Corporate Finance - CH 12

Decision Rules for IRR - Independent Projects

If IRR is greater than ra, do the project(s)!

There is no way to determine how short the payback periods must be to

justify accepting a proejct. This is a flaw of payback period.

Decision rules for NPV (Independent Projects):

- If NPV is positive, ACCEPT project. - If NPV is negative, REJECT project. * If both are positive, then you can pick both projects.

How to calculate NPV:

1. Calculate the present value of each cash flow discounted at the project's risk-adjusted cost of capital 2. Sum up all CFs. *Discount all CF to present value and then sum up all PV*

Measures that have been established for screening projects and deciding which to accept or reject:

1. NPV 2. IRR 3. MIRR 4. Profitability Index (PI) 5. Regular Payback 6. Discounted Payback

A decision rule should consider:

1. Time Value of Money (Interest) 2. All cash flows; future, not just until you breakeven 3. Be able to tell which mutually exclusive project is most profitable.

The regular payback period has three flaws

1. Time value of money is ignored (doesn't consider interest) 2. Cash flows beyond the payback year are given no consideration whatsoever. 3. Unlike the NPV and IRR, which tells us how much wealth a project adds or how much a project's rate of return exceeds the cost of capital, the payback merely tells us how long it takes to recover our investment. Fails all 3 tests.

Internal Rate of Return (IRR)

A project's IRR is the discount rate that focus the PV of the expected future cash flows to equal the initial cash flow. ***This is equivalent to forcing the NPV to equal zero.*** IRR is an estimate of the rate of return the company would actually earn if it invested in the project. If this return is greater than cost of capital, then it benefits the stockholders. If this return is less than cost of capital, stockholders suffer a loss.

Capital Budget

A summary of planned investments of assets that will last for more than a year.

Problems with Using the IRR to Evaluate Mutually Exclusive Projects

Always choose the project that provides the greatest increase in wealth (aka NPV) even though it may not have the highest rate of return (IRR).

Modified Internal Rate of Return

Assumes that cash flows from all projects are reinvested at the cost of capital (ra), not at the project's own IRR. This makes the MIRR a better indicator of a project's true profitability.

IRR: Scale/Size Differences

Both projects have the same scale when each of them require an initial investment of the same amount. <1,000> and <1,000>.

Payback is a what type of calculation?

Break-even!! If cash flows come in at the expected rate, then the project will at least break even.

Capital

Refers to long-term assets used in production.

2nd Step in Project Analysis

Calculate the evaluation measures (NPV, IRR, etc)

Mutually Exclusive Projects

Can only choose one; can't choose both. Example: Open up factory in either NY or CA You will choose option with higher return. Accepting one will reject the other.

Pure Cost Project

Choose the less expensive project according to NPV.

The point where the projects touch each other on the NPV Profile is called the....

Crossover Point/Rate - discount rate where NPV profiles intersect.

IOS is what type of function?

Decreasing function because it represents a firm's potential investment projects in decreasing order of profitability.

1st Step in Project Analysis

Estimate the project's expected cash flows.

Project S NPV: $804.38 Project L NPV: $1,048.02 Project S IRR: 14.69% Project L IRR: 13.79%

Even though Project S has higher IRR, we are going to choose Project L because of its higher NPV, if it was mutually exclusive. If independent: Pick both

Multiple IRRs Example:

For Project X, the NPV equals $0 when IRR = 25%, but it also equals $0 when IRR = 400%. Therefore, Project X has 2 IRRs.

IOS is in terms of

IRR and Total Investing

If you are evaluating an independent project with normal cash flows, and NPV says accept, what does IRR say?

IRR will also say accept.

MCC is what type of function?

Increasing because it costs more to issue more and more securities.

IOS assumes:

Independent Projects Ranks projects by IRR (so assume there are no IRR deficiencies) Do highest IRR first DO THE MOST PROFITABLE PROJECT UNTIL THE NEXT ONE COSTS MORE THAN IT RETURNS.

Decision Rules

Independent: ??? Mutually Exclusive: Pick project with less time.

IF managers want to know the expected rates of return on projects, it would be better to give them

MIRRs than IRRs because MIRRs are more likely to be the rates that are actually earned if the project's cash flows are reinvested in future projects.

Profitability Index

Measures how much value a project creates for each dollar of the project's cost. Found by dividing the project's present value of future cash flows by its initial cost. A profitability index greater than 1 is equivalent to a project having positive NPV.

For normal, independent projects, if the IRR says to accept it, then so will the

NPV.

IF ra < rc, then....

NPV and IRR disagree on best project.

Which is the best measure??

NPV is the MVP! Why? Because it directly relates to a firm's central goal of maximizing intrinsic value.

IRR: Timing Differences (pg. 464)

Occurs when future cash flows between two projects are not similar in $$ or sign (+/-). Project X may have most of its future cash flows sooner in the life of the project while Project Y has mots of its future cash flows later in the life of the project. This causes their differences to be positive in the first year and negative in the second year.

Normal Cash flow pattern

One or more cash OUTFLOWS followed ONLY by cash inflows. orrrrr the reverse: One or more cash inflows followed ONLY by outflows. Normal Examples: - + + + - - + + + + + - - Sign of the cash flows only changes ONCE, either from negative to positive or positive to negative.

Decision rules for NPV (Mutually Exclusive - can only pick one):

Pick Project with higher NPV. * Can only pick uno.

Budget

Plan that outlines projected expenditures during a future period.

Decision Rule for IRR - Mutually Exclusive Projects

Project with higher IRR might not be the most profitable project. So, pick the one with the larger NPV.

Projects must be either mutually exclusive or independent!!!

So one of these rules always applies.

Mutually Exclusive ----

Still choose highest NPV

Payback Period

The number of years it takes a firm to pay back its initial investment from its operating cash flows. Start with the project's cost: <$10,000> Then add the cash inflow for each year until the cumulative cash flow turns positive.

Discounted Payback Period

The number of years it takes a firm to recover its project initial investment BASED ON DISCOUNTED CASH FLOWS. This counters the first test: Considers time value of money, but doesn't consider all cash flows. Use ra/wacc

How to calculate Payback Period

The payback year is the year PRIOR to the full recovery PLUS a fraction equal to the cummulative CF at the end of the prior year divided by the CF during the year when full recover occurs. Payback = Number of years prior to full recovery + (Unrecovered cost at start of the year/CF during full recovery year)

Net Present Value (NPV)

The present value of the project's expected future cash flows, discounted at the appropriate cost of capital. The NPV measures how much wealth the project contributes to shareholders. Best deciding factor!!

Optimal Capital Budget

The set of projects that maximizes the value of the firm.

Capital Budgeting

The whole process of analyzing projects and deciding which ones to accept and thus include in the capital budget.

However, some projects have cash flows with signs that change more than once.

These are called NONNORMAL Cash Flow Patterns. Examples: - + + + - - + + + - + + +

Independent Project

Two independent projects where you can pick Project A, Project B, or both.

Investment Opportunity Schedule

Will rank projects by highest IRR. Vertical Axis: IRR Horizontal Axis: Total Investing

Net Present Value Profile

X - Axis: Cost of Capital (r) Y - Axis: $NPV The IRR for each project (point at which the project has a $0 NPV) is where the curve crosses the X- Axis.

For mutually exclusive projects, if the cost of capital (ra) is less than the crossover rate, then

a conflict arises. NPV favors one project while IRR favors the other. In this situation, select the project with the highest NPV, even if it has a lower IRR.

A firm's IOS (Investment Opportunity Schedule) represents

a firm's potential investment projects.

All idenpendent projects with positive NPV should be

accepted.

The mutually exclusive project with the highest NPV should be

accepted.

The intersection of the IOS and MCC indicates the

amount of capital the firm should raise and invest. Common analogy: intersection of a marginal rev curve with marginal cost curve.

For mutually exclusive projects, if the cost of capital (ra) is greater than the crossover rate, then

both methods agree about the same project being the best.

The discounted payback does consider what kinds of costs?

capital costs.

There will be a conflict when ra/wacc is to the left of the

crossover point. (rc) Conflict: One project's NPV will be greater than the other, but the other project will have a greater IRR.

Summary: IOS is a

decreasing stair-step function

A firm's MCC (Marginal Cost of Capital) represents

its weighted average cost of capital (ra) for various levels of financing.

When a project has multiple IRRs, then

don't use IRR as a decision rule because it is misleading. From previous ex: even though the 400% IRR is greater than the 25% IRR, the 25% IRR might have a higher $NPV than the 400% IRR.

MCC - As the amount of total financing increases, ra....

increases due to the increasing cost of each component of capital (debt, ps, ce)

MCC is a

increasing stair-step function

Payback methods DO provide info about

liquidity and risk.

IF r is big, NPV will be

lower.

The increasing WACC represents the

marginal cost of capital on the MCC.

If a projects' cash flows have a non normal pattern, it is possible for the project to have

more than one positive IRR, aka Multiple IRRs.

Initial investment is a

negative cash flow Year 0: <$10,000>

For a crossover rate to exist, the difference in cash flows between 2 projects must have a

normal pattern cash flow. The cash flows must have one and ONLY one sign change.

Projects with the same scale must have timing differences in future cash flows for there to be

one and only sign change.

IF a project has a NORMAL cash flow pattern, then the project can have at most...

one positive IRR.

MCC is in term of

ra and total financing

For independent projects, NPV, IRR, and MIRR always

reach the same accept or reject conclusion.

There is no conflict if the ra/wacc is to the......

right of the crossover point.

Cash flows expected in the distant future are generally

riskier than near-term cash flows. So, the payback is also a risk indicator.

Therefore, the optimal capital budget consists of

the above types of projects.

The intersection point of the MCC and IOS is the point where

the amount of dollars raised through financing and the amount of dollars invested in projects MAXIMIZES THE VALUE OF THE FIRM.

Increasing marginal cost of capital

the cost of capital may increase as the capital budget increases.

The shorter the payback,

the greater the project's liquidity.

A crossover rate only can exist for projects with positive NPVs if the cash flows have

timing differences and/or size differences.

The MIRR is superior to the regular IRR as an indicator of a projects'

true rate of return since it assumes reinvestment rate is at ra, not IRR.