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FIN201 | Managerial Finance - BASE | Fall 2021
SESSION 10: MID-COURSE REVIEW
Professors Peter DeMarzo & Paul Pfleiderer
Stanford Graduate School of Business
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SESSION 1:
INTRO
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GOOD DECISIONS
Every decision has
future consequences
Some are Costs …
and some are Benefits
What makes a Good
Decision?
Value of Benefits > Value of Costs
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Decision making follows from
valuation
The net benefit of a decision is referred
to as its Net Present Value:
NPV
= Value of Benefits − Value of Costs
= Contribution to Stakeholder Value
Good
decisions have
positive NPV!
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competitive market
A market in which an asset or good can be
either bought or sold at the same price.
When a competitive market price exists,
it determines the asset’s value for all investors.
law of one price
If an asset trades in a competitive market,
then all equivalent assets must trade for
the same price in every market.
Competitive
prices are
information!
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RULES OF TIME TRAVEL
FV: Compound (multiply by 1+r)
to move cash flows forward in
time
PV: Discount (divide by 1+r) to
move cash flows backward in
time
A2A: Only compare or combine
values at the same point in time
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NPV SUMMARY (RISK-FREE CASE)
To compute the NPV of an investment:
Determine incremental cash flows from the
decision
• Negative for outflows, positive for inflows
• Show the cash flows in a timeline
Use the current interest rate to convert risk-free
cash flows to present values
Combine present values of all costs and benefits
NPV = ∑ t
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FCFt
(1 + rt )t
NPV represents the net
benefit (in terms of $ today)
from making the investment
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SESSION 2:
TIME VALUE OF MONEY
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PERPETUITIES
Perpetuity
A series of equal payments at equally spaced intervals that goes on forever.
C1
PV =
r
0
1
2
3
C
C
C
Growing Perpetuity
A perpetuity with cash flows that grow at a constant rate g each period.
C1
PV =
r−g
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0
1
2
3
4
C
C x (1 + g)
C x (1 + g)2
C x (1 + g)3
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ANNUITIES
Annuity
Equal payments at the end of N equal intervals
0
1
2
N
C
C
C
1
1
C
C
C

−
=
1
−
PV (annuity) =
r
r  (1 + r )N
(1 + r)N r

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



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ANNUITIES
Annuity
Equal payments at the end of N equal intervals
0
Growing Annuity
0
1
2
N
C
C
C
1
2
N
C
C(1+g)
C(1+g)N-1
N+1
C(1+g)N
N
C
1
C(1 + g)N
C   1+ g  
PV (growing annuity) =
−
=
1 − 


N

r−g
r−g
r − g   1 + r  
(1 + r)
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KEY FORMULAS FOR CALCULATING PRESENT VALUES
PV of cash flows (generally)
CFt
𝑃𝑃𝑃𝑃 = �
t
t (1 + rt )
Applications: net-present value
𝑁𝑁𝑁𝑁𝑁𝑁 = �
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𝐹𝐹CFt
t
t (1 + rt )
Perpetuity and versions thereof
𝐶𝐶1
𝑟𝑟
PV of constant eternal
payments
𝑃𝑃𝑃𝑃0 =
PV of eternal payments
growing at constant rate
(Applications: e.g. Terminal value,
Dividend discount model)
𝐶𝐶1
𝑃𝑃𝑃𝑃0 =
𝑟𝑟 − 𝑔𝑔
PV of annuity (buying a perpetuity
today and selling a perpetuity in N)
(Applications: e.g. mortgage
payments, retirement income, ..)
𝐶𝐶1
1
𝑃𝑃𝑃𝑃0 =
1−
𝑟𝑟
1 + 𝑟𝑟
𝐶𝐶1
1 + 𝑔𝑔
𝑃𝑃𝑃𝑃0 =
1−
𝑟𝑟 − 𝑔𝑔
1 + 𝑟𝑟
PV of growing annuity
(Applications: e.g., retirement income)
𝑁𝑁
𝑁𝑁
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SESSION 3:
INTEREST RATES
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THE ROLE OF INTEREST RATES
Recall that a key input in our NPV calculation is the
cost of capital, which depends on interest rates:
NPV = ∑ t
FCFt
(1+ rt )t
For a typical project
• Costs occur upfront (initial investment in equipment, R&D, etc.)
• Benefits occur in the (sometimes distant) future
When interest rates go up
• Benefits are discounted at a higher rate, reducing their PV
• If the cash flows are the same ⇒ NPV falls
When interest rates fall
• Benefits are discounted at a lower rate, raising their PV
• If the cash flows are the same ⇒ NPV rises
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Low interest
rates stimulate
investment
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CAGRS, RATES, AND APRS
CAGRS
CAGR = compound annual growth rate
RATES
Given rate r per period
• Expresses a total gain in terms of a growth rate per year
• CAGR = (Final / Initial)1/N – 1
Equivalent 𝑛𝑛−period interest rate = 1 + 𝑟𝑟
APRs
𝑛𝑛
Given an APR with K compounding intervals/yr
K
Equivalent Annual Rate :
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 APR 
 1+
 = 1+EAR
K 

−1
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COMPUTING LOAN PAYMENTS
To compute loan payments, we can use the fact that
Loan Balance = PV(future payments)
where the PV is calculated using the loan interest rate
Most consumer loans (mortgages, car
loans) have equal payments over the
life of the loan
0
1
2
N-1
N
c
c
c
c



Annuity Factor
1
1
L c ×  1−
=
N
th
r
r
(1
)
+
• Given any 3, we can solve for the 4 …
 
• These are called fully amortizing loans
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given N payments
and discount rate r
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KEY POINTS TO REMEMBER
To compute loan
payments
To EVALUATE a
loan
To compare
alternatives
Loan Balance =
PV(Loan Pmts) using
the loan rate
Cost = PV(Loan Pmts)
at your opportunity
cost
Always focus on the
• What is your best
alternative use of the
funds (with
comparable risk)?
cash flows of each
alternative
Be sure to discount
based on opportunity
cost of funds
Compare PVs
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THE YIELD CURVE
• Often the 1-yr, 2-yr, … 10-yr
interest rates are not
identical
• This can be depicted in a
graph called a Yield Curve
U.S. Treasury Zero Coupon Yield Curve (2/18/11)
5%
Yield to Maturity
Interest rates depend on
the investment horizon
4%
3%
2%
1%
0.34%
0.85%
1.32%
1.87%
2.35%
2.82%
1
2
3
4
5
6
Maturity (years)
When discounting risk-free cash flows
• Discount cash flow in year t using the rate rt from the yield curve
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3.37%
3.88%
0%
0
NPV = C0 +
3.13%
3.65%
C3
C1
C2
C4
+
+
+
+ ...
2
3
4
1.0034 1.0085 1.0132 1.0187
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8
9
10
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TAXES AND INFLATION
If interest is taxed at rate 𝜏𝜏
• $1 => $1 + interest – tax on interest = $1 + r –𝜏𝜏r
• Effective after-tax return = r (1 – 𝜏𝜏)
• Same formula applies if interest on a loan is
tax-deductible
Given (nominal) interest rate r and inflation i
• Purchasing power grows at the real interest rate
1+rreal =
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growth in money 1+r
=
growth in prices 1+ i
When rates are low
rreal ≈ r − i
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SESSION 4:
BONDS
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PRICE VS YIELD TO MATURITY (YTM)
A bond can be quoted in two ways
1.) Price observed in the market
2.) Yield to Maturity (ytm) – determined by the price and the contract characteristics
The yield to maturity (ytm) is the discount rate that equates the discounted
cash flows to the price
c+F
c
c
c
+
+
+ +
Price =
2
3
M
1 + ytm (1 + ytm ) (1 + ytm )
(1 + ytm )
› F (or FV) is the face value in $ Remember: these are fixed when the bond is issued. They do
› c is one coupon payment in $ not change over time!
› The Price of the bond and its ytm can and usually do change over the lifetime of the
bond, based on changes in market conditions
FIN-201 | FALL 2019
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THE ZERO-COUPON TREASURY YIELD CURVE, YTMS AND PRICING
Treasury Zero-Coupon Yield Curve
10.00%
9.00%
8.00%
7.00%
6.00%
5.00%
4.00%
3.00%
2.00%
1.00%
0.00%
4.09%
4.98%
5.78%
6.50%
7.15%
7.74%
8.26%
8.74%
Assume you own a three-year 10% coupon bond with FV
equal to 1,000. Assume coupons are paid annually. Using
the yield curve, we can find the price of the bond:
100
100
100 + 1,000
Price =
+
+
1 + 2.00% (1 + 3.10% )2 (1 + 4.09% )3
3.10%
2.00%
0
1
2
3
4
5
6
7
8
9
10
Price =
98.04
= 1,167.48
To calculate the yield to maturity we start
knowing the price and search for single
discount rate that discounts the all the cash
flows so that their sum equals the known price.
+
94.08
+
975.36
Note that this bond is
trading “Above Par”
$1,167.48 > $1,000
100
100
100 + 1,000
1,167.48 =
+
+
1 + ytm (1 + ytm )2 (1 + ytm )3
Through trial and error or an Excel function (e.g., IRR) we find that: ytm = 3.969%
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DURATION: A MEASURE OF A BOND’S SENSITIVITY TO
INTEREST RATE CHANGES
Duration (D) is measured in years.
It is a weighted average of the
number of years in the future that
each cash flow of the bond is
received. The weight for year t is
PV of cash flow in year t
PV of all cash flows
t =M
D=
∑ PV ( c ) × t
t =1
t =M
t
∑ PV ( c )
t =1
t
A bond with a duration equal to D will
 decrease in value by approximately
D% for a 1% increase in yields
 increase in value by approximately
D% for a 1% decrease in yields
% change in value ≈ − D × ( change in yield)
Note the minus sign: an
increase in rates leads to a
decrease in value.
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BOND PRICES WHEN YIELDS CHANGE
The duration and the sensitivity of the bond price to changes in the yield
» Increases with bond maturity (if coupon is unchanged)
» Decreases with the coupon rate (if maturity is unchanged)
If you sell a bond at the same YTM as you bought it for, you will earn its
YTM
If you sell a bond at the different YTM than you bought it for, you will
earn …
» More than the initial YTM if its yield has fallen
» Less than the initial YTM if its yield has risen
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BALANCE SHEET EFFECTS OF RATE CHANGES
For a firm whose assets and liabilities are essentially like bonds (fixed payments in the future)
we can calculate how its balance sheet values would be affected by a change in interest rates.
Amount
Duration
% change in
value for a 1%
increase in
rates
New
value
% change in
value for a 2%
increase in
rates
New
value
Asset 1
100.00
5.5
−5.5%
94.50
−11.0%
89.00
Asset 2
150.00
3.0
−3.0%
145.50
−6.0%
141.00
Asset 3
300.00
4.0
−4.0%
288.00
−8.0%
276.00
Total Assets
550.00
528.00
506.00
Liability 1
50.00
2.5
−2.5%
48.75
−5.0%
47.50
Liability 2
150.00
1.0
−1.0%
148.50
−2.0%
147.00
Liability 3
150.00
0.0
0.0%
150.00
0.0%
150.00
Total Liabilities
350.00
347.50
344.50
Shareholder Equity
200.00
180.75
161.50
9.625% Loss
19.25% Loss
141.00= 150 × (1 − 6%)
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SESSION 5:
INVESTMENT DECISION RULES
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THE NPV RULE
To evaluate an investment decision
• Estimate the (incremental) cash flows Ct at each point time
• Estimate the opportunity cost of capital rt
• Risk-free project: risk-free rate (from the yield curve)
• Risky project: risk-free rate + appropriate risk premium
• Compute NPV:
NPV = ∑ t
“Rate of return
available taking
comparable risk”
Ct
(1 + rt )t
• Take the alternative with the highest NPV
The NPV Rule is the most reliable estimate of value creation
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INTERNAL RATE OF RETURN (IRR)
IRR = discount rate that makes project NPV = 0
• “Return on Investment” (ROI) generated by the project
NPV ($ millions)
• IRR Rule:
40
35
30
25
20
15
10
5
0
(5) 0%
(10)
Accept projects with
IRR > Cost of Capital
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NPV Profile
IRR = 32%
5%
10%
15%
20%
Discount Rate
25%
30%
35%
40%
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INTERNAL RATE OF RETURN (IRR)
The IRR Decision Rule
Only works if all negative cash flows
precede positive cash flows:
−, −, −, +, +, +, +
In that case:
IRR Rule = NPV Rule IRR
when deciding to accept or reject a
project
A BIGGER Problem: Never use IRR
to compare or rank projects
• IRR can only tell you if project is
better than doing nothing
• It cannot be used to choose
between projects
• This is a common error!
Note: these problems are common to all return-based decision metrics
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IRR RULE & MUTUALLY EXCLUSIVE PROJECTS
Don’t use IRR when projects differ in…
•
•
•
Scale of cash flows
+ Do you prefer a return of 500% on $1 ($5 return) or 20% on $1
million ($200,000 return)? Remember: You can’t eat IRR!
Timing of cash flows
+ Projects A and B require $100 investment have IRRs of 25%.
Project A lasts 1 year, and B lasts 5 years.
+ If your cost of capital is 10%, which is better?
Risk of cash flows
+ Project R has an IRR of 30%. Project S has an IRR of 29%.
+ If R is risky, and S is completely safe, which is better?
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LEVERAGE AND IRR
• We can increase the IRR by adding leverage
• Suppose Bidder #3 proposes a lease instead:
Pay $20M upfront, then $35M per year
Bid #3
Lease
Bid #3L
Year 0
-100
80
-20
Year 1
60
-35
25
Year 2
60
-35
25
• Should you take Bid #3L rather than Bid #3?
c.) No, it is negative NPV and will decrease total NPV
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Year 3
60
-35
25
IRR
36%
15%
112%
NPV
$44.1
–$4.1
$40.0
Beware:
IRR is easily
manipulated!
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PROFITABILITY INDEX
What if Engineering Headcount
is the critical constraint:
• Suppose max headcount ~ 130
Project
Project B
Project A
Project F
Project G
Project H
PROJECT X
Project D
Project E
Project C
Total
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NPV
61.8
79.9
72.4
52.8
43.3
45.0
30.6
20.9
56.3
463.0
“Bang for your Buck”
Profitability Index =
Engineering
Headcount
10
15
20
20
20
25
20
15
45
190
Value Created
Resource Consumed
NPV/EHC
6.18
5.33
3.62
2.64
2.17
1.80
1.53
1.39
1.25
2.44
Total
Headcount
10
25
45
65
85
110
130
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SESSION 6-7:
CAPITAL BUDGETING
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IMPORTANT INSIGHTS
When evaluating the earnings contribution of a decision…
• Track changes to each earnings line item based on the incremental effect of the decision (with
vs. without)
Include:
Exclude:
• Firm-wide effects (not just the business unit)
• Sunk costs
E.g. cannibalization or complementarities
• Opportunity costs (alternative uses of
required resources)
• Price changes due to inflation, market
changes, etc.
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• Interest expenses or
financing costs
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NETPHONE INCREMENTAL EARNINGS
NetPhone Incr. Income
(With vs. Without)
Year 0
Year 1
Year 2
Year 3
Year 4
52.5
52.5
52.5
52.5
Cost of Sales
(24.0)
(24.0)
(24.0)
(24.0)
Gross Profit
28.5
28.5
28.5
28.5
(2.5)
(2.5)
(2.5)
(2.5)
(5.0)
(5.0)
(5.0)
(5.0)
(23.0)
21.0
21.0
21.0
21.0
(23.0)
21.0
21.0
21.0
21.0
(23.0)
21.0
21.0
21.0
21.0
(8.4)
(8.4)
(8.4)
(8.4)
12.6
12.6
12.6
12.6
Total Sales
Operating Expenses:
R&D
(22.5)
Selling, General & Admin
(0.5)
Depreciation/Amort
Operating Income
Other Income/Loss
EBIT
Interest Income/Expense
Income Before Tax
Taxes
(Incremental) Net Income
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9.2
(13.8)
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FREE CASH FLOW
From Earnings to Free Cash Flow (FCF)
1. FCF = EBIT – Taxes + Depreciation – Inc. in NWC – Capital Exp.
2. Depreciation: not a true cash expense, just a tax deduction
3. Capital expenditures should be included at the time they are incurred
4. NWC
= Net Working Capital
= Inventory + Cash Requirements + Receivables – Payables
NWC is the capital needed to “run the business”
Adjusts for the lag
between when goods are
manufactured and paid for,
and when the cash from
the sale is actually
received.
Firm Buys
Inventory
Firm Pays for
Inventory
Inventory
Firm Sells
Product
Accounts Receivable
Accounts Payable
Cash Out
Cash In
Cash Cycle
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Firm Receives
Payment
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NETPHONE INCREMENTAL EARNINGS
Year 0
Year 1
Year 2
Year 3
Year 4
Total Sales
-
52.5
52.5
52.5
52.5
-
Cost of Sales
-
(24.0)
(24.0)
(24.0)
(24.0)
-
60 days / 365 = 16%
36 days / 365 = 10%
Year 5
Calculation
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
Inventory
None
-
-
-
-
-
-
Cash Requirements
None
-
-
-
-
-
-
Accounts Receivable
16% of Sales
-
8.4
8.4
8.4
8.4
-
Less: Accounts Payable
10% of COGS
-
(2.4)
(2.4)
(2.4)
(2.4)
-
-
6.0
6.0
6.0
6.0
-
6.0
-
-
-
(6.0)
Net Working Capital
Increase in NWC
NWCt-NWCt-1
What if sales were growing? … or shrinking?
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NETPHONE INCREMENTAL EARNINGS
Incremental Earnings
Year 0
Year 1
Year 2
Year 3
Year 4
52.5
52.5
52.5
52.5
Cost of Sales
(24.0)
(24.0)
(24.0)
(24.0)
Gross Profit
28.5
28.5
28.5
28.5
(2.5)
(2.5)
(2.5)
(2.5)
(5.0)
(5.0)
(5.0)
(5.0)
Total Sales
R&D
(22.5)
SG&A
(0.5)
Depreciation
Year 5
EBIT
(23.0)
21.0
21.0
21.0
21.0
Taxes
9.2
(8.4)
(8.4)
(8.4)
(8.4)
Net Income
(13.8)
12.6
12.6
12.6
12.6
Free Cash Flow
Year 0
Year 1
Year 2
Year 3
Year 4
EBIT
(23.0)
21.0
21.0
21.0
21.0
9.2
(8.4)
(8.4)
(8.4)
(8.4)
Plus: Depreciation
-
5.0
5.0
5.0
5.0
Less: Inc. in NWC
-
(6.0)
-
-
-
6.0
11.6
17.6
17.6
17.6
6.0
Less: Taxes
Less: CapEx
Free Cash Flow
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Year 5
(20)
(33.8)
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DCF SUMMARY
From Earnings to NPV
Free Cash Flow
Cost of Capital
• Net cash generated or
consumed by decision
• What investors could earn
taking similar risk
elsewhere
EBIT
- Tax on EBIT
Unlevered Net Income*
+ Depreciation
- Increase in NWC
- Cap Ex
Free Cash Flow
*Also known as NOPAT = Net Operating Profit After Tax
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• r = rf + risk premium
NPV
• Value created above and
beyond what investors
could have earned
investing elsewhere
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BEYOND NPV
So, we have computed the project’s NPV –
are we ready to make a decision?
The real value of a financial model is that it
allows us to
• Understand the true sources of value in an investment
• Allocate resources more efficiently within the firm
• Reevaluate and reoptimize our decisions
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SENSITIVITY ANALYSIS
NPV allows us to determine the $ value and break-even point for each
parameter
Base Case
Worst Case
Market Penetration
Best Case
7.5%
30%
$55
Phone ASP
Production Cost
$75
$7.25
Cannibalization
Receivable Days
Cost of Capital
-20
-10
0
10
530
30
15%
32.1%
9%
20
30
Project NPV ($ m)
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$51.81
149%
20%
75
12.4%
$8.12
$5
60%
Break Even
40
50
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FCF: A MORE DIRECT METHOD
Recall our FCF formula:
= EBIT × (1 − τ) + Dep − CapX − ∆NWC
FCF
EBIT =( Rev − Costs − Dep )
Depreciation Tax
Shield
and so…
FCF =( Rev − Costs ) × (1 − τ) + τ × Dep − CapX − ∆NWC
After-tax profits
Total investment
And so 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑖𝑖𝑖𝑖 𝐹𝐹𝐹𝐹𝐹𝐹 = Δ𝐹𝐹𝐹𝐹𝐹𝐹 = ∆𝑅𝑅𝑅𝑅𝑅𝑅 − ∆𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 × (1 − 𝜏𝜏) + 𝜏𝜏 × ∆𝐷𝐷𝐷𝐷𝐷𝐷 − ∆𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 − ∆ Δ𝑁𝑁𝑁𝑁𝑁𝑁
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43
SUMMARY OF THE COURSE THUS FAR…
Finance is about decision making
• Good decisions maximize shareholder value: select
projects with the highest net present value (NPV)
To calculate NPV we need:
• Free cash flows and
• Discount rate (cost of capital)
Remember:
• Earnings are not free cash flows
• Money has a time value
• Investors demand a premium for taking risk
Which assumptions and
risks matter most?
What are the scenarios
to consider?
How might you improve
NPV further?
What is your expected
NPV across key
scenarios?
Use DCF Model to test assumptions and learn drivers of value and sources of risk
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44
SESSION 8-9:
VALUING FIRMS
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45
VALUING SECURITIES
What determines the
value of an investment
today?
• Value of Investment =
PV(Cash Flows)
• This is the $ amount you
would need today to
replicate those cash flows
on your own at
competitive market prices
• Valuation Principle
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Law of One Price:
In competitive markets,
equivalent opportunities
must trade for the
same price
• Why?
“No Arbitrage”
• Price of any Security =
PV(Cash Flows)
•
E.g. bonds
Today we’ll consider
how to apply this to
value:
• Stocks (equity)
→ Dividends, repurchases
• Firms (business
enterprise)
→ Free cash flows
46
METHOD I: COMPS / MULTIPLES
Equity multiples
• Price/Earnings
• Price/Book
Enterprise Value
multiples
• EV/EBIT
• EV/EBITDA
• EV/Sales
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Estimate Share Price ≈
EPStarget x (P/E)peers
Estimate EV ≈
EBITtarget x (EV/EBIT)peers
Estimate Share Price ≈
EV + Cash – Debt
# Shares
47
VALUATION BY COMPARABLES
Advantages
Disadvantages
• Easy to explain, simple to apply
• No way to incorporate unique qualities,
special circumstances, synergies, etc.
• Reflects current market conditions
• Seems to rely on few assumptions
• Provides a quick “reality check”
• Lack of precision
• Relies on other firms being “correctly”
valued
• Provides no information regarding target
growth rates or other metrics for future
performance
• Encourages short-term view
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48
METHOD II: EQUITY PAYOUTS
For a 1-yr investment:
We can rearrange this as
or
Dividend Yield
+ Capital Gain Rate
Total Return
The expected total return of the stock should equal the
expected return available on other securities with similar risk
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49
DIVIDEND-DISCOUNT MODEL
N-year Horizon:
Div1
Div 2
Div N + PN
P
=
+
+ ... +
0
2
1 + rE (1 + rE )
(1 + rE )N
In the limit: “Buy and Hold” Investor
• Assuming the firm is never acquired,
Div1
Div 2
...
P=
+
+=
0
2
1 + rE (1 + rE )
∞
Div n
∑ (1 + r )n
n =1
E
That is, the stock price should equal the present value of all future dividends
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50
CONSTANT EXPECTED GROWTH
To apply the DDM, we need to forecast future dividends
• This is hard to do!!
Simplifying assumption:
• Div/share expected to grow
at constant long-run rate g
• Best applied to mature firms
0
1
2
3
-P0
Div1
Div1×(1+g)
Div1×(1+g)2
Dividends can be valued as a constant growth perpetuity:
P0 =
Div1
rE − g
or equivalently,
=
rE
Div1
+g
P0
Three main drivers of stock prices:
1 Higher dividends
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2 Higher growth
3 Lower interest rates or risk premia
51
PAYOUTS AND THE P/E MULTIPLE
Price of Equity = PV of total payouts
=
P0
Suppose the firm pays out
a target fraction of its earnings:
Value of Equity PV (Divs & Repurchases)
=
# shares
# shares
× Total Payout Rate
EPS
Retained
Earnings
× Retention Rate
(= 1 – TPR)
Then if ge is the expected
growth rate of earnings
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P0 =
Dividends +
Repurchases
(Total Payout Rate) × EPS1
rE − g e
or
52
METHOD III: ENTERPRISE VALUE AND DCF
=
The Enterprise
Free Cash
Flow
• This is the underlying
business that the firm
operates
• E.g. the rental property
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Share Price,
Market Cap
Bond Price,
Debt Value
Enterprise Value
+
Debt
Equity
• Interest
• Dividends
• Principal
• Share buybacks
53
METHOD III: ENTERPRISE VALUE AND DCF
Market Value Balance Sheet
Assets
Cash
Enterprise
Value
= PV(FCF)
Liabilities
Debt
Tangible
Plant/Prop/Equip
Net Working Cap, etc.
Intangible
IP, Human Cap, Brands,
etc.
Last Step
Share Price =
Equity Value /
Shares Outstanding
Equity
Enterprise Value = Equity + Debt – Cash = PV(FCF)
Value of Equity
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= PV(FCF) + Cash – Debt
Net PV from all
ongoing and future
investments
54
DCF: KEY STEPS
STEP 1:
FCF
STEP 2:
Terminal Value
STEP 3:
Discount
STEP 4:
Share Price
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- Net Investment
FCF = EBIT × (1 − τ) − ∆NWC + Dep − CapX
V10 =
=
V0
P0 =
rwacc
FCF11
− ( Long-run growth )
or
EV


multiple 
V10 = EBIT10 ×  Long-run
EBIT


FCF10
V10
FCF1
FCF2
...
+
+
+
+
1 + rwacc (1 + rwacc ) 2
(1 + rwacc )10 (1 + rwacc )10
V0 + Cash − Debt
# shares
55
EXAMPLE: QUALCOMM VALUATION
Based on analysts projections, FYE 2011
Basic DCF Stock Valuation QCOM
1
Year
Revenues
2011
14,957
yoy growth
EBIT
Taxes
Net Investment
Additions to NWC
FCF
2
wacc
discount factor
Present Value
28.0%
20.0%
80.0%
0.0%
9.50%
Total Enterprise Value
Cash & Marketable Securities
Total Firm Value
Debt & Capital Leases
Other Securities / Pensions
Total Equity Value
(diluted) shares outstanding
Value per Share
actual price
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3
2012
19,295
2013
21,224
2014
23,193
2015
25,177
2016
27,150
2017
29,080
2018
30,938
2019
32,691
2020
34,308
2021
35,756
2022
37,008
29.0%
10.0%
9.3%
8.6%
7.8%
7.1%
6.4%
5.7%
4.9%
4.2%
3.5%
5,402
(1,080)
(3,470)
0
852
5,943
(1,189)
(1,544)
0
3,211
6,494
(1,299)
(1,575)
0
3,620
7,050
(1,410)
(1,578)
0
4,052
7,602
(1,520)
(1,578)
0
4,504
8,142
(1,628)
(1,545)
0
4,969
8,663
(1,733)
(1,486)
0
5,444
9,154
(1,831)
(1,403)
0
5,920
0.834
2,678
0.762
2,757
0.696
2,819
0.635
2,861
0.580
2,883
0.530
2,884
0.484
2,864
10,012
(2,002)
(1,159)
0
6,851
121,476
0.404
51,782
10,362
(2,072)
(1,001)
0
7,289
0.913
778
9,606
(1,921)
(1,293)
0
6,392
Terminal
0.442
2,824
$75,130
21,978
$97,108
(1,077)
$96,031
1,702
56.42
$55.00
5
4
Terminal Value
6
𝐹𝐹𝐹𝐹𝐹𝐹11
$7289
=
𝑟𝑟𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 − 𝑔𝑔 9.5% − 3.5%
= $121,476
= projected value of firm in 2021
𝑉𝑉10 =
Initial Multiples
13.9 x TEV/EBIT+1
5.0 x TEV/Rev
Terminal Multiples
11.7 x TEV/EBIT+1
4
3.4 x TEV/Rev
56
BOTTOM LINE ON DCF
Advantages
Disadvantages
• Makes assumptions explicit
• Many degrees of freedom (manipulable)
• Fundamentals-based (avoid bubbles)
• Sensitive to terminal value assumption
• Allows adjustment for firm profitability,
growth, investment, and tax efficiency
• Not directly tied to current market pricing
• Provides performance metrics and targets,
and insight into “investor expectations”
• Allows sensitivity analysis
• Encourages long-term view
Remember:
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• Budget for growth
• Cross check terminal value (multiples, growth rate)
• Discount using weighted-avg. cost of capital (rwacc)
57
TYPES OF MULTIPLES
Equity multiples
• Price/Earnings
• Price/Book
Enterprise Value multiples
• EV/EBIT or Operating Income
• EV/EBITDA
• EV/Sales
Stanford Graduate School of Business
Estimate Share Price ≈ EPStarget x (P/E)peers
Estimate EV ≈ EBITtarget x (EV/EBIT)peers
Estimate Share Price ≈
EV + Cash – Debt
# Shares
58
VALUATION BY COMPARABLES
Advantages
Disadvantages
• Easy to explain, simple to apply
• No way to incorporate unique qualities,
special circumstances, synergies, etc.
• Reflects current market conditions
• Seems to rely on few assumptions
• Provides a quick “reality check”
• Lack of precision
• Relies on other firms being “correctly”
valued
• Provides no information regarding target
growth rates or other metrics for future
performance
• Encourages short-term view
Stanford Graduate School of Business
59
REMEMBER
Each approach to equity
valuation has advantages and
disadvantages
Be cognizant of the implicit and
explicit assumptions embedded
within each method
• Premiums paid
• Profit margins, Growth Rates
• Comparables
• Free cash flows
• Discounted cash flow analysis
• Discount Rates, Terminal values
The best analysis combines insights from all 3 methods to reach a
decision
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