1. Valuation Methods & Capital Budgeting
Moeller-Finance
Valuation Methods & Capital Budgeting
Payback/Discounted Payback
IRR
MIRR
Benefit Cost Ratio (BCR)
NPV (DCF)
FCF: Free cash flow
FTE: Flow to equity
APV: Adjusted present value
Notes-Capital Budgeting

2. Moeller-Finance
Payback Rule
Payback period: The amount of time it takes to recover the original cost.
Payback rule: If the calculated payback period is less than or equal to some pre-specified payback period, then accept the project. Otherwise reject it.
The Payback Rule
Payback period: the length of time until the accumulated cash flows from the investment equal or exceed the original cost. We will assume that cash flows are generated continuously during a period.
The Payback Rule: An investment is accepted if its calculated payback period is less than or equal to some pre-specified number of years. Otherwise reject it.
Notes-Capital Budgeting

3. Moeller-Finance
The Payback Rule
$200
$420
$645
$855
Time 1 2 3 4
Example The marketing department of your firm is considering whether to invest in a new product. The costs associated with introducing this new product are $600 and the expected cash flows over the next four years are $200, $220, $225 and $210.
It has been decided that the project should be accepted if the payback period is 3 years. The appropriate discount rate for these cash flows is 20%. Using the payback rule, should this project be undertaken?
By looking at the accumulated cash flows we know that the payback occurs sometime during the second year because at the end of three years we have more than $600 while we have less than $600 at the end two years.
Since we get paid back in 2.8 years which is less than our payback period, we should accept the project.
$-600
Payback period=2+(( )/225)=2.8 years Accept because payback < 3 years
Notes-Capital Budgeting

4. Advantages and Disadvantages of the Payback Rule
Moeller-Finance
Advantages and Disadvantages of the Payback Rule
Advantages
Easy
Biased toward liquidity
Quick evaluation
Adjusts long term cash flow uncertainty (by ignoring them)
Disadvantages
Ignores TVM
Ignores cash flow beyond payback period
Biased against long term projects
Popular among many large companies
Commonly used when the:
capital investment is small
merits of the project are obvious so more formal analysis is unnecessary
Notes-Capital Budgeting

5. The Discounted Payback Rule
Moeller-Finance
The Discounted Payback Rule
Accumulated discounted cash flows
Time 1 2 3 4
The Discounted Payback Rule
Discounted Payback period: The length of time until the accumulated discounted cash flows from the investment equals or exceeds the original cost. We will assume that cash flows are generated continuously during a period.
The Discounted Payback Rule: An investment is accepted if its calculated discounted payback period is less than or equal to some pre-specified number of years.
Example: Consider the previous investment. The initial cost is $600 million. The discounted payback period is 3 years. The appropriate discount rate for these cash flows is 20%. Using the discounted payback rule, should the firm invest in the new product?
$-600
The project never pays back so reject. What is the NPV?
Notes-Capital Budgeting

6. Discounted Payback Rule?
Moeller-Finance
Discounted Payback Rule?
Things to Consider
Involves discounting
How do you choose r?
How do you choose the cut-off period?
Advantages
If project ever pays back then NPV>0
Biased toward liquidity
Easy
Disadvantages
May reject NPV>0 projects
Cut-off period is arbitrary
Biased against long term projects
Bottom Line: Why not just use NPV?
Notes-Capital Budgeting

7. Benefit-Cost Ratio (BCR)
Moeller-Finance
Benefit-Cost Ratio (BCR)
Rato of discounted inflows to outflows.
Rule: Accept project if BCR greater than 1.
Use caution if using to compare mutually exclusive projects.
Similar BCRs can have radically different NPV’s.
Benefit-Cost Ratio (BCR)
This measure is closely related to NPV and the decision criteria is accept the project if the BCR is greater than 1 (give all cash outflows a positive sign).
The measure can be misleading if the two projects are mutually exclusive because the measure is normalized by the investment (cash outflows). For instance, say you want to introduce one product and are evaluating two possibilities whose BCRs are identical, are you indifferent between the two products?
Here are the two possibilities:
Product A: PV(Inflows)=4,500 PV(Outflows)=3,000 BCR=1.5
Product B: PV(Inflows)= PV(Outflows)= BCR=1.5
NO! Clearly Product A is preferred!
Notes-Capital Budgeting

8. Internal Rate of Return (IRR) Rule
Moeller-Finance
Internal Rate of Return (IRR) Rule
IRR is that r that makes the NPV=0
The Internal Rate of Return (IRR) Rule
Internal rate of return: The discount rate that makes the present value of future cash flows equal to the initial cost of the investment. Equivalently, the IRR is the discount rate that gives the project a zero NPV. .
Notes-Capital Budgeting

9. Moeller-Finance
IRR Rule
Accept the project if the IRR is greater than the required rate of return. Otherwise, reject the project.
Comparison of NPV and IRR
If cash flows are conventional and project is independent, then NPV and IRR lead to same accept and reject decisions.
IRR Rule: An investment is accepted if its IRR is greater than the required rate of return. An investment should be rejected otherwise
Calculating IRR: Like YTMs, IRR more difficult to calculate without tools.
Need financial calculator
Trial and error
Spreadsheet
Comparison of IRR and NPV
IRR and NPV rules lead to identical decisions when the following conditions are satisfied.
Conventional Cash Flows: The first cash flow (the initial investment) is negative and all the remaining cash flows are positive
Project is independent: A project is independent if the decision to accept or reject the project does not affect the decision to accept or reject any other project.
When one or both of these conditions are not met, problems with using the IRR rule can result.
Notes-Capital Budgeting

10. IRR Rule and Unconventional Cash Flows
Moeller-Finance
IRR Rule and Unconventional Cash Flows
Unconventional cash flows: A negative cash flow after a positive one.
Strip Mining Project
Year Cash Flows
Problems with the IRR Rule
Unconventional Cash Flows: Cash flows come first and investment cost is paid later. In this case, the cash flows are like those of a loan and the IRR is like a borrowing rate. Thus, in this case a lower IRR is better than a higher IRR
Multiple rates of return problem: The possibility that more than one discount rate makes the NPV of an investment project zero.
Notes-Capital Budgeting

11. Moeller-Finance
Problems with the IRR Rule Unconventional cash flows lead to multiple IRR’s 25% and 33.33%
Notes-Capital Budgeting

12. Mutually Exclusive Taking one project means another is not taken
Moeller-Finance
Mutually Exclusive
Taking one project means another is not taken
The highest IRR may not have the highest NPV
To evaluate we need to find the crossover rate
Take the differences between the two projects cash flows and compute the IRR for those incremental flows
Problems with the IRR Rule (continued)
Mutually Exclusive Projects
Mutually exclusive projects: If taking one project means another project is not taken, the projects are mutually exclusive. The one with the highest IRR may not be the one with the highest NPV.
Crossover Rate: The discount rate that makes the NPV of the two projects the same.
Finding the Crossover Rate
Use the NPV profiles
Take the difference in the projects' cash flows each period and calculate the IRR.
Notes-Capital Budgeting

13. Mutually Exclusive Cash Flows
Moeller-Finance
Mutually Exclusive Cash Flows
Example: If project A has a cost of $500 and cash flows of $325 for two periods, while project B has a cost of $400 and cash flows of $325 and $200 respectively, the incremental cash flows are:
Notes-Capital Budgeting

14. NPV Profiles of Mutually Exclusive Projects
Moeller-Finance
NPV Profiles of Mutually Exclusive Projects
Crossover Rate = 11.8
IRRB=22.17
The crossover rate is 11.8%. At this rate, NPVA = NPVB = $50.71
IRRA=19.43
Notes-Capital Budgeting

15. Reinvestment Rate Assumption
Moeller-Finance
Reinvestment Rate Assumption
During the life of a project, what are the investment assumptions of the intermediate cash flows?
Implicitly the PV oriented methods assume that the cash flows can be reinvested at r.
Is this reasonable?
NPV
IRR
Implicit in any PV type calculations, the implicit assumption is that the intermediate cash flows can be reinvested at r.
Think back to what the appropriate r is, the r that reflects the riskiness of the cash flows. In other words, r should reflect what you could make on other similar risk investments.
The r in the NPV calculations should be a reasonable proxy for the return you could make on similar risk investments so assumption that you could find reinvest the intermediate cash flows at that rate is reasonable.
However, the r in the IRR calculations has no theoretic relationship to alternative investments returns so the reinvestment rate assumption can be problematic for IRR.
Notes-Capital Budgeting

16. Modified IRR (MIRR) Solves the reinvestment rate problem
Moeller-Finance
Modified IRR (MIRR)
Solves the reinvestment rate problem
Example: A project’s cash flows are -400, 325 and Appropriate r is 12%
Accept the project because 18.74%>12%
Note: The IRR on this project is 22.16%
How to compute MIRR: Say you have a project whose appropriate r is 12% and has the following estimated cash flows starting in year 0: -400, 325 and 200.
1. Compute the PV(outflows) using the appropriate r. Take all negative flows and discount them back to time zero.
2. Compute the FV(inflows) using the appropriate r. Take all positive yearly flows and move them forward to the last year of the project.
Compute the r (r=MIRR) that causes PV to equal FV over the life of the project
Decision rule: If MIRR > required rate of return, accept the project % is greater than 12% so accept the project.
Notes-Capital Budgeting

17. Summary of IRR/MIRR Advantages: Easy to understand Disadvantages:
Moeller-Finance
Summary of IRR/MIRR
Advantages: Easy to understand
Conventional Cash Flows and Independent Projects:
Same Decisions as NPV Rule
Required Rate of Return Benchmark
Often same discount rate in NPV
MIRR has more realistic reinvestment rate (use instead of IRR if possible)
Disadvantages:
Unconventional cash flows may result multiple answers
If projects are mutually exclusive may lead to incorrect decisions
Not always easy to calculate
Difficult to interpret (particularly if the project has multiple r’s)
IRR may have unrealistic reinvestment rate
Very Popular: People like to talk in terms of returns
Survey of 100 largest Fortune 500 Ind.
99% use IRR Rule
85% use NPV Rule
Notes-Capital Budgeting

18. NPV(DCF) Valuation Methods
Moeller-Finance
NPV(DCF) Valuation Methods
FCF: All relevant cash flows excluding financing costs discounted by the “whole firm” r (typically estimated with WACC(adjusted for taxes))
FTE: FCF minus payments to other finance sources (typically debt holders) discounted by re
APV: All relevant cash flow components separately discounted by the appropriate r’s
Note:
re (e=equity) is the same as rS (S=stock)
rd (d=debt) is the same as rB (B=bond)
Notes-Capital Budgeting

19. Compare Methods FCF FTE APV
Moeller-Finance
Compare Methods
FCF
Very strict assumptions of constant proportion capital structure (from WACC)
Can adjust r if risk or capital structure is different from existing firm
Tax debt shield must be tcD (for WACC(adjusted))
FTE
Probability of payments to other finance sources, i.e. debt holders
Option to default usually not considered so FTE value is usually low
Difficult to extrapolate entire firm value
APV
Flexible and works well for changing capital structure
Usually will need an estimate of unlevered r
Potential for estimation error depending on NPV of financing
Notes-Capital Budgeting

20. Moeller-Finance
Relevant Cash Flows
Incremental cash flows: Only the incremental portion of any flow is relevant
Otherwise known as the Stand-Alone Principle
Project = "Mini-firm"
Allows us to evaluate the investment project separately from other activities of the firm
Allows us to make optimal decisions with a relatively simple process
Estimating Cash Flows for NPV
Relevant Cash Flows: Cash flows which are generated because a project is undertaken.
“If we do the project, what will the cash flow be?”
“If we don’t do the project, what will the cash flow be?”
The cash flow difference between these two statements is the incremental cash flow.
Incremental Cash Flows: Any changes in the firm's future cash flows that are a direct consequence of taking the project.
Note: Incremental cash flows are a way of thinking about what is relevant, do not think of them as an alternative to relevant cash flows.
The Stand-Alone Principle: The evaluation of a project based on it's incremental cash flows. View each project as a "mini-firm" with its own assets, revenues and costs. Usually this will simplify the process and as long as, each decision is optimal (accept if NPV>0) and the relevant cash flows are estimated correctly, this method will maximize firm value.
Notes-Capital Budgeting

21. Relevant Cash Flows? Sunk Costs No Opportunity Costs Yes
Moeller-Finance
Relevant Cash Flows?
Sunk Costs No
Opportunity Costs
Yes
Side Effects (Erosion)
Net Working Capital
Value of cash flow volatility change
Financing Costs
No (there are some methods where this is relevant)
Allocated Overhead Costs
Which Costs Should Be Included In Incremental Cash Flows?
Sunk Costs: A cash flow already paid or already promised to be paid.
Opportunity Costs: Any cash flow lost by taking one course of action rather than another.
Side Effects: Projects often hurt or help one another
Erosion: Revenues gained by a new project at the expense of the firm's other products or services.
Net Working Capital (NWC): In all capital budgeting projects we will assume that net working capital is recovered at the end of the project.
Value of cash flow volatility change: Investor’s value changes in volatility to the extent that it affects the value of the firm due to convex costs such as bankruptcy costs and taxes.
Financing Costs: Interest, principle on debt and dividends
Allocated Overhead Costs: Overhead costs include general headquarter costs, such as rent and salaries.
ALL CASH FLOWS SHOULD BE AFTER TAX!
All Cash Flows should be after-tax cash flows
Notes-Capital Budgeting

22. How do we make reasonable cash flow estimates?
Moeller-Finance
How do we make reasonable cash flow estimates?
Estimate them from scratch
Pro forma financial statements
Probably the best current estimate of future flows.
Make sure you adjust the financial statements for the difference between accounting flows and finance flows.
Finance flows are based on the principle of opportunity costs and the timing of the flows is based on when the money is actually paid/received
Accounting flows (as presented in financial statements) are based on historical costs and the timing of the flows is usually based on accrual (not cash) accounting
Use statements to get the basic project cash flow
Need an after tax terminal value
Assume the project goes on forever and use a perpetuity
Assume the project ends and the balance sheet is zeroed out (everything is sold and settled)
Pro forma financial statements: Financial statements forecasting future years' operations. It is probably the best current estimate of future cash flows.
Use pro forma income and balance sheet statements for capital budgeting.
Make sure you adjust the financial statements for the difference between accounting flows and finance flows.
Finance flows are based on the principle of opportunity costs and the timing of the flows is based on when the money is actually paid/received.
Accounting flows (as presented in financial statements) are based on historical costs and the timing of the flows is usually based on accrual (not cash) accounting.
For instance: Accounting rules (FASB) previously did not require the cost of stock options granted as compensation to be recognized as a cost. However, from a finance flow perspective, these options have an opportunity cost of what you could have ‘sold’ similar options for. If you strictly use the financial accounting statements as a basis for cash flows, you would miss the relevant cost of stock options.
Note: The thought of adjusting for the difference between accrual and cash accounting may seem daunting but we have a reasonably simple solution of including the cost of net working capital in the relevant cash flows. In this way, we effectively account for the difference in the timing of when the flows are received and paid.
After tax terminal value: Depending on the nature of the project either assume the project reaches a steady state (use a growing or non-growing perpetuity to value) or the project ends. Make sure if you choose a steady state that either the firm’s assets are naturally long lived or cash flows include asset replacement and/or major maintenance.
Holden Book: Chapter 15
Notes-Capital Budgeting

23. Moeller-Finance
Two Approaches
Item by item Discounting: Separately forecast relevant flows then discount them
Very flexible: Can use different discount rates for each flow
Whole Project Discounting: determine project’s relevant cash flows, sum them in each year then discount the yearly sum
FCF=OCF + Net Capital Spending - Changes in NWC
Operating Cash Flows (OCF): EBIT+Depreciation+Other Non-Cash Expenses-Taxes
Net Capital Spending
Project specific assets, initial costs
After tax salvage value (if project ends)
Changes in NWC
NWC=CA-CL
Changes in NWC = NWC(t)-NWC(t-1)
Recover all NWC at the end of the project (if project ends)
Two Approaches to Estimate the Capital Budgeting NPV
1. Item by item discounting
Separately forecast revenues, costs, depreciation, capital spending and NWC and discount each item.
Flexible: Can use different discount rates for different cash flows if it is a reasonable assumption.
2. Whole project discounting (the sum of these relevant cash flows are called ‘free cash flow’).
Determine project cash flows from financial statements and project estimations then sum them in each period and then discount each period’s sum.
Operating Cash Flow: OCF=EBIT+Depreciation+Other Non-Cash Expenses-Taxes
NOTE: This formula for OCF assumes you are starting with a fairly simple set of financial statements. If your statement is more complicated, though there will be more adjustments to get the relevant flows, the principles will not change. When the estimation is possible, always use estimates for expected cash flows, i.e. forward looking, not yesterdays value.
b. Net Capital Spending: Estimate the capital (project specific assets) cash flows. These are the flows that are not included in (a) or (c) such as the cost of the new plant and equipment. At the end of the project if you assume the capital assets are sold the final capital cash flow should be the after-tax cash flow from the sale (salvage value).
c. Changes to NWC
NWC=Current Assets-Current Liabilities
Changes in NWC=NWC(t)-NWC(t-1)
We will always recover all NWC at the end of the project.
Notes-Capital Budgeting

24. Alternate Ways to Compute OCF
Moeller-Finance
Alternate Ways to Compute OCF
GOAL: Make sure that all relevant cash inflows and outflows are included (Holden shows several of these methods)
Bottom Up: OCF=Net Income + Non-cash deductions
CAUTION: This method only works if there are no financing costs already taken out of net income!
Top Down: OCF=Sales - Costs - Taxes
Subtract all deductions except non-cash items
Tax Shield: OCF=(Sales-Costs) x (1-tc) + (non-cash deductions x tc)
Notes-Capital Budgeting

25. Scenario Analysis WHAT IF? Estimate NPV with various assumptions
Moeller-Finance
Scenario Analysis
WHAT IF?
Estimate NPV with various assumptions
Statistical distribution
Best case, worst cast, most likely case
Sensitivity analysis: Change in NPV due to one or a few items
Scenario Analysis
One approach to evaluating cash flow and NPV estimates that involves asking "what-if" questions.
Assess the degree of forecast risk and identify those components of the analysis that are most critical to the success or failure of an investment.
Steps involved.
1.Estimate NPV estimates based on most likely projected cash flows. Call this the base case.
2.After completing the base case, investigate the impact of different assumptions about the future of our estimates.
a.Put an upper and lower bound on various components of the projects. For example, estimate NPV using +10 and -10 percent of sales in the base case.
b. Estimate a worst case (pessimistic case) and best case (optimistic case).
i. Worst case: Higher costs and lower sales than base case.
ii. Best case: Lower costs and higher sales than base case.
3. After looking at alternative scenarios, we can determine which ones results in positive NPVs.
a. Are these the most plausible scenarios? Do the economic assumptions underlying these scenarios make sense?
b. Probability theory can be used to assess various likelihoods of each scenario, multiply the NPV by the probability and add them up (make sure the probabilities add up to 100%).
Sensitivity analysis: A variation of scenario analysis. An investigation of NPV estimates when only one variable is changed.
Notes-Capital Budgeting

26. Capital Rationing NPV>0 then accept, is based on unlimited capital
Moeller-Finance
Capital Rationing
NPV>0 then accept, is based on unlimited capital
NPV is still the best criteria but we need to ration
Profitability Index is NPV per investment dollar
Order the projects by PI
Choose projects until PI<0 or you run out of money
Capital Rationing
The previous investment criteria we discussed assumes that the firm has unlimited access to the capital markets. Though this is a reasonable assumption in a well functioning capital market, what if a firm is capital constrained? How should the firm decide which project(s) to accept?
Instead of looking at the NPV alone, we use a measure that quantifies the NPV per initial investment dollar, the Profitability Index(PI).
Notes-Capital Budgeting

27. You have $500,000 to spend Project B, $200,000 Project D, $250,000
Moeller-Finance
You have $500,000 to spend
Project
Investment
NPV PI A
500,000
80,000
16% B
200,000
45,000
22.5% C
300,000
55,000
18.3% D
250,000
50,000
20%
Project B, $200,000
Project D, $250,000
Project C, $50,000 (partial investment)
What if you can’t do partial investments?
Assume your firm has the following investment projects they can invest in this year and the firm can make partial investments in each project. However you only have $500,000 in capital. Which of the following project(s) would you recommend?
Order the projects by the PI and choose those project(s) until the PI is negative or you run out of capital.
What if you can’t do partial investments? The optimization becomes more complicated and you either need to manually compare the sum of the NPV’s over all possible investment combinations or utilize an integer linear program.
Notes-Capital Budgeting

28. Evaluating projects with different economic lives
Moeller-Finance
Evaluating projects with different economic lives
Assumptions
Different lives
The project can go on forever
Equivalent Annual Cash (EAC) flows
A firm is choosing between two projects under the following circumstances
1. The projects have different economic lives
2. Whatever project the firm chooses, it needs it indefinitely. As a result, the capital assets will be replaced when it wears out.
The first way to determine the optimal project is to find a common number of years and just line the projects up in time, compute the NPV of the string of projects and pick the best.
The second way is to find the Equivalent Annual Cash flow (EAC): The equivalent annual cash flow (EAC) is the present value of a project's cash flows calculated on an annual basis. In other words, use the PV annuity formula and substitute EAC for C.
Note that this is sometimes called the Equivalent Annual Cost and if the periodic cash flow you compute (EAC) is a cost then you pick the process with the lowest EAC. Alternatively if the EAC you compute is a cash inflow (i.e., NPV), you pick the highest EAC.
Notes-Capital Budgeting

29. EAC Example Assume you need to choose between two production processes
Moeller-Finance
EAC Example
Assume you need to choose between two production processes
Original process: NPV=4,402,679, 8 year life
Alternative: NPV=3,200,000, 4 year life
Which process is better?
Assume you plan on producing this product indefinitely and the cost structure will stay the same. In addition, assume you have a different type of production facility it could use for production. This facility would have a NPV of $3.2 million and a 4 year project life. Assume you can extend your use of this production facility indefinitely you will have the same cost structure. Which production facility should you choose? The one with the higher yearly cash flow (EAC).
Alternatively, because it is easy to find a common number of years for these two projects, we can move them both to eight year projects and compare. The first project is an eight year project so it’s NPV is simply $4,402,679. The next project is 3.2 million today plus 3.2 million in year 4 or $5,233,658. (3.2m + 3.2m/1.124) Again, we would rather choose the second option.
Notes-Capital Budgeting

30. Biases Systematic deviation from the actual value
Moeller-Finance
Biases
Systematic deviation from the actual value
Dealing with Bias in Capital Budgeting
What is Bias?
Bias is the deviation of the expected value of an estimate from the actual quantity it estimates.
Biases are systematic
Being aware of bias does not automatically eliminate it.
Two types of biases:
1. Cognitive
2. Motivational
Notes-Capital Budgeting

31. Cognitive Bias When conscious beliefs do not reflect the information
Moeller-Finance
Cognitive Bias
When conscious beliefs do not reflect the information
Easy to recall/available information is used
Adjustment and anchoring
Representative
Cognitive Bias
Cognitive Bias occurs when conscious beliefs do not reflect the information
Availability of information: If information is easy to recall, a greater weight is put on this information.
Adjustment and anchoring: A tendency to anchor an initial estimate of future cash flows and not adjusted to new information
Representative: If an outcome "seems to be" representative of the possibilities, it is given greater weight.
Unstated assumptions are not communicated with the estimates.
Notes-Capital Budgeting

32. Motivational Bias Statements do not reflect beliefs Dishonesty Greed
Moeller-Finance
Motivational Bias
Statements do not reflect beliefs
Dishonesty
Greed
Asymmetric Reward
Brown-nosing
Fear
Motivational Bias
Motivational Bias occurs when statements do not reflect conscious beliefs
Reasons for motivational bias:
1. Dishonesty: What does the project require to look good?
2. Greed: Will my career benefit if I change the answer?
3. Asymmetric Reward: How will I be rewarded for going under/over the budget?
4. Brown-nosing: What does my boss want to hear?
5. Fear: What does my boss want to hear? Will I be perceived as indecisive?
Motivational biases are controllable but it depends on the corporate culture of the organization.
Notes-Capital Budgeting

33. Managing Bias Recognize it! Keep going back to the economics
Moeller-Finance
Managing Bias
Recognize it!
Keep going back to the economics
Sensitivity analysis
Information management
Check and recheck assumptions
Notes-Capital Budgeting