Advanced Corporate Finance
FINA 7330
Ronald F. Singer
Making Investment Decisions
Lecture 2
Fall 2010
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Capital Budgeting Decisions Check List
1.
Net Present Value is the "Discounted value of
incremental cash flow”
2.
Cash flow is:
CASH MONEY IN - CASH MONEY OUT
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Capital Budgeting Decisions Check List
3. Consider only if it is an incremental cash flow,
and consider all incremental cash flows:
(a) not historical, or averages;
(b) consider only cash flows that appear as a
result of the project
(c) consider the impact of the project on cash
flows from other projects
(d) exclude fixed or sunk costs
(e) exclude allocated overhead unless it will
change as a result of the project.
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Capital Budgeting Decisions Check List
4. Treat inflation consistently:
Discount real cash flow by real discount rates
Discount nominal cash flows by nominal discount rates
Note: Revenues and costs will not necessarily react
uniformly to inflation.
5. All Cash Flow should be on an After-Tax basis.
Use actual tax changes when paid!
Don't forget to allow for the tax on capital gains
Use future marginal tax rates applied to future taxable
income
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Capital Budgeting Decisions Check List
6. Include the opportunity cost of the project, even if there
is no explicit cash flow realized
Account for assets sold and not sold as a result of
adoption of a project.
7. Account for changes in working capital and only
changes in working capital. Recognize that working
capital will in general be re-couped at the end of the
project.
8. Ignore financing including the tax shield on interest
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Capital Budgeting Decisions Check List
9. Include Asset's Entire Life
10. Include the depreciation tax shield, but not
depreciation itself.
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Capital Budgeting Decisions Check List
No matter how complicated the decision: What is
important?
MAXIMIZE NPV
PLAN TO TAKE ALL PROJECTS WITH A POSITIVE
NET PRESENT VALUE AND REJECT ALL PROJECTS
WITH A NEGATIVE NET PRESENT VALUE
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Application of the NPV Rule and
Capital Budgeting
• For now we are going to assume that the
appropriate discount rate is known.
• The problem we want to tackle is to forecast the
relevant cash flows.
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Only Cash Flows Affect Wealth.
What is and is not Cash Flow
-Expenses are cash flow regardless of whether the
accountant capitalizes and depreciates them or
expenses them.
-Capital expenditures are cash outflows regardless of the
fact that accountants depreciate them over a period.
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3. Only Incremental cash flows are
relevant
• Not historical cash flows, not averages, not sunk costs!
• Example 1: Consider a firm having made an investment
one year in the past. The project required an initial
investment of $10,000; with the expectation of $14,000
to be generated within two years. At a discount rate of
10% should the firm have made the investment?
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Only Incremental cash flows are
relevant
14,000
-1---------------0-----------------1
10,000
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Only Incremental cash flows are
relevant
14,000
-1---------------0-----------------1
10,000
• Of course it should have. The NPV was: NPV = 1,564
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Only Incremental cash flows are
relevant
• NOW THINGS CHANGE. A NEW DEVICE
INTRODUCED BY A COMPETITOR MAKES THE
PRODUCT OBSOLETE. THUS EXPECTED CASH
FLOWS DECLINE TO $7,000. THAT IS THE
INVESTMENT, DID NOT PAY OFF AS EXPECTED
AND THE PROJECT IS NOW A LOSER.
• SUPPOSE THAT FOR AN ADDITIONAL INVESTMENT
OF $5,000, YOU CAN REGAIN YOUR COMPETITIVE
POSITION, SO THAT EXPECTED CASH FLOW
INCREASES TO THE ORIGINAL $14,000. SHOULD
YOU MAKE THE NEW INVESTMENT?
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Only Incremental cash flows are
relevant
14,000
-1---------------0-----------------1
-10,000
-5,000
• Note that the project, looked at as a whole is still a loser:
NPV(t = -1) = -10,000 - 5,000 + 14,000
(1.1)
(1.1)2
= - 2,975
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Only Incremental cash flows are
relevant
14,000
-1---------------0-----------------1
-10,000
-5,000
• Note that the project, looked at as a whole is still a loser:
NPV(t = -1) = -10,000 - 5,000 + 14,000
(1.1)
(1.1)2
= - 2,975
BUT the additional investment should be made.
• Determine the incremental cash flows.
• Determine Net Present Value of the incremental cash
flows
Incremental Cash Flow: -5,000 + 7,000/(1.1) = 1,363.65
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Only Incremental cash flows are
relevant
• Example 2: Assume that the original cash flow estimates
were accurate. But that you can; by making an
additional investment of 1,000, generate total second
period cash flow of 15,050. Should the additional
investment be made?
(Still Assume r= 10%)
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Only Incremental cash flows are
relevant
14,000
-1---------------------0-----------------------1
-10,000
-5,000
1,050
-1---------------------0-----------------------1
-1,000
NPV (of Additional Investment) = -1000 + 1050
1.1
initial
Incremental
= - 45.45
• Even though, the original project is a winner, do not
make the additional investment
• You must Ignore Sunk Costs, and consider only
incremental cash flows.
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4. Treat inflation consistently
•
Make sure that inflation is accounted for in a consistent
manner. Either:
1.
State cash flows in terms of actual dollars, at the time the cash
flows are received. These are nominal cash flows
Or
2.
State cash flows in terms of dollars, at the time the projections
are made. These are real cash flows.
•
If cash flows are in nominal terms, use nominal
discount rates to discount the cash flows.
•
If cash flows are in real terms use real discount rates
to discount the cash flows.
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Example
• Suppose you are buying a machine that you believe will produce
10,000 widgets per year at a unit cost of $3.00. The machine will
last for 10 years.
• You can sell the widgets for $5.00 per unit.
• The risk of widget production is about average, relative to the
economy as a whole. (i.e. has a Beta of 1).
• Your CFO thinks the return on the market will average 10% per
year, over the next 10 years.
• What is the NPV of this project if the machine costs $130,000?
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Standard Result
• Annuity is $20,000 per year for 10 years
• Discount rate is
10%
• NPV = 122,891 – 130,000 = -7109
• Reject
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Treat inflation consistently
• Example: There is 3% anticipated inflation per year.
The real price of Honda Accords is expected to remain
constant into the foreseeable future at $20,000. What
will the nominal price be after 5 years?
Nominal Price = (Real Price) (1.03)5
= $23,185.48
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Treat inflation consistently
• IN GENERAL TERMS:
CONVERTING NOMINAL CASH FLOWS TO REAL CASH
FLOWS, AND NOMINAL INTEREST RATES TO REAL
INTEREST RATES.
• If Y(t) is the nominal cash flow in period t, in is the
annual anticipated inflation rate, then the real cash
flow, y(t) is:
y(t) = Y(t)
(1+in)t
and
Y(t) = y(t)*(1+in)t
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Treat inflation consistently
• if R is the annual nominal interest rate, and r is the real
interest rate, then:
(1+R) = (1+r)(1+in)
(1+r) = (1+R)/(1+in)
• Don't assume that all cash flows will be affected equally
by inflation.
• BEWARE OF THE APPROXIMATION:
R = r + in
This works only if r times in is small.
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Treat Inflation Consistently
• The problem is what is convenient and
conventional is typically inconsistent with
this rule:
• How do you project CF over time?
• How do you determine the appropriate
discount rate?
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Example
• Suppose you are buying a machine that you believe will produce
10,000 widgets per year at a unit cost of $3.00. The machine will
last for 10 years.
• You can sell the widgets for $5.00 per unit.
• The widget industry has an asset Beta which is similar to the Beta of
the S&P 500
• Your CFO thinks the return on the market will average 10% per
year, over the next 10 years.
• What is the NPV of this project if the machine costs $130,000?
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Standard Result
• Annuity is $20,000 per year for 10 years
• Discount rate is
10%
• NPV = 122,891 – 130,000 = -7109
• Reject
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But:
• Assume that inflation is anticipated to be
3% per year:
• Now we have a growing annuity:
• CF(1) = 20,600
• CF(2) = 21,218
• ……….
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Problem
• We had made the classic error of mixing
real CF with nominal discount rates.
• Use Real CF and Real interest rates:
– Real rate = (1.10/1.03) -1 = 6.80%
– Then NPV = $141,780 – 130,000 = 11,780
– Accept Project
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6. Tying up assets uses a valuable
resource and must be accounted for.
• Example: A firm is considering installing a brick
manufacturing kiln. The initial investment will
require $300,000 in building and equipment. The
kiln will be located on a vacant lot having an
estimated market value of $1,000,000. The
project is expected to generate net cash flow of
$50,000 per year for 20 years. After 20 years,
the kiln will be worthless. It is anticipated that
the lot could be sold for $2,653,000 at the end of
20 years. At a 10% discount rate, is this a good
investment? (Ignore taxes)
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Tying up assets uses a valuable
resource and must be accounted for.
• ALTERNATIVE ONE
Ignoring the opportunity cost of the (tied-up) land.
NET PRESENT VALUE CALCULATION:
NPV= -300,000 + PVA(20, 10%, 50,000)
= -300,000 + 425,693.05 = 125,693.05
ACCEPT PROJECT
• The problem with this is that you ignore the fact that you
lose the use of $1,000,000 that you could have had if
you had not adopted the project and sold the land (or
used it in an alternative project).
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Tying up assets uses a valuable
resource and must be accounted for.
• ALTERNATIVE TWO
Explicitly consider the land as part of the inputs: You
estimate that the land will be worth $2,653,000 in 20
years.
PRESENT VALUE CALCULATION:
NPV = -1,000,000 -300,000 + PVA(20, 10%50,000)
+ PV(20, 10%, $2,653,000)
= - 1,300,000 + 425,678 + 394,352
= - 479,970
REJECT PROJECT
• NOTICE HOW THE TIED UP LAND IS TREATED!
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Tying up assets uses a valuable
resource and must be accounted for.
•
ALTERNATIVE THREE
Consider this as two projects:
1. Consider land as priced correctly in the
market (In fact the return to the land is
(and assume should be 5%)
2. So NPV of investment in land is 0
•
What is the right way to do this?
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7. Account for changes in working
capital and only changes in w.c.
• Other Incremental Costs Are
Increases in overhead costs as a result of project.
Increases in working capital as a result of project.
• Notice the reduction in working capital would be a cash
inflow at that time.
• Do not use allocated overhead, or allocated working
capital.
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Account for changes in working capital
and only changes in wc.
• Example:
Suppose, due to the adoption of the project, the firm is
required to increase working capital from $100,000 to
$110,000 per annum for the life of the project. How do
you account for the working capital?
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Account for changes in working
capital and only changes in wc.
• Example:
• Suppose, due to the adoption of the
project, the firm is required to increase
working capital from $100,000 to $110,000
per annum for the life of the project. How
do you account for the working capital?
+10,000
-10,000
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Account for changes in working capital
and only changes in wc.
• Example:
Suppose, due to the adoption of the project, the firm is
required to increase working capital from $100,000 to
$110,000 per annum for the life of the project. How do
you account for the working capital?
So you see that this is simply a timing problem
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Remember taxes
1. Calculate all cash flows after taxes
2. Include non-cash expenses (depreciation) for its effect on taxes, but
not as a cash flow itself.
•
HOW TO HANDLE THE DEPRECIATION TAX SHIELD
We want the project's AFTER TAX CASH FLOW
Equals: Before Tax Cash Flow Less Corporate Taxes
Taxes = tc [Cash revenue - Cash Expenses - Depreciation]
Therefore, for each year:
After Tax Cash Flow =(Cash Revue - Cash Expenses)(1 - tc)+ tc Depr
Where: tc x Depr is the Depreciation Tax Shield)
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5. Remember taxes on Capital Gains
3. Tax on gains/(losses) from sale of assets is an
additional negative/positive cash flow
Tax on
Gains/Losses
On sale
= tc x (Market Value - Book Value)
• If Market Value > Book Value, then tax on gain is cash
outflow.
• If Market Value < Book Value, then we have a loss on
sale, tax is negative, and there is a cash inflow.
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Remember taxes on Capital Gains
• Example:
• XYZ Corp. has a project which is going to last 5
years. P & E for this project of $1,000,000, we
can assume a scrap value of 300,000 at the end
of 5 years. On a straight line basis, that means
the firm depreciates the assets @ $140,000 per
year, leaving 300,000 when the project ends.
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Remember taxes and the effect
of selling assets
• However, you expect that you can sell the asset
for $500,000 at the end of 5 years. Thus there is
a taxable capital gain of: (MV-BV) = $200,000.
• At a 35% Corporate Capital Gain Tax rate, that
means that after tax cash flow from the disposal
of P&E is
0.35 * $200,000 = $70,000
Thus the Cash flow from selling the asset is:
$500,000 -70,000 = $430,000
(Remember to add back Book Value)
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8. Ignore the means of financing both as a
direct cash flow and as its effect on taxes.
• Interest payments are not cash flows when doing project
analysis. Discounting already takes the time value of money
into account. To deduct interest would be double counting.
• Example: Suppose that you borrow $500, and put in $500 of
your money into the following project. (Bank charges 8% on
loan)
0
1
Cash Flow
-1000
1125
Interest
-40
Net
-1000
1085
• To say that we reject the project since NPV (of net cash flow) is
negative at 10% (NPV = -13) is double counting. We penalize
the project twice, one by deducting interest, second by
discounting.
• The NPV of this project is:- 1,000 + (1,125)/1.10 = 23
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STEPS IN PROJECT ANALYSIS
1. MAKE INITIAL PROJECTIONS
Made by operations manager
Generally in form of income statement
Clarify assumptions
2. ADJUST FOR INFLATION IF APPROPRIATELY
3. REARRANGE IN CASH FLOW FORM
4. PERFORM NET PRESENT VALUE CALCULATIONS
5. PERFORM "WHAT IF" CALCULATIONS
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