Chapter 8
Using Discounted Cash Flow
Analysis to Make Investment
Decisions
Topics Covered
Discounted Cash Flows, Not Profits
Incremental Cash Flows (Ping King
Example)
Treatment of Inflation
Separate Investment & Financing
Decisions
Calculating Cash Flows
Wednesday Example: TBA
Learning Objectives
 Identify the cash flows attributable to a proposed
new project.
 Calculate the cash flows of a project from
standard financial statements.
 Understand how the company’s tax bill is
affected by depreciation and how this affects
project value.
 Understand how changes in working capital
affect project cash flows.
Capital Budgeting Steps

1.
2.
3.
For a potential project:
Forecast the project cash flows.
Estimate the opportunity cost of capital
Discount the future cash flows at the
opportunity cost of capital.
4. Find NPV of project = PV of future cash
flows – required investment, and accept
if NPV > 0.
Incremental Cash Flows
 Discount incremental cash flows
 Include All Indirect Effects
 Forget Sunk Costs
 Include Opportunity Costs
 Recognize the Investment in Working Capital
 Beware of Allocated Overhead Costs
Incremental
Cash Flow
=
cash flow
with project
-
cash flow
without project
Incremental Cash Flows
IMPORTANT
Ask yourself this question
Would the cash flow still exist if the project
does not exist?
If yes, do not include it in your analysis.
If no, include it.
Calculating Cash Flow
Total Cash Flow =
Cash Flow from Investment in Plant &
Equipment +
Cash Flow from Investments in Working Capital
+
Cash Flow from Operations
Cash Flow from Investment in Plant &
Equipment Calculations for Ping Kings
 In general, initial cost at beginning of project and
possible inflow from after-tax salvage (selling)
value at end of project.
 Ping will need to buy and install new
manufacturing equipment costing $4,500,000,
which would be depreciated to zero over 5 years
using straight-line depreciation.
 At the end of the project’s 3-year life, Ping
estimates they can sell this equipment for
$800,000. (tax rate = 40%)
Cash Flow from Investment Calculations
for Ping Kings
 Initial investment in equipment today (t = 0) = -$4,500,000
 For operating cash flow calculation, annual depreciation =
$4,500,000/5 = $900,000
 Book Value of Equipment = Original Cost – Total
Depreciation
 Book Value at end of year 3 (BV) = $4,500,000 –
3($900,000) = $1,800,000
 Year 3 Salvage Value (SV) = $800,000
 Tax on SV = Tax Rate x (SV – BV) = 0.4($800,000 $1,800,000) = $400,000 tax savings
 Year 3 after-tax salvage value = $800,000+$400,000 =
$1,200,000: year 3 cash flow from investments
Sunk Costs
 These are costs that cannot be recovered if a
project is rejected.
 Examples:
Completed Marketing & Feasibility Studies,
Previous new product development and testing
 For the Ping Kings Project, Ping has already
spent $500,000 to research and design the Ping
Kings.
 This cost is to be ignored because it is a sunk
cost.
Investment in Working Capital
 (Net) Working Capital = Current Assets –
Current Liabilities
 Most new projects require additional short-term
(current) assets and often additional current
liabilities, such as
Additional receivables from increased credit sales.
Additional inventory (raw materials) necessary to
produce additional new products.
Additional trade credit (accounts payables) and taxes
and wages payable.
 Any needed increase in (net) working capital is
an outflow of cash, but these outflows are
recovered at the end of the project.
Calculation of Cash Flow from Investments in
Working Capital for Ping Kings Project ($000s)
 Ping estimates they will need working capital equal to 10% of sales
revenue for the following year. Ping estimates they can sell 10,000 sets
of Ping Kings in year 1, 15,000 sets in year 2, and 9,000 in year 3. They
also estimate they can sell the Ping Kings for $640 a set in years 1 & 2,
but they will only be able to sell them for $540 a set in year 3.
Year
0
1
2
3
Sales
6400
9600
4860
WC need 640
960
486
0
WC Chg. 640
320
(474)
(486)
 Increase in WC is an outflow, decrease in WC is an
inflow
Methods of Calculating CF from
Operations (Oper. CF)
Method 1: Oper. CF = revenues – cash
expenses – taxes
Method 2: Oper. CF = net accounting profit
+ depreciation
Method 3: (revenues – cash expenses) x
(1 – tax rate) + depreciation x tax rate
All these methods give the same result!
Ping King CF for Operations Info.
 Ping estimates they can sell 10,000 sets of Ping
Kings in year 1, 15,000 sets in year 2, and 9,000
in year 3. They also estimate they can sell the
Ping Kings for $640 a set in years 1 & 2, but
they will only be able to sell them for $540 a set
in year 3. Variable costs will be $350 a set for all
three years and Ping also expects to have
$300,000 in fixed manufacturing costs annually
for this project.
 Ping’s marginal tax rate is 40%.
Cash Flow from Operations for Ping
Kings (using Method 2)
Year
Unit Sales
$/Unit
VC/Unit
Sales($000)
-Variable Costs
-Fixed Costs
-Depreciation
Pre-tax Profit
-Tax(40%)
Net Profit
+Depreciation
Operating Cash Flow
1
10,000
$640
$350
6,400
3,500
300
900
1,700
680
1,020
900
1,920
2
15,000
$640
$350
9,600
5,250
300
900
3,150
1,260
1,890
900
2,790
3
9,000
$540
$350
4,860
3,150
300
900
510
204
306
900
1,206
Year 1 Ping King CF from Operations
using Methods 1 & 3
Method 1: Oper. CF = revenues – cash
expenses – taxes = 6400 – 3800 - 680 =
1920
Method 3: (revenues – cash expenses) x
(1 – tax rate) + depreciation x tax rate =
(6400 – 3800)(1 – 0.4) + 900(0.4) = 1920
Total Incremental Cash Flows & Decision
for Ping Kings ($000s)
Year
0
1
2
Cap Inv (4500)
WC Inv
(640)
(320)
474
Oper CF
1920
2790
Total CF (5140)
1600
3264
CF0
C01
C02
NPV at 18% = 320.247 or $320,247
IRR = 21.5%
3
1200
486
1206
2892
C03
Indirect CF Effects
Include impact that a new project would
have on existing company sales and
expenses.
Example: Callaway Golf considers making
a new line of irons. They must consider
lost sales on existing product line of irons.
What about this?
Ping’s current line of irons is the Ping i3,
which have an estimated product life of 1
year remaining. Should Ping go ahead
with the Ping Kings project if they thought
next year’s Ping i3 sales and variable
costs would decrease by $1,000,000 and
$500,000 respectively on a BEFORE-TAX
basis.
This would affect the year 1 CF from
Operations: Indirect Effect
Year
Orig 1
Change
Revenue($000)
6,400
(1,000)
-Variable Costs
3,500
(500)
-Fixed Costs
300
-Depreciation
900
Pre-tax Profit
1,700
(500)
Tax(40%)
680
(200)
Net Profit
1,020
(300)
+Depreciation
900
Oper Cash Flow
1,920
(300)
 New year 1 total cash flow = 1620 – 320 = 1300,
 NEW NPV at 18% = 66.009 or $66,009
 New IRR = 18.7%
New 1
5,400
3,000
300
900
1,200
480
720
900
1,620
Inflation and Projected Cash Flows
INFLATION RULE
 Be consistent in how you handle inflation!!
 Use nominal interest rates to discount
nominal cash flows.
 Use real interest rates to discount real cash
flows.
 You will get the same results, whether you use
nominal or real figures
Separation of Investment &
Financing Decisions
 When valuing a project, ignore how the project is
financed (exclude interest expense from cash
flow forecast).
 Following the logic from incremental analysis
ask yourself the following question: Is the project
existence dependent on the financing? If no, you
must separate financing and investment
decisions.
MACRS Depreciation vs. Straight-Line for
Ping Kings

Fastest depreciation method that corporations are allowed to use for tax
purposes.

Assume our Ping Kings equipment (cost = $4,500,000) falls into the 5-year
MACRS class. (recall tax rate of 40%, r = 18%). Should MACRS be used?

Depreciation Tax Shield (Savings) = Deprec. X tax rate
Dep
Diff in
PV of
Year
Dep%
M Dep S-L Dep
Diff
TaxShd
TaxShd
1
20.00
900,000 900,000
0
0
0
2
32.00
1,440,000 900,000
540,000 216,000
155,128
3
19.20
864,000 900,000
(36,000) (14,400)
(8,764)
4
11.52
518,400 900,000
146,364
5
11.52
518,400 900,000
6
5.76
259,200

MACRS Year 3 Book Value = 1,296,000

Straight-Line Year 3 Book Value = 1,800,000

*Difference in After-tax Salvage Value = .4(1,296,000 – 1,800,000) = -201,600

PV of After-Tax Salvage Value Difference = -201,600/(1.18)3 = -122,700

Change in NPV = 146,364 – 122,700 = 23,664
MACRS Cash Flows for Ping Kings (using
Method 2)
Year
1
2
Unit Sales
10,000
15,000
$/Unit
$640
$640
VC/Unit
$350
$350
Sales($000)
6,400
9,600
-Variable Costs
3,500
5,250
-Fixed Costs
300
300
-Depreciation
900
1,440
Pre-tax Profit
1,700
2,610
-Tax(40%)
680
1,044
Net Profit
1,020
1,566
+Depreciation
900
1,440
Operating Cash Flow
1,920
3,006
WC Cash Flow
(320)
474
After-Tax SV
Total Cash Flow
1,600
3,480
Initial CF (T=0) = 5140
NPV at 18% = $343,910 vs. $320,247 under straight-line depreciation
3
9,000
$540
$350
4,860
3,150
300
864
546
218
328
864
1,192
486
998
2,676
Comprehensive Example (Last half of
Wednesday’s Lecture)
Will post example on website Monday, that
we will work through in Wednesday’s
lecture.