principles of corporate finance - fgv epge

Principles of Corporate Finance

Chapter 6. Why the NPV rule leads to better investment decisionsthan other criteria

Ciclo Profissional 2o Semestre / 2009

Graduacao em Ciencias Economicas

V. Filipe Martins-da-Rocha (FGV) Principles of Corporate Finance August, 2009 1 / 34

Topics covered

1 A review of the basicsI Net Present Value and its competitors

2 The payback periodI The book rate of return

3 Internal Rate of Return4 Capital rationing


Cash Transfers


Investment in a Project

Consider a firm with total market value (price per share times thenumber of shares outstanding) of $10 millionThe firm has $1 million cash (the value of the other assets must be$9 million)There is a project X with present value PV

To evaluate the PV of the project we should measure precisely theopportunity cost associated to the risk class of the project

If PV > 1 or NPV > 0, the project should be financed


CFO Decision Tools

The NPV criterium is not the only one used by managers


Features of the NPV

The NPV rule recognizes that a dollar today is worth more than adollar tomorrow

I Any investment rule that does not recognize the time value ofmoney cannot be economically sensible

The NPV rule depends solely onI forecasted cash flowsI opportunity cost of capital

Any investment rule that is affected byI the manager’s tastesI the company’s choice of accounting methodI the profitability of the company’s existing business

will lead to inadequate decisionsBecause present values are all measured in today’s dollars, we canadd them up. If there are two projects A and B, then

NPV(A ∪B) = NPV(A) + NPV(B)


Book rate of return

Some managers evaluate a project through its book rate of return

Book rate of return =book incomebook assets

The book income and book assets are accounting measuresThese components reflect tax and accounting figures, not marketvalues or cash flowsThey depend on which items the accountant chooses to treat ascapital investment and how rapidly they are depreciated


The Payback rule

Criterium

Some companies require that the initial outlay on an project should berecoverable within a specified period

Definition

The payback period of a project is the number of years before thecumulative forecasted cash flow equals the initial investment

The payback rule

There is a cutoff date

If the payback period of a project his greater than the cutoff date,then the project is rejected


The Payback rule: example

Assume the opportunity cost of capital for the three following projectsis 10%:

If the firm uses the payback rule with a cutoff period of two years, thenit accepts project B and C!


The Payback rule: drawbacks

The playback rule ignores all cash flows after the cutoff dateThe playback rule give equal weight to all cash flows before thecutoff date

I In particular, money has no time value

Occasionally companies discount the cash flows before theycompute the payback period


The Payback rule: drawbacks

The discounted payback rule will never accept a negative NPVprojectOn the other hand, it still takes no account of cash flows after thecutoff date, so that good long-term projects such as A continue torisk rejection


Internal (or Discounted-Cash-Flow) Rate of Return

Consider a project that generates a single payoff after one periodC0 C1

- investment payoff

We can define the Internal Rate of Return (IRR) as follows

IRR =payoff− investment

investment

The IRR is the discount rate that makes NPVIRR = 0 where

NPVIRR = C0 +C1

1 + IRR

If r is the opportunity cost of the project’s risk class then

NPVr > 0⇐⇒ IRR > r



If a project generates a single payoff then a correct criterium to acceptthe investment is to check if

IRR > r

in other words,

Internal Rate of Return of the Project > Opportunity Cost



Consider now a project generating payoffs until period T

We can generalize the definition of IRR as follows

Definition

The Internal Rate of Return of a project A defined by a sequence

(Ct)06t6T

of cash flows is the solution of the following equation

NPVIRR(A) = 0

i.e.,

C0 +C1

1 + IRR+

C2

(1 + IRR)2+ . . .+

CT(1 + IRR)T

= 0


Internal Rate of Return: Example

There is no general method to find the Internal Rate of ReturnCalculations usually involve trials and errors

Consider a project A with the following sequence of cash flows:

Choosing ρ = 0, we get NPVρ = +$2, 000

Choosing ρ = 50%, we get NPVρ = −$889

Choosing ρ = 28%, we get NPVρ = +$4

Choosing ρ = 29%, we get NPVρ = −$46


Internal Rate of Return: Example


Internal Rate of Return: the Rule

Definition

The Internal Rate of Return rule is to accept an investment project ifthe opportunity cost of capital is less than the internal rate of return

Proposition

The IRR rule coincides with the NPV rule if the project is such thatthe function

ρ 7−→ NPVρ

is strictly decreasing

Observe that

dNPVdρ

(ρ) = − C1

(1 + ρ)2− 2C2

(1 + ρ)3− . . .− TCT

(1 + ρ)T+1

In particular, if all payoffs after investment are nonnegative then theIRR rule coincides with the NPV rule


Pitfall 1: Lending or Borrowing?

Not all cash-flow streams have NPVs that decline as the discountrate increases

If we lend money, we want a high rate of returnIf we borrow money, we want a low rate of return


Pitfall 2: Multiple Rates of Return

Vale is proposing to develop a new strip mine in North BrazilThe mine involves an initial investment of R$ 600 millionIt is expected to produce a cash inflow of R$ 120 million a year forthe next nine yearsAt the end of that time the company will incur R$ 150 million ofcleanup costs

Computing the IRR and NPV, we get



There are cases in which no internal rate of return existsFor example, project C described below has positive net presentvalue at all discount rates but has no IRR


Pitfall 3: Mutually Exclusive Projects

Assume that a firm has to choose among two mutually exclusiveprojects D and EThe IRR rule can be misleading in this case



One can salvage the IRR rule in this case by looking at theinternal rate of return on the incremental flows



Observe that the Internal Rate of Return of the cash flow E-D isgreater that the opportunity cost of capital, i.e.,

IRR(E −D) > r

Since the functionρ 7−→ NPVρ(E −D)

is strictly decreasing, this implies that

NPVr(E)−NPVr(D) = NPVr(E−D) > NPVIRR(E−D)(E−D) = 0

The project E should be chosen since it has a larger Net PresentValue under the opportunity cost of capital r



We propose another example



Can we use the internal rate of return on the incremental flows?


Pitfall 4: The Term Structure Assumption

We have simplified our discussion of capital budgeting byassuming that the opportunity cost of capital is the same for allcash flows, C1, C2, C3, etc.The correct DCF formula is

NPV = C0 +C1

1 + r1+

C2

(1 + r2)2+ . . .+

Ct(1 + rt)t

+ . . .

To which opportunity cost of capital should the IRR be compared?


Sensitivity to Errors on Cash FlowsConsider the two following projects

Both projects have the same NPVIf the real cash flows differ from the plant manager’s forecasts by asmall percentage, then project A may still keep an IRR greaterthan the opportunity cost of capital (in particular a positiveNPV), while there is almost no room for error in project BWe will see that

I when projects are deep-in-the-money (project A), it generally paysto invest right away and capture the cash flows

I in the case of projects that are close-to-the-money (project B) itmakes more sense to wait and see


Capital Rationing

A company has the following opportunities

All the three projects are attractive but the firm is limited tospending $10 million in year 0It can

I either invest in project AI or invest in projects B and C

The best choice is to invest in projects B and C


Capital Rationing: Profitability IndexWhen capital is limited, it makes sense to look for the highest netpresent value per dollar of initial outlay

Definition

Profitability index =Net Present Value

Investment

We should rank the projects by profitability indexWe should follow the order of the list and take the maximumamount of projects satisfying the capital limit


Capital Rationing: Profitability Index

There are some limitations to the simple ranking methodIt breaks down whenever more than one resource is rationedFor example, suppose that the firm can raise only up to $10million for investment in each of years 0 and 1Consider the following menu of possible projects

The optimal decision under the constraints is to accept projects A and D


Capital Rationing: Validity of the NPV rule

The NPV rule is based on the assumption that shareholders canborrow or lend, sell their shares, or buy moreA barrier between the firm and capital markets does notundermine net present value so long as the barrier is the onlymarket imperfectionThe important is that the firm’s shareholders have free access towell-functioning capital markets


Capital Rationing: Validity of the NPV rule

Example

Suppose that Nevada Aquaculture, Inc. (NAI) is solely owned byits founder, Alexander TurbotMr. Turbot has no cash or credit remainingHe is convinced that expansion of his operation is a high-NPVinvestmentHe has tried to sell stock but has found that investors, skeptical ofprospects for fish farming in the desert, offer him much less thanhe thinks his firm is worthFor Mr. Turbot capital markets hardly exist and it makes (very)little sense for him to discount prospective cash flows at a marketopportunity cost of capital


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