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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 Payback Rule Payback period: The amount of time it takes to recover the original cost.

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valuation methods capital budgeting
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
payback rule
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
The Payback Rule












Payback period=2+((600-420)/225)=2.8 yearsAccept because payback < 3 years

advantages and disadvantages of the payback rule
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

The Discounted Payback Rule

Accumulated discounted cash flows








The project never pays back so reject.What is the NPV?

discounted payback rule
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?
benefit cost ratio bcr
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.

internal rate of return irr rule

Internal Rate of Return (IRR) Rule

IRR is that r that makes the NPV=0

irr rule
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 isindependent, then NPV and IRRlead to same accept and reject decisions.
irr rule and unconventional cash flows
IRR Rule and UnconventionalCash Flows
  • Unconventional cash flows: A negative cash flow after a positive one.
  • Strip Mining Project
  • Year Cash Flows
  • 0 -60
  • 1 155
  • 2 -100
mutually exclusive
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
npv profiles of mutually exclusive projects
NPV Profiles of Mutually Exclusive Projects

Crossover Rate = 11.8



reinvestment rate assumption
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
modified irr mirr
Modified IRR (MIRR)
  • Solves the reinvestment rate problem
  • Example: A project’s cash flows are -400, 325 and 200. Appropriate r is 12%
  • Accept the project because 18.74%>12%
  • Note: The IRR on this project is 22.16%
summary of irr mirr
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
npv dcf valuation methods
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)
compare methods
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

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

Relevant Cash Flows?

  • Sunk Costs
  • No
  • Opportunity Costs
  • Yes
  • Side Effects (Erosion)
  • Yes
  • Net Working Capital
  • Yes
  • Value of cash flow volatility change
  • Yes
  • Financing Costs
  • No (there are some methods where this is relevant)
  • Allocated Overhead Costs
  • No

All Cash Flows should be after-tax cash flows


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)

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)
alternate ways to compute ocf
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)
scenario analysis
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
capital rationing
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
you have 500 000 to spend
You have $500,000 to spend
  • Project B, $200,000
  • Project D, $250,000
  • Project C, $50,000 (partial investment)
  • What if you can’t do partial investments?
evaluating projects with different economic lives
Evaluating projects with different economic lives
  • Assumptions
    • Different lives
    • The project can go on forever
  • Equivalent Annual Cash (EAC) flows
eac example
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?
  • Systematic deviation from the actual value
cognitive bias
Cognitive Bias
  • When conscious beliefs do not reflect the information
    • Easy to recall/available information is used
    • Adjustment and anchoring
    • Representative
motivational bias
Motivational Bias
  • Statements do not reflect beliefs
    • Dishonesty
    • Greed
    • Asymmetric Reward
    • Brown-nosing
    • Fear
managing bias
Managing Bias
  • Recognize it!
  • Keep going back to the economics
  • Sensitivity analysis
  • Information management
  • Check and recheck assumptions