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Chapter 8: Fundamentals of Capital Budgeting
Note: Read the chapter then look at the following.
Fundamental question: How do we determine the cash flows we need to calculate the net present
value of a project?
Key: most managers estimate a projectโs cash flows in two steps:
Impact of the project on the firmโs incremental earnings
Use incremental earnings to determine the projectโs incremental cash flows
Notes:
incremental = change as a result of the investment decision
revenues and expenses occur throughout the year, but we will treat them as if they
come at end of the year
=> this is a standard assumption used by the text
8.1 Forecasting Earnings
Basic Question: How do firmโs unlevered earnings change as result of an investment
decision?
A. Excel
=> for real projects, difficult to do by hand => use Excel
Note: donโt hardcode (enter numbers) directly into formulas. Have your formulas refer to
the section of your spreadsheet where you input the numbers (the text makes this
point on p. 245).
B. Calculating by hand:
๐๐๐ผ = ๐ธ๐ต๐ผ๐ ร ( 1 โ ๐
๐
๐
where:
UNI = incremental unlevered net income
=> counting only incremental operating cash flows, but no financing cash flows
EBIT = incremental earnings before interest and taxes
c
= firmโs marginal corporate tax rate
R = incremental revenues
E = incremental expenses (or costs)
Note: Book uses costs, I will use โexpensesโ so can have an โEโ instead of a โCโ
in the equation. Will use โCโ for cash in new working capital in section 8.
D = incremental depreciation
C. Identifying Incremental Earnings
- General Principles
Basic question: How do the earnings (and cash flows) for the entire firm differ with
the project verses without the project?
=> count anything that changes for the firm
=> count nothing that remains the same
Example of costs that often donโt change with new project: fixed overhead
expenses
=> donโt count previous or committed spending unless can get some back if donโt
proceed
=> part canโt get back is called sunk costs
Ex. money already spent to research and develop a product
Ex. completed feasibility studies
Ex. money spent on a partially completed building that can be sold
MACRS Depreciation:
=> From appendix
Keys:
multiply cost of project by % listed in MACRS table
Year 1 = year asset first put into use
the following table is in the Chapter 8 Appendix
Fixed assets that able to sell because invest in the project
a) count after-tax cash flow from sale
b) count loss of tax shield would have realized if had kept asset
- Use of existing assets
=> cost equals value of its best alternative use (such as sale or rental)
=> called an opportunity cost
Concept Check: 2, 3
MACRS Depreciation Rate for Recovery Period
Year 3 years 5 years 7 years 10 years 15 years 20 years
1 33.33 20.00 14.29 10.00 5.00 3.
2 44.45 32.00 24.49 18.00 9.50 7.
3 14.81 19.20 17.49 14.40 8.55 6.
4 7.41 11.52 12.49 11.52 7.70 6.
5 11.52 8.93 9.22 6.93 5.
6 5.76 8.92 7.37 6.23 5.
7 8.93 6.55 5.90 4.
8 4.46 6.55 5.90 4.
9 6.56 5.91 4.
10 6.55 5.90 4.
11 3.28 5.91 4.
12 5.90 4.
13 5.91 4.
14 5.90 4.
15 5.91 4.
16 2.95 4.
17 4.
18 4.
19 4.
20 4.
21 2.
8.2 Determining Free Cash Flow and NPV
A. Calculating Free Cash Flow from Earnings
Keys:
start with incremental unlevered net income
back out non-cash items in UNI
add cash items not in UNI
FCF = UNI + D โ CE - ๏ NWC (8.5a)
where:
CE = incremental after-tax capital expenditures
๏ NWC = change in net working capital associated with project
๏NWCt = NWCt โ NWCt- 1 (8.4)
NWC = CA โ CL = C + AR + I โ AP (8.3)
CA = incremental current assets
CL = incremental current liabilities
C = incremental cash
AR = incremental accounts receivable
I = incremental inventory
AP = incremental accounts payable
ร
๐
- ๐ท โ ๐ถ๐ธ โ โ๐๐๐ถ (8.5b)
ร
๐
๐
ร ๐ท (8.6)
Note: ๐
๐
ร ๐ท is the depreciation tax shield
=> reduction in taxes that stem from deducting deprecation for tax purposes
=> depreciation increases cash flows because reduce tax payments
B. Notes
- Depreciation (D)
=> add back to FCF since subtracted from UNI but doesnโt involve a cash outlay
8.3 Choosing Among Alternatives
A. Evaluating Manufacturing Alternatives
Note: To decide between alternatives, can compare the NPVs of alternatives.
However, can also decide by calculating the NPV of the difference in cash flows.
Example from text (p. 247):
Differences in Cash Flows (In-House โ Outsourced):
Yr 0 = โ 30 00 = โ 3000 โ 0
Yr 1 = โ 117 = โ 5067 โ (โ 4950)
Yr 2 โ 4 = +900 = โ 5700 โ (โ 6600)
Yr 5 = +1017 = โ 633 โ (โ 1650)
NPV (differences) = โ 3000 โ
117
- 12
900
. 12
1
- 12
3
1
- 12
1017
( 1. 12 )
5
Note: Same result as text
Difference in text = โ 20,107 โ (โ 19,510) = โ 597
Video Solution
Concept Check: all
8.4 Further Adjustments to Free Cash Flow
- Other non-cash items
=> should back out (from UNI) any other non-cash items
- Timing of Cash Flows
=> cash flows likely spread throughout year instead of at end of year
=> might increase accuracy if estimate cash flows over smaller time periods
- Accelerated Depreciation
Key issue: accelerated depreciation allows earlier recognition of depreciation
=> get cash flows from tax shield earlier
=> present value of tax shield higher
Note on Example 8.5: Firms can start depreciating the asset as soon as it is put into use.
Unless stated otherwise, I will assume that if we build or acquire an asset today, it
will be put into use at some point during the first year and so recognize depreciation
for the first time in year 1.
- Liquidation or Salvage Value
G = SP โ BV (8.8)
where:
G = gain
SP = sales price
BV = book value
BV = PP โ AD (8.9)
where:
PP = purchase price
AD = accumulated depreciation
ATCF = SP โ ๏ด c ร G (8.10)
where:
ATCF = after-tax cash flow from asset sale
- Terminal or Continuation Value
Key issue: often assume cash flows grow at some constant rate forever beyond horizon
over which forecast cash flows.
- Tax Carryforwards and Carrybacks
Key issue: can carryback losses to offset profits for previous two years and/or can
carryforward losses to offset profits for following 20 years.
A. Examples
Note: In the following examples, we start with the simplest case in which free cash flow
equals unlevered net income. Each subsequent example builds on the previous
example by adding (or changing) an assumption. The new assump are underlined in
each example.
Example 2:
Assume you are trying to decide whether to rent a building for $30,000 a year for the
next 2 years (payments are due at the end of the year). A year from today you plan
to purchase inventory for $50,000 that you will sell immediately for $110,000.
Two years from today you plan to purchase inventory for $70,000 that you will
sell immediately for $150,000. Assume also that need to hold cash balances (to
facilitate operations) of $1000 a year from today and $1500 two years from today.
Calculate the storeโs incremental unlevered net income and free cash flow for
each year of operation if the corporate tax rate is 35%. Note: You would probably
take the cash out of the store when you close your doors two years from
todayโฆbut I am assuming you leave it to better demonstrate changes in net
working capital.
๐๐๐ผ = ๐ธ๐ต๐ผ๐ ร
๐
๐
NWC = C + AR + I โ AP
FCF = UNI + D โ CE - ๏ NWC
UNI 1 = (110,000 โ (30,000+50,000) โ 0)(1 โ .35) = $19,
UNI 2 = (150,000 โ (30,000+70,000) โ 0)(1 โ .35) = $32,
Note: holding cash doesnโt affect UNI
Net Working Capital:
t = 0 t = 1 t = 2 t = 3
Cash 0 1000 1500 0
A/R - - - -
Inventory - - - -
A/P - - - -
NWC 0 1000 1500 0
๏NWC 0 1000 500 โ 1500
FCF 1 = 19,500 โ 1000 = 18,
FCF
2
FCF
3
Key: donโt have access to all of the cash flows generated by sales since must hold
some cash at the store.
Video Solution
Example 3:
Assume you are trying to decide whether to rent a building for $30,000 a year for the
next 2 years (payments are due at the end of the year). A year from today you plan
to purchase inventory for $50,000 that you will sell immediately for $110,000.
Two years from today you plan to purchase inventory for $70,000 that you will
sell immediately for $150,000. Seventy-five percent of sales will be on credit that
you will collect one year after the sale. Assume also that need to hold cash
balances (to facilitate operations) of $1000 a year from today and $1500 two
years from today. Calculate the storeโs incremental unlevered net income and free
cash flow for each year of operation if the corporate tax rate is 35%.
๐๐๐ผ = ๐ธ๐ต๐ผ๐ ร ( 1 โ ๐
๐
๐
NWC = C + AR + I โ AP
FCF = UNI + D โ CE - ๏ NWC
UNI
1
UNI 2 = (150,000 โ (30,000+70,000) โ 0)(1 โ .35) = $32,
Note: doesnโt change from Examples 1, 2, or 3
Net Working Capital:
AR 1 = .75(110,000) = 82,
AR 2 = .75(150,000) = 112,
t = 0 t = 1 t = 2 t = 3
Cash 0 1000 1500 0
A/R 0 82,500 112,500 0
Inventory - - - -
A/P - - - -
NWC 0 83,500 114,000 0
๏NWC 0 83,500 30,500 โ 114,
FCF
1
FCF
2
FCF
3
Video Solution
Keys:
=> sales on credit generate revenue but not cash flow
=> collections of receivables generate cash flows but not revenues
=> UNI overstates early cash flow and understates late cash flow
Example 5:
Assume you are trying to decide whether to buy a building for $250,000. You expect
to sell it in two years for $225,000. In the mean time you will depreciate it using
the 3-year MACRS class. Today you plan to purchase inventory for $50,000 that
you will sell a year from today for $110,000. A year from today you plan to
purchase inventory for $70,000 that you will sell two years from today for
$150,000. Sixty percent of all inventory purchases will be on credit due one year
after you buy it. Seventy-five percent of sales will be on credit that you will
collect one year after the sale. Assume also that need to hold cash balances (to
facilitate operations) of $1000 a year from today and $1500 two years from today.
Calculate the storeโs incremental unlevered net income and free cash flow for
each year of operation if the corporate tax rate is 35%.
๐๐๐ผ = ๐ธ๐ต๐ผ๐ ร
๐
๐
NWC = C + AR + I โ AP
FCF = UNI + D โ CE - ๏ NWC
D 1 = .3333(250,000) = 83,
D 2 = .4445(250,000) = 111,
Proceeds from sale of building:
Book value 2
Gain = 225,000 โ 55,550 = 169,
After-tax proceeds = 225,000 โ 169,450(.35) = 225,000 โ 59,307.50 = 165,692.
CE 2 = - 165,692.
Video Solution (Part a)
Net Working Capital:
t = 0 t = 1 t = 2 t = 3
Cash 0 1000 1500 0
A/R 0 82,500 112,500 0
Inventory 50,000 70,000 0 0
A/P 30,000 42,000 0 0
NWC 20,000 111,500 114,000 0
๏NWC 20,000 91,500 2500 โ 114,
UNI 1 = (110,000 โ 50,000 โ 83,325)(1 โ .35) = โ $15,161.
UNI 2 = (150,000 โ 70,000 โ 111,125)(1 โ .35) = โ $20,231.
FCF
0
FCF
1
FCF 2 = โ $20,231.25 + 111,125 โ (โ165,692.50) โ 2,500 = 254,086.
FCF 3 = 0 โ (โ114,000) = 114,
Video Solution (Part b)
Concept Check: all
8.5 Analyzing the Project
Key to all of section 8.5: Using goal seek and data tables in Excel.
Break-even: level of one input variable that makes NPV = 0
Sensitivity analysis: examines impact on NPV of changing one input variable
Key concern: identify which worse-case assumptions lead to a negative NPV
Scenario analysis: examines impact on NPV of changing multiple related input variables
Concept Check: all
Chapter 8 Appendix: MACRS Depreciation
=> covered earlier in notes
