Corporate finance: lecture 4

NPV & Investment criteria

By Muhammad Shafiq.forshaf@gmail com

:// . . /http www slideshare net forshaf

Sequence• Introduction• Basic terms review• Capital budgeting introduction• Capital budgeting technique • Sensitivity analysis• Scenario analysis

•Lets Begin

A review of Basics:Present Value, Net Present value and future value• Present value (PV) is the current worth of a future sum of money or

stream of cash flows given a specified rate of return. In other words, present value, also known as present discounted value, is the value of an expected income stream determined as of the date of valuation

• Difference between a project’s value and its cost is its NPV• Future value is the value of an asset at a specific date. It measures

the nominal future sum of money that a given sum of money is "worth" at a specified time in the future assuming a certain interest rate, or more generally, rate of return; it is the present value multiplied by the accumulation function.

Few formulas

Discount factor; 1/(1+r)t

PV= C1/1+r + C2/(1+r)2 . . . + Ct/(1+r)t

Present value = DF2* C2

NPV = Investment + PV

A review of Basic: Example• a CEO of corporation is looking to invest Rs. 1 million in project X• He asks from you (FINANCIAL MANAGER) whether to invest or not, and if

yes then what should be the grounds Your answer may be:

first: forecast the cash flows may be generated by the projectSecond: determine the appropriate opportunity cost of Capital.

That should reflect both; time value of money and Risk factorThird: use the opportunity cost of capital to discount the project's future

cash flowsFourth: calculate NPV by subtracting the 1 million investment from

present value: (Both formulas are given below)PV= C1/1+r + C2/(1+r)2 . . . + Cn/(1+r)t NPV= C0 +C1/1+r + C2/(1+r)2 . . . + Cn/(1+r)t

Note: Invest in Project if its NPV is greater or equal to zero

Net Present Value• Example: building costs 700,000 it can be sold for Rs. 800,000. if the discount rate

is 10%, calculate: Present Value Net Present Value

PV= C1/1+r + C2/(1+r)2 . . . + Cn/(1+r)n

=800,000/(1+.10) PV= RS. 727273

NPV= C0 +C1/1+r + C2/(1+r)2 . . . + Cn/(1+r)n

= 700,000 -727273NPV= /RS. +27273

NPV Strengths and Weaknesses

Strengths:• Cash flows

assumed to be reinvested at the

hurdle rate.• Accounts for TVM.• Considers all

cash flows.

Weaknesses:• May not include

managerial options

embedded in the project. See Chapter 14.

Net Present Value Profile

Discount Rate)%( 0 3 6 9 12 15

IRRNPV@13%

Sum of CF’s Plot NPV for eachdiscount rate.

Three of these points are easy now

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A review of Basic: Example … continue• CEO asks, why Greater NPV is so important?You answer:NPV is important as if the firm does not earn equal or more than what the shareholders expect than they might sell their share in the market.

“ Investors would forecast the dividends that Project X pay and discount those dividends by the expected rate of return of securities having similar

risk.” Only thing to answer is where the discount rate comes from?

It is the opportunity cost of investing in the project rather than in the capital market.

if the firm does not earn from the project what its shareholders expect (cost of capital) than it should return the cash to the shareholders and let them to invest in Financial Markets by purchasing financial Asset

Investment Project X

If 10% or return

Cash

Financial Manager

Share holders(If project return less than

10%)

Investment (Financial Asset)

First option:Invest

Second option:Pay dividend toShare holders

ShareholdersInvest

themselves

Figure 1;Deision through NPV if discount rate is 10%

Important Points to be remembered about Net Present Value• First: NPV rule recognizes that a rupee today is worth more than a

rupee tomorrow (time value of money).• Second: NPV depends on the forecasted cash flows from the project

and the opportunity cost of capital• Third: PV measures in todays money, therefore we add them up.• NPV depends on Cash flows, not on book returns. Book returns are

the accounting record rather than cash as:Book rate of Returns= book income/book assets

Capital Budgeting

The Capital Budgeting Process ofgenerating Investment Project Proposals andestimating Project “After-Tax Incremental Operating Cash

Flows”

The Capital Budgeting Process

• Generate investment proposals consistent with the firm’s strategic objectives.

• Estimate after-tax incremental operating cash flows for the investment projects.

• Evaluate project incremental cash flows.

The Capital Budgeting Process

• Select projects based on a value-maximizing acceptance criterion.

• Reevaluate implemented investment projects continually and perform post audits for completed projects.

Classification of Investment Project Proposals

1. New products or expansion of existing products

2. Replacement of existing equipment or buildings

3. Research and development4. Exploration5. Other (e.g., safety or pollution related)

Payback method• Payback period in capital budgeting refers to the period of time

required to recoup the funds expended in an investment, or to reach the break-even point.

For example, a $1000 investment which returned $500 per year would have a two-year payback period. The time value of money is not taken into account.

Payback methodCash flows

NPV at 10% Payback period (years)

C3 C2 C1 C0 Project

2,624 3 5,000 500 500 -2000 A

-58 2 0 1,800 500 -2000 B

50 2 0 500 1,800 -2000 C

Payback is calculated by taking the accumulated of all CFs NPV is calculated with the help of the following formula

NPV= C0 +C1/1+r + C2/(1+r)2 . . . + Cn/(1+r)n

Discounted paybackSome companies discount the cash flows before they compute payback period

Discounted Cash flows Rs

NPV at 10% Payback period (years)

C3 C2 C1 C0 Project

2,624 3 5,000/1.13 500/1.12

=413

500/1.12

=455-2000 A

-58 - 0 1,800/1.12

=1,488500/1.1

=455-2000 B

50 2 0 500/1.12

=413

1,800/1.1

= 1,636-2000 C

Why payback can give misleading answers• Payback rule ignores all cash flows after the cutoff date.• Its rule gives equal weight to all cash flows before the cutoff date• Companies still frequently use it because it is the simplest way to

communicate the idea. • Everyone can understand it• Manager like it as it tell short span period; good for their promotion

PBP Strengths and Weaknesses

Strengths:• Easy to use and understand

• Can be used as a measure of liquidity

• Easier to forecast ST than LT flows

Weaknesses:• Does not account

for TVM• Does not consider cash flows beyond the PBP• Cutoff period is

subjective

Internal Rate of Return (IRR)

IRR is the discount rate that equates the present value of the future net cash flows from an

investment project with the project’s initial cash outflow.

CF1 CF2 CFt (1+IRR)1 (1+IRR)2 (1+IRR)t

+ . . . ++ICO=

Example Project Data

A financial manager is evaluating a new project for her firm. She has determined that the after-tax cash flows for the project will be $10,000; $12,000; $15,000; $10,000; and $7,000, respectively, for each of the Years 1 through 5. The initial cash outlay will be $40,000.

Independent Project

• Independent -- A project whose acceptance (or rejection) does not prevent the acceptance of other projects under consideration.

For this project, assume that it is independent of any other potential projects.

15,000$ 10,000$ 7,000$

IRR Solution

10,000$ 12,000$(1+IRR)1 (1+IRR)2

Find the interest rate (IRR) that causes the discounted cash flows to equal $40,000.

+ +

++40,000$=

(1+IRR)3 (1+IRR)4 (1+IRR)5

IRR Solution (Try 10%)

$40,000 = $10,000(PVIF10%,1) + $12,000(PVIF10%,2) +$15,000(PVIF10%,3) + $10,000(PVIF10%,4) + $

7,000(PVIF10%,5) $40,000 = $10,000(.909) + $12,000(.826) +

$15,000(.751) + $10,000(.683) + $ 7,000(.621)

$40,000 = $9,090 + $9,912 + $11,265 + $6,830 + $4,347

= $41,444 [Rate is too low!!]

IRR Solution (Try 15%)

$40,000 = $10,000(PVIF15%,1) + $12,000(PVIF15%,2) + $15,000(PVIF15%,3) + $10,000(PVIF15%,4) + $

7,000(PVIF15%,5) $40,000 = $10,000(.870) + $12,000(.756) +

$15,000(.658) + $10,000(.572) + $ 7,000(.497)

$40,000 = $8,700 + $9,072 + $9,870 + $5,720 + $3,479

= $36,841 [Rate is too high!!]

.10 $41,444.05 IRR $40,000 $4,603

.15 $36,841

($1,444)(0.05) $4,603

IRR Solution (Interpolate)

1,444$X

X= X = .0157

IRR = .10 + .0157 = .1157 or 11.57%

IRR Acceptance Criterion

No! The firm will receive 11.57% for each dollar invested in this project at a cost of

13%. [ IRR < Hurdle Rate ]

The management of a company has determined that the hurdle rate is 13% for

projects of this type. Should this project be accepted?

IRRs on the Calculator

We will use the cash flow registry to solve

the IRR for this problem quickly and

accurately!

Actual IRR Solution Using Your Financial Calculator

Steps in the ProcessStep 1: Press CF keyStep 2: Press 2nd CLR Work keysStep 3: For CF0 Press -40000 Enter keysStep 4: For C01 Press 10000 Enter keysStep 5: For F01 Press 1 Enter keysStep 6: For C02 Press 12000 Enter keysStep 7: For F02 Press 1 Enter keysStep 8: For C03 Press 15000 Enter keysStep 9: For F03 Press 1 Enter keys

Actual IRR Solution Using Your Financial Calculator

Steps in the Process (Part II)Step 10:For C04 Press 10000 Enter keysStep 11:For F04 Press 1 Enter keysStep 12:For C05 Press 7000 Enter keysStep 13:For F05 Press 1 Enter keysStep 14: Press keysStep 15: Press IRR keyStep 16: Press CPT key

Result: Internal Rate of Return = 11.47%

IRR Strengths and Weaknesses

Strengths: • Accounts for

TVM• Considers all

cash flows• Less

subjectivity

Weaknesses: • Assumes all cash

flows reinvested at the IRR

• Difficulties with project rankings and Multiple IRRs

NPV on the Calculator

We will use the cash flow registry to solve the NPV for this problem quickly

and accurately!

Hint: If you have not cleared the cash flows from your calculator, then you may skip to Step 15.

Actual NPV Solution Using Your Financial

CalculatorSteps in the Process

Step 1:PressCF keyStep 2:Press2ndCLR Workkeys

Step 3: For CF0 Press -40000 Enter keysStep 4: For C01 Press10000 Enter keysStep 5: For F01 Press 1 Enter keysStep 6: For C02 Press12000 Enter keysStep 7: For F02 Press 1 Enter keysStep 8: For C03 Press15000 Enter keysStep 9: For F03 Press 1 Enter keys

Steps in the Process (Part II)Step 10:For C04 Press10000 Enter keysStep 11:For F04 Press 1 Enter keysStep 12:For C05 Press 7000 Enter keysStep 13:For F05 Press 1 Enter keys

Step 14: Press keysStep 15: PressNPV key

Step 16: For I=, Enter13Enter keysStep 17: PressCPT key

Result:Net Present Value = -$1,424.42

Actual NPV Solution Using Your Financial

Calculator

Creating NPV Profiles Using the Calculator

Hint: As long as you do not “clear” the cash

flows from the registry, simply start at Step 15 and enter a different discount rate. Each

resulting NPV will provide a “point” for your NPV

Profile!

Profitability Index (PI)

PI is the ratio of the present value of a project’s future net cash flows to the project’s initial cash outflow.

CF1 CF2 CFn (1+k)1 (1+k)2 (1+k)n

+ . . . ++ ICOPI =

PI = 1 + [ NPV / ICO ]

<< OR >>

PI Acceptance Criterion

No! The PI is less than 1.00. This means that the project is not profitable. [Reject as PI < 1.00

]

PI = $38,572 / $40,000. =9643 (Method #1, 13-33)

Should this project be accepted?

PI Strengths and Weaknesses

Strengths:• Same as NPV• Allows

comparison of different scale projects

Weaknesses:• Same as NPV• Provides only relative

profitability• Potential Ranking

Problems

Other Project Relationships

• Mutually Exclusive -- A project whose acceptance precludes the acceptance of one or more alternative projects.

Dependent -- A project whose acceptance depends on the acceptance of one or more other projects.

Potential Problems Under Mutual Exclusivity

A. Scale of InvestmentB. Cash-flow PatternC. Project Life

Ranking of project proposals may create contradictory results.

A. Scale Differences Compare a small (S) and a large (L) project.

NET CASH FLOWSProject S Project LEND OF YEAR

0- 100$- 100,000$ 1 0 0 2 400$ 156,250$

Scale DifferencesCalculate the PBP, IRR, NPV@10%, and PI@10%.

Which project is preferred? Why?Project IRR NPV PI

S 100% $ 231 3.31 L 25% $29,132 1.29

B. Cash Flow PatternLet us compare a decreasing cash-flow (D) project and

an increasing cash-flow (I) project.

NET CASH FLOWSProject D Project IEND OF YEAR

0- 1,200$- 1,200$ 1 1,000 100 2 500 600 3 100 1,080

D 23% $198 1.17 I 17% $198 1.17

Cash Flow Pattern Calculate the IRR, NPV@10%, and PI@10%.

Which project is preferred?

Project IRR NPV PI

C. Project Life Differences

Let us compare a long life (X) project and a short life (Y) project.

NET CASH FLOWSProject X Project YEND OF YEAR

0- 1,000$- 1,000$ 1 0 2,000 2 0 0 3 3,375 0

X 50% $1,536 2.54 Y 100% $ 818 1.82

Project Life Differences

Calculate the PBP, IRR, NPV@10%, and PI@10%.Which project is preferred? Why?

Project IRR NPV PI

Another Way to Look at Things

1. Adjust cash flows to a common terminal year if project “Y” will NOT be replaced.Compound Project Y, Year 1 @10% for 2 years.

Year 0 1 2 3CF -$1,000 $0 $0 $2,420

Results: IRR* = 34.26% NPV = $818*Lower IRR from adjusted cash-flow stream. X is still Best.

Replacing Projects with Identical Projects

2. Use Replacement Chain Approach (Appendix B) when project “Y” will be replaced.

0 1 2 3

-1,000$ 2,000$- 1,000 2,000$

- 1,000 2,000$-1,000$ 1,000$ 1,000$ 2,000$

Results:IRR* = 100% NPV* = $2,238.17

*Higher NPV, but the same IRR. Y is Best.

Capital RationingCapital Rationing occurs when a constraint (or budget ceiling) is placed on the total size of capital expenditures during a particular period.

Example: Julie Miller must determine what investment opportunities to undertake for Basket Wonders (BW). She is limited to a maximum expenditure of $32,500 only for this capital budgeting period.

Available Projects for BW

Project ICO IRR NPV PIA $ 500 18% $ 50 1.10 B 5,000

25 6,500 2.30 C 5,000 37 5,500 2.10 D 7,500 20 5,000 1.67

E12,500 26 500 1.04 F15,000 28 21,000 2.40 G17,500 19 7,500

1.43 H25,000 15 6,000 1.24

Choosing by IRRs for BW

Project ICO IRR NPV PIC $ 5,00037% $ 5,500 2.10 F15,000 28

21,000 2.40 E12,50026 500 1.04 B 5,00025 6,500 2.30

Projects C, F, and E have the three largest IRRs.

The resulting increase in shareholder wealth is $27,000 with a $32,500 outlay.

Choosing by NPVs for BW

Project ICO IRR NPV PI F $15,000 28% $21,000 2.40 G17,500

19 7,500 1.43 B 5,00025 6,500 2.30

Projects F and G have the two largest NPVs.The resulting increase in shareholder wealth is

$28,500 with a $32,500 outlay.

Choosing by PIs for BW Project ICO IRR NPV PI

F $15,000 28% $21,000 2.40B 5,000 25 6,500 2.30 C 5,000 37 5,500 2.10 D 7,500 20 5,000 1.67 G

17,500 19 7,500 1.43Projects F, B, C, and D have the four largest PIs.

The resulting increase in shareholder wealth is $38,000 with a $32,500 outlay.

Summary of Comparison

Method Projects Accepted Value Added PI F, B, C, and D $38,000

NPV F and G $28,500 IRRC, F, and E $27,000

PI generates the greatest increase in shareholder wealth when a limited capital budget exists for a

single period.

Post-Completion Audit

Post-completion AuditA formal comparison of the actual costs and benefits

of a project with original estimates.

• Identify any project weaknesses• Develop a possible set of corrective actions• Provide appropriate feedbackResult: Making better future decisions!

Multiple IRR Problem*

Two!! There are as many potential IRRs as there are sign changes.

Let us assume the following cash flow pattern for a project for Years 0 to 4:

-100$+ 100$+ 900$- 1,000$How many potential IRRs could this project

have?

*Refer to Appendix A

Project analysis• Investment process starts with the preparation of an annual capital

budget.• Project authorization and problem of biased forecasts• Post audits

• Identification of problems• Accuracy of forecast

Any suggestion

Sensitivity analysis

• Uncertainty means more things can happen than will happen.• Example

A company is introducing new scooters for city use with Rs. 15 b Net investment for 10 years, producing NCF of Rs. 3 B in ten years. Staff have prepared the forecasts at 10% NPV.= (-15)+3/(1.1)10 = Rs. +3.43 billions Production department estimated cost per unit is Rs. 300,000 and 100,00 scooter can be made in the year. If calculated the revenue as the firm has 1% market share, it will be:Unit sales= new product share in market*size of scooter market

37.5 billions(Revenue) = 100,000*375,000

Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be apportioned to different sources of uncertainty in its inputs.

Sensitivity analysisPreliminary cash-flow forecast for company

Year 1- 10 (one to ten years) Year 0 (zero) Description

NIL 15 billion Investment

37.5 NIL Revenue

30 NIL Variable cost

3 NIL Fixed cost

1.5 NIL Depreciation

3 NIL Pretax profit

1.5 NIL Tax

1.5 NIL Net profit

3 NIL Operating cash flow

3 NIL Net cash flow

1. Investment is depreciated over 10 years straight line2. Income is taxed at a rate of 50%

Sensitivity analysis…• Value Information

• Suppose that production department is worried about the machine which will not work properly and the firm has to purchase another method which incure per unit cost an extra Rs. 20,000:

units sales*additional unit cost*(1-tax rate)Rs.1 Billion= 100,000*20,000*.50

It will reduce the NPV by:1(/1.10)10

• Limits of sensitivity analysis• Giving ambiguous results

Scenario analysis• Scenario analysis is a process of analyzing possible future events by

considering alternative possible outcomes (sometimes called "alternative worlds").

• Thus, the scenario analysis, which is a main method of projections, does not try to show one exact picture of the future.