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Corporate FinanceNPV and other investment rules

Yrjö Koskinen

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Outline

Net Present Value

Alternative Decision Rules Payback

IRR

Project Selection with Resource Constraints» Profitability Index

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Net Present Value

The investment project generates the following cash flows:

CF0 , CF1 , CF2 , ... , CFT

NPV of the project is just a present values of all (incremental) cash flows:

- where rWACC is the weighted average cost of capital- we assume here that WACC remains constant

- often CF0 is a negative number (initial investment)

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Example

The investment project has the following cash flows:

If the WACC (the discount rate) is 8%, what is the NPV?

Note: in Excel, deduct the initial investment separately» NPV in Excel assumes that first cash flow occurs one period from now

Period 0 1 2 3

Cash flow -850 200 400 500

04.7508.1

500

08.1

400

08.1

200850

32NPV

Microsoft Excel Worksheet

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Good Attributes of the NPV Rule

Benefit/loss in today’s money» The dollar value of the project today

Uses all cash flows of the project Discounts all cash flows properly Good for accepting/rejecting proposals

» Objective benchmark from the capital markets» Accept if NPV>0, reject if NPV<0

Good for ranking proposals» The higher the NPV, the better the project

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Alternative Rules Versus the NPV Rule

Sometimes alternative investment rules may give the same answer as the NPV rule, but at other times they may disagree.

» When the rules conflict, the NPV decision rule should be followed.

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The Payback Rule

The payback period is the amount of time it takes to recover or pay back the initial investment.

If the period is less than a pre-specified length of time, you accept the project. Otherwise, you reject the project.» The payback rule is used by many companies because of its simplicity.» However, the payback rule does not always give a reliable decision

since it ignores the time value of money and the cash flows after the payback period.

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Payback Rule

Year A B C

0 - 100 -100 -100

1 50 20 50

2 30 30 30

3 20 50 20

4 60 60 100

What are the payback periods?

What is the best project? What is the problem

with payback rule?

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Pros and Cons of Payback Rule

Disadvantages:» Ignores the time value of money» Ignores cash flows after the payback period» Biased against long-term projects» Requires an arbitrary acceptance criteria» A project accepted based on the payback criteria may not have a

positive NPV Advantages:

» Easy to understand» Biased toward liquidity» Helps keep management accountable

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The Internal Rate of Return

IRR: the discount that sets NPV to zero

Rule: » Take any investment where the IRR exceeds the cost of

capital: » Turn down any investment whose IRR is less than the

cost of capital:

0

1)(

10

tt

t

IRR

CCIRRNPV

WACCrIRR

WACCrIRR

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Example

The investment project has the following cash flows:

What is the IRR?

32 1

500

1

400

1

2008500

rrr

Microsoft Excel Worksheet

%20.12IRR

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The Internal Rate of Return

The IRR Investment Rule will give the same answer as the NPV rule in many, but not all, situations.

In general, the IRR rule works for a stand-alone project if all of the project’s negative cash flows precede its positive cash flows.

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IRR Problems

There could be several issues with IRR approach:» Borrowing versus Lending» Different horizons» Multiple or no IRR» Different scales

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IRR Problems: Borrowing or Lending

Consider the following example» Project A is an investment (lending)» Project B is a financing opportunity (borrowing)

The IRR for both projects is the same – NPV only accepts project A If we want to use IRR rule, we have to modify it:

» If cash outflows are followed by cash inflows, accept the project if IRR exceeds the cost of capital

» If cash inflows are followed by cash outflows, accept the project if IRR is below the cost of capital

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IRR Problems: Different Horizons

Consider choosing between C and D:

Project C has higher IRR, but project D has higher NPV

The IRR rule fails to recognize that a long-lived project D provides a superior return over longer horizon, whereas project C gives high return only for one period

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Cross-Over Rate

With low discount rates D is better (higher NPV), but with high discount rates C is better

What is the cross-over rate?

The IRR of project D-C is 22.5%» If cost of capital is less than 22.5%, choose D» If cost of capital is greater than 22.5%, choose C

Period 0 1 2

Project C -5000 8000 0

Project D -5000 0 9800

D-C 0 -8000 9800

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IRR Problems: Multiple IRR or no IRR

Consider projects E and F:

Project E has two IRRs. Project F has no IRR!

There can be as many IRR as there are changes in sign on cash flows. Sometimes, there are no real IRR.

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IRR Problems: Different Scale

Compare projects A and G:

The IRR rule suggests using A over G But A has much lower NPV!

IRR rule cannot be used to compare projects with different scale

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The Bottom Line for IRR

The IRR rule has shortcomings for making investment decisions and you should know the limitations of IRR.

The IRR itself remains useful. IRR measures:

» The average return of the investment

» The break-even level for the cost of capital

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The Profitability Index (PI)

Minimum Acceptance Criteria: » Accept if PI > 1

Ranking Criteria: » Select alternative with highest PI

Investment Initial

FlowsCash Future of PV TotalPI

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Example

The project has the following cash flows.

With r=8%, the NPV is 75.04 What is the PI?

09.1850

04.75850

PI

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The Profitability Index

Disadvantages:» Problems with mutually exclusive investments

Advantages:» May be useful when available investment funds are limited» Easy to understand and communicate» Correct decision when evaluating independent projects

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Conclusion

Always calculate NPV when evaluating investments IRR very useful, but be aware of the pitfalls Payback problematic, but widely used and simple Profitability index is useful if the firm is financially

constrained» Most bang for the buck