Chapter – 5 & 6: NPV & Other Investment Rules,

Cash flows

-NPV Rule- Determining Cash flows-Payback period Rule-Discounted Payback Period-Internal Rate of Return-Independent VS Mutually Exclusive-Profitability Index

Net Present Value RuleInvestment decisions from the

perspective of corporate finance is known as capital budgeting.

Net present value is one of the criteria to choose between capital budgeting projects.

NPV is the difference between intrinsic value and the cost of the project◦NPV = (PV of future cash flows) – cost

NPV Rule: Accept the project if NPV is positive, reject if NPV is negative.

Net Present Value RuleExample: The Alpha Corporation is

considering investing in a riskless project costing $100. The project receives $107 in one year and has no other cash flows. The discount rate is 6%. The NPV is

This example deals with a riskless project which is impossible in reality. To incorporate the risk in calculation the discount rate can be increased, which will be discussed in later chapter

Net Present Value RuleBenefits of NPV:

◦One way of determining the value of a firm is to add the values of different projects, divisions, or other entities within the firm. This property is called “value additivity” and it

implies that the contribution of any project to the firm’s value is the NPV of the project.

◦NPV uses cash flows and not accounting profit

◦NPV uses all cash flows of the project including the initial cost and salvage value

◦NPV discounts the cash flows properly

Determining the Cash FlowsThe cash flows that should be included

in a capital budgeting analysis are those that will only occur if the project is accepted

These cash flows are called incremental cash flows◦Cash basis calculation is needed not accrual

basis The stand-alone principle allows us to

analyze each project in isolation from the firm simply by focusing on incremental cash flows

Determining the Cash FlowsSunk costs – costs that have already been incurred in

the past and cannot be removed◦ Should not be considered in investment decision

Opportunity costs – the most valuable alternative that is given up if a particular investment is undertaken.◦ Should be included in investment decision calculations◦ Always an outflow (negative) adjusted with initial outlay

Side effects◦ Positive side effects – benefits to other existing

projects◦ Negative side effects (a.k.a. erosion) – costs to other

existing projects◦ Should be included in investment decision

calculations

Determining the Cash FlowsChanges in net working capital – the extra

amount of cash required for daily operations of the project◦Should be included in the investment decision

Financing costs – interest expense, dividends, principal paid etc.◦Should not be included in investment decision◦These cashflow do not depend on operation.

Taxes – If a particular component is taxed then after-tax cashflow needs to be considered.

Determining the Cash FlowsIncremental project cash flows

with all these components suggest that it is the Free Cash Flow (FCF) of the project◦Another name is Cash Flow From

Asset (CFFA)◦FCF = EBIT(1-T) + Depreciation –

Change in NWC – Change in capital expenditure

Payback Period RulePayback Period is the method for

measuring the time it takes to recover the initial cost of a project

If a project requires an initial investment of $50,000 and the following cash flows of $30,000; $25,000; and $10,000 then its payback period is◦ -$50,000 + $30,000 + $20,000 (out of

$25,000)= 0◦Payback = 1 + (20,000/25,000) = 1.8 years

Payback period rule: Set a cutoff date and select projects with payback shorter than cutoff.

Payback Period RuleProblems of Payback Period:

◦Payback period does not consider time value of money

◦Payback period does not consider the cash flows after the payback

◦The choice of the cutoff date is random and does not have any proper standard.

Discounted Payback PeriodTo address the timing issue of the

payback period an alternative method used is discounted payback period.

Discounted payback period is the method for measuring the time it takes to recover the initial cost of a project with the present value of all the future cash flows.

Discounted Payback PeriodSuppose the discount rate is 10%

and the cash flows on a project are given by -$100, $50, $50, $20. ◦The discounted cash flows are: [-

$100, ($50/1.1), ($50/1.12), ($20/1.13)] = (-$100, $45.45, $41.32, $15.03)

◦Discounted period is 2 + [(100-45.45-41.32)/15.03] = 2.88 years

Internal Rate of Return (IRR)A project’s IRR is the discount rate that

forces the PV of cash inflows to equal the cost◦This is equivalent to forcing the NPV to equal

zero.◦Thus IRR does not depend on market interest

rate. It is completely intrinsic.◦There is no fixed formula to calculate IRR other

than the trial and error methods to make NPV zero.

◦ IRR Rule: Accept the project if IRR is greater than discount rate, reject it if IRR is less than discount rate.

Internal Rate of Return (IRR)The IRR rule mentioned in the previous slide

is applicable only to projects which has the cash flow pattern of a single outflow followed by several inflows. ◦ In this sequence the decision of NPV and IRR

almost always matchIf the pattern of cash flow is an inflow

followed by outflows then the rule is reversed.

If the pattern involves several changes of cash flow signs (i.e. outflow, inflow, inflow, outflow etc.) then there are multiple IRRs for a single project

Internal Rate of Return (IRR)IRR= Ra + (NPVa) * (Rb - Ra) (NPVa - NPVb)

Here, ◦Ra = discount rate that gives the

positive net present value◦NPVa = positive NPV ◦NPVb = negative NPV◦Rb = discount rate that gives the

negative net present value

Modified IRR (MIRR)When multiple IRR arises an

alternative method can be modified IRR (MIRR)◦MIRR combines multiple cash flows until

only one change of sign remains and then the IRR rule is applied.

◦Using the discount rate the future cash outflows are discounted to present time

◦They are then added with the initial investment to have single negative cash flow while the others are positive.

◦Then the IRR method is applied

The Rule Chart

Independent VS Mutually ExclusiveThe rules of capital budgeting decisions

discussed so far are applicable to choose in between independent projects only.◦ Independent projects are those whose

acceptance or rejection is independent of each other or any other projects.

These rules will be different in cases of mutually exclusive projects.◦ If two projects are mutually exclusive then you

can accept either one and have to reject the other or reject both. You cannot accept both projects.

Independent VS Mutually ExclusiveMutually Exclusive Investment

Rules:◦Accept the project with the higher NPV if

both NPV are positive. If both are negative then reject both

◦Accept the project with the shorter payback or discounted payback period if both are below cutoff date. If both are above cutoff date then reject both

◦Accept the project with higher IRR if both are above discount rate. If both are below discount rate then reject both

Profitability IndexProfitability Index (PI) = (PV of

cash flows after initial investment)/Initial investment◦Very similar to NPV◦Does not work with mutually

exclusive projects. Then revert back to NPV.

PI Rule: Accept project if PI>1, reject if PI<1