPV = ?

150 (.4)

80
The Zircon Subductor Project
Information:
1)   The investment required is \$12m and may last up to 10 years.
Throughout the project life the company can sell the asset for a
certain salvage value that depreciates over time. At year 10 it is
worth \$5.99m.
2)   Revenues: \$2.5 million per year (at today’s prices). Revenues are
proportional to price. Risk-adjusted rate is 9%.
3)   The fixed cost are constant at \$700k per year and are risk fee.
Risk free discount rate is 6%.
4)   NPV without abandonment option is negative at \$ -1.108m.
5)   Prices of Subductor follow a random walk with a 20% standard
deviation. Assuming log normal distribution this leads to a
binomial tree of either 22% up or 82% down.

81
Option to Abandon

Example – Ms. East - Revenues
3.73

3.05

2.50                     2.50

2.05

1.68

82
Option to Abandon
Solving Procedure:
1) Have the salvage value in each of the years 1-10 (e.g.,
5% deprecation per year)
2) Start at far right (year t=10) and work recursively
backwards to the present. At year 10, the project is
valued at the ending salvage value.
3) Work backwards to year t-1, use risk neutral
probabilities to calculate PV of continuation project.
4) If salvage value of year t-1> PV of continuation value,
than the value at the nod=salvage value. If salvage
value< PV of continuation project then value at nod =
PV of continuation project.

83
Temporary Abandonment

• Suppose you own an oil tanker and you
million a year to operate and produces
\$5.25 in revenue.
• What happens if tanker rates go down by
10%, do you close the business
immediately?

84
Tanker Example

Value of
Tanker                   Value in
operation

Cost of
reactivating

Value if
Mothballing                    mothballed
costs

Tanker
Rates

85

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