1. Capital Budgeting: Estimating Cash Flows and Analyzing Risk
CHAPTER 13
Capital Budgeting: Estimating Cash Flows and Analyzing Risk

2. Topics Estimating cash flows: Risk analysis: Real options
Relevant cash flows
Working capital treatment
Risk analysis:
Sensitivity analysis
Scenario analysis
Real options

3. Rules Incremental cash flows Noncash charges such as depreciation
Changes in NOWC (changes in inventory, A/R, A/P, accruals, and minimum cash balance)
Interest payment
Sunk cost
Opportunity cost
Externality (e.g., cannibalization)

4. Proposed Project Data
Machine: $200,000 cost + $10,000 shipping + $30,000 installation.
Economic life = 4 years.
Salvage value = $25,000.
MACRS 3-year class (modified accelerated cost recovery system).
Continued…

5. Project Data (Continued)
Annual unit sales = 1,250.
Unit sales price = $200.
Unit costs = $100.
Net working capital:
NWCt = 12%(Salest+1)
Tax rate = 40%.
Project cost of capital = 10%.

6. Incremental Cash Flow for a Project
Project’s incremental cash flow is:
Corporate cash flow with the project
Minus
Corporate cash flow without the project.

7. Treatment of Financing Costs
Should you subtract interest expense when calculating CF?
NO.
We discount project cash flows with a cost of capital that is the rate of return required by all investors (including debtholders).
Interest expense are part of the costs of capital. If we subtracted them from cash flows, we would be double counting capital costs.

8. Sunk Costs
Suppose $100,000 had been spent last year to improve the production line site. Should this cost be included in the analysis?
NO. This is a sunk cost. Focus on incremental investment and operating cash flows.

9. Incremental Costs
Suppose the plant space could be leased out for $25,000 a year. Would this affect the analysis?
Yes. Accepting the project means we will not receive the $25,000. This is an opportunity cost and it should be charged to the project.
A.T. opportunity cost = $25,000 (1 – T) = $15,000 annual cost.

10. Externalities
If the new product line would decrease sales of the firm’s other products by $50,000 per year, would this affect the analysis?
Yes. The effects on the other projects’ CFs are “externalities.”
Net CF loss per year on other lines would be a cost to this project.
Externalities will be positive if new projects are complements to existing assets, negative if substitutes.

11. What is an asset’s depreciable basis?
Basis = Cost
+ Shipping
+ Installation
$240,000

12. Annual Depreciation Expense
Year
% X
(Initial Basis)
= Deprec. 1
0.3333
$240,000
$79,992 2
0.4445
106,680 3
0.1481
35,544 4
0.0741
17,784

13. Include inflation 3% when estimating cash flows
Nominal r > real r. The cost of capital, r, includes a premium for inflation.
Continued…

14. Annual Sales and Costs Year 1 Year 2 Year 3 Year 4 Units Unit Price
1,250
Unit Price
$200
$206
$212.18
$218.55
Unit Cost
$100
$103
$106.09
$109.27
Sales
$250,000
$257,500
$265,225
$273,188
Costs
$125,000
$128,750
$132,613
$136,588

15. Operating Cash Flows Year 1 Year 2 Year 3 Year 4 Sales 250,000 257,500
265,225
273,188
Costs
125,000
128,750
132,613
136,591
Deprec.
79,992
106,680
35,544
17,784
EBIT
45,008
22,070
97,069
118,807
Taxes (40%)
18,003
8,828
38,827
47,523
EBIT(1 – T)
27,005
13,242
58,241
71,284
+ Deprec.
Net Op. CF
106,997
119,922
93,785
89,068

16. Cash Flows Due to Investments in Net Working Capital (NWC)
Sales
NWC
(12% of sales)
CF Due to
New Investment
in NWC
Year 0
$30,000
-$30,000
Year 1
$250,000
30,900
-900
Year 2
257,500
31,827
-927
Year 3
265,225
32,783
-956
Year 4
273,188

17. Salvage Cash Flow at t = 4 Salvage Value $25,000 Book Value
Gain or loss
Tax on SV (40%)
10,000
Net Terminal CF
$15,000

18. Net Cash Flows Year 0 Year 1 Year 2 Year 3 Year 4 Init. Cost
($240,000)
Op. CF
$106,997
$119,922
$93,785
$89,068
NWC CF
($30,000)
($900)
($927)
($955)
$32,782
Salvage CF
$15,000
Net CF
($270,000)
$106,097
$118,995
$92,830
$136,850

19. Project Net CFs Time Line
I/YR = 10
NPV = $88,010.
IRR = 23.9%. 1 2 3 4
(270,000)
106,097
118,995
92,830
136,850

20. What if you terminate a project before the asset is fully depreciated?
Basis = Original basis – Accum. deprec.
Taxes are based on difference between sales price and tax basis.
Taxes paid –
Sale proceeds
Cash flow from sale =

21. Example: If Sold After 3 Years for $25 ($ thousands)
Original basis = $240.
After 3 years, basis = $17.8 remaining.
Sales price = $25.
Gain or loss = $25 – $17.8 = $7.2.
Tax on sale = 0.4($7.2) = $2.88.
Cash flow = $25 – $2.88 = $22.12.

22. Example: If Sold After 3 Years for $10 ($ thousands)
Original basis = $240.
After 3 years, basis = $17.8 remaining.
Sales price = $10.
Gain or loss = $10 – $17.8 = -$7.8.
Tax on sale = 0.4(-$7.8) = -$3.12.
Cash flow = $10 – (-$3.12) = $13.12.
Sale at a loss provides a tax credit, so cash flow is larger than sales price!

23. Example in textbook (Fig 13-1, 13-2)

25. What is sensitivity analysis?
Shows how changes in a variable such as unit sales affect NPV or IRR.
Each variable is fixed except one. Change this one variable to see the effect on NPV or IRR.
Answers “what if” questions, e.g. “What if sales decline by 30%?”

26. Example: sensitivity analysis

27. What are the weaknesses of sensitivity analysis?
Says nothing about the likelihood of change in a variable.
Ignores relationships among variables.

28. What is scenario analysis?
Examines several possible situations, usually worst case, most likely case, and best case.
Provides a range of possible outcomes.

29. Figure 13-5 Repeated Here for convenience.
Inputs and Key Results for Each Scenario (Dollars in Thousands)
Scenarios:
Scenario Name
Base
Worst
Best
Probability of Scenario
50%
25%
Inputs:
Equipment cost
$7,750
$8,250
$7,250
Salvage value, equipment, Year 4
$639
Opportunity cost $0
Externalities (cannibalization)
Units sold, Year 1
10,000
8,500
11,500
Annual change in units sold, after Year 1
15% 5%
Sales price per unit, Year 1
$1.50
$1.25
$1.75
Annual change in sales price, after Year 1 4%
Variable cost per unit (VC), Year 1
$1.07
$1.17
$0.97
Annual change in VC, after Year 1 3%
Nonvariable cost (Non-VC), Year 1
$2,120
$2,330
$1,910
Annual change in Non-VC, after Year 1
Project WACC
10%
Tax rate
40%
30%
Working capital as % of next year's sales
Key Results:
NPV
$1,048
−$7,543
$19,468
IRR
13.79%
−29.40%
62.41%
MIRR
12.78%
−22.23%
43.49%
Profitability index
1.10
0.23
2.90
Payback
3.39
Not found
1.83
Discounted payback
3.80
2.07

30. Example: scenario analysis1

31. Are there any problems with scenario analysis?
Only considers a few possible out-comes.
Assumes that inputs are perfectly correlated—all “bad” values occur together and all “good” values occur together.

32. What is a real option?
Real options exist when managers can influence the size and risk of a project’s cash flows by taking different actions during the project’s life in response to changing market conditions.

33. What are some types of real options?
Investment timing options—delay the decision.
Growth options
Increase the capacity of an existing product line
Add new products
Expand into new geographic markets
Abandonment options
Contraction
Temporary suspension
Flexibility options

34. Simple decision tree

35. Staged decision tree
Read page

36. Example: staged decision tree

37. Assignment Review Chapter 12 slides from FINC3131
Chapter 13 problems:1,2,3,4,6,7,8 (a),9,17.