Net Present Value and Other Investment Criteria

Copyright © 2015 by The McGraw-Hill Companies, Inc. All rights reserved

Chapter 8

Net Present Value and Other Investment Criteria

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Topics Covered

8.1 Net Present Value

8.2 The Internal Rate of Return Rule

8.3 The Profitability Index

8.4 The Payback Rule

8.5 More Mutually Exclusive Projects

8.6 A Last Look

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2

Net Present Value

Net Present Value – Present value of cash flows minus initial investments

Opportunity Cost of Capital – Expected rate of return given up by investing in a project

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4

Net Present Value

Example

Q: Suppose we can invest $50 today & receive $60 later today. What is our increase in value?

Initial Investment

Added Value

$50

$10

A: Profit = −$50 + $60

= $10

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6

Net Present Value

Example

Suppose we can invest $50 today and receive $60 in one year. What is our increase in value given a 10% expected return?

This is the definition of NPV

Initial Investment

Added Value

$50

$4.55

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8

Valuing an Office Building

Step 1: Forecast cash flows

Cost of building = C0 = 350,000

Sale price in Year 1 = C1 = 400,000

Step 2: Estimate opportunity cost of capital

If equally risky investments in the capital market

offer a return of 7%, then

Cost of capital = r = 7%

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Valuing an Office Building

Step 3: Discount future cash flows

Step 4: Go ahead if PV of payoff exceeds investment

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Risk and Present Value

Higher risk projects require a higher rate of return

Higher required rates of return cause lower PVs

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Risk and Present Value

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Risk and Present Value

New NPV = 357,143 − 350,000 = $7,143

Higher risk = Lower value

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Net Present Value

NPV = PV – required investment

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Net Present Value

C0 = Initial cash flow (often negative)

C1 = Cash flow at time 1

C2 = Cash flow at time 2

Ct = Cash flow at time t

t = Time period of the investment

r = Opportunity cost of capital

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Net Present Value

Net Present Value Rule

Managers increase shareholders’ wealth by accepting all projects that are worth more than they cost

Therefore, they should accept all projects with a positive net present value

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Net Present Value

Example

You have the opportunity to purchase an office building. You have a tenant lined up that will generate $25,000 per year in cash flows for three years. At the end of three years you anticipate selling the building for $450,000. How much would you be willing to pay for the building?

Assume a 7% opportunity cost of capital.

$$$$$$$$$$

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Example – continued

Net Present Value

$25,000

$25,000

$25,000

$450,000

$475,000

0 1 2 3

Present Value

23,364

21,836

387,741

$432,942

$$$$

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Net Present Value

Example – continued

If the building is being offered for sale at a price of $375,000, would you buy the building? What is the added value generated by your purchase and management of the building?

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17

Invest

Sell

Rent

Rent

Rent

Net Present Value

Example – continued

If the building is being offered for sale at a price of $375,000, would you buy the building and what is the added value generated by your purchase and management of the building?

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18

Internal Rate of Return

Internal Rate of Return (IRR) – Discount rate at which NPV = 0

Rate of Return Rule – Invest in any project offering a rate of return that is higher than the opportunity cost of capital

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Internal Rate of Return

Example

You can purchase a building for $350,000. At the end of the year you will sell the building for $400,000. What is the rate of return on this investment?

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Internal Rate of Return

IRR = 14.29%

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24

NPV (,000s) 0 5 10 15 20 25 30 35 50 46.039603960396022 42.15686274509801 38.349514563106759 34.615384615384627 30.952380952380945 27.358490566037712 23.831775700934582 20.370370370370335 16.972477064220175 13.636363636363589 10.360360360360355 7.1428571428571015 3.9823008849557953 0.87719298245612298 -2.1739130434782128 -5.17241379310342 -8.1196581196581246 -11.016949152542336 -13.865546218487376 -16.666666666666629 -19.421487603305781 -22.131147540983626 -24.796747967479693 -27.419354838709697 -30 -32.539682539682545 -35.039370078740177 -37.5 -39.922480620155049 -42.307692307692314 -44.656488549618345 -46.969696969696962 -49.248120300751879 -51.492537313432841 -53.703703703703709

Discount rate (%)

NPV (,000s)

Internal Rate of Return

Example

You can purchase a building for $375,000. The investment will generate $25,000 in cash flows (i.e. rent) during the first three years. At the end of three years you will sell the building for $450,000. What is the IRR on this investment?

IRR = 12.56%

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Internal Rate of Return

IRR=12.56%

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NPV (,000s) 0 5 10 15 20 25 30 35 150 135.29019674832887 121.14213236236438 107.52903058128879 94.425637232589821 81.80812007342611 69.653976101076637 57.941945711293315 46.651933140273265 35.764932677183239 25.262960180315421 15.128989471575245 5.3468932215742537 -4.0986120284399368 -13.222017030881368 -22.037067477603326 -30.556808397228249 -38.793625551241043 -46.759284055331783 -54.464964433623187 -61.921296296296291 -69.138389815535575 -76.125865160520007 -82.892880039250471 -89.448155483199628 -95.8 -101.95633220954461 -107.9247020698766 -113.71231079101562 -119.32602952733261 -124.77241693218023 -130.05773565216001 -135.18796783259594 -140.16882970045958 -145.00578528608912 -149.7040593405477

Discount rate (%)

NPV (,000s)

Internal Rate of Return

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Internal Rate of Return

Calculating the IRR can be a laborious task. Fortunately, financial calculators can perform this function easily. Note the previous example.

HP-10B EL-733A BAII Plus

-375,000 CFj -375,000 CFi CF

25,000 CFj 25,000 CFfi 2nd {CLR Work}

25,000 CFj 25,000 CFi -375,000 ENTER

475,000 CFj 475,000 CFi 25,000 ENTER

{IRR/YR} IRR 25,000 ENTER

475,000 ENTER

IRR CPT

All produce IRR=12.56

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Internal Rate of Return

Example

You have two proposals to choice between. The initial proposal (H) has a cash flow that is different than the revised proposal (I). Using IRR, which do you prefer?

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Internal Rate of Return

50

40

30

20

10

0

-10

-20

NPV $, 1,000s

Discount rate, %

8 10 12 14 16

Revised proposal

Initial proposal

IRR= 14.29%

IRR= 12.56%

IRR= 11.72%

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Internal Rate of Return

Example

You have two proposals to choose between. The initial proposal has a cash flow that is different than the revised proposal. Using IRR, which do you prefer?

Project C0 C1 C2 C3 IRR NPV@7%

Initial Proposal -350 400 14.29% $ 23,832

Revised Proposal -375 25 25 475 12.56% $ 57,942

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Internal Rate of Return

Pitfall 3 – Mutually Exclusive Projects

IRR sometimes ignores the magnitude of the project

The following two projects illustrate that problem

Pitfall 1 – Lending or Borrowing?

With some cash, the NPV of the project increases as the discount rate increases

This is contrary to the normal relationship between PV and discount rates

Pitfall 2 – Multiple Rates of Return

Certain cash flows can generate NPV = 0 at two different discount rates

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Profitability Index

Profitability Index

Ratio of net present value to initial investment

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Profitability Index

Cash Flows

Project C0 C1 C2 NPV @ 10% Profitability Index

C -10 30 5 21.40 2.1

D -5 5 20 16.07 3.2

E -5 5 15 11.94 2.4

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Capital Rationing

Capital Rationing – Limit set on the amount of funds available for investment

Soft Rationing – Limits on available funds imposed by management

Hard Rationing – Limits on available funds imposed by the unavailability of funds in the capital market

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Payback Method

Payback Period – Time until cash flows recover the initial investment of the project

The payback rule specifies that a project be accepted if its payback period is less than the specified cutoff period

The following example will demonstrate the absurdity of this statement

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Payback Method

Cash Flows

Project C0 C1 C2 Payback NPV @ 10%

F -2,000 +1,000 +10,000 2 +7,249

G -2,000 +1,000 0 2 -264

H -2,000 +2,000 0 2 -347

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Project Interactions

When you need to choose between mutually exclusive projects, the decision rule is simple:

Calculate the NPV of each project

From those options that have a positive NPV, choose the one whose NPV is highest

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Mutually Exclusive Projects

Example

Select one of the two following projects, based on highest NPV

Assume a 7% discount rate

System C0 C1 C2 C3 NPV

Faster -800 350 350 350 +118.5

Slower -700 300 300 300 +87.3

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Investment Timing

Sometimes you have the ability to defer an investment and select a time that is more ideal at which to make the investment decision

A common example involves a tree farm

You may defer the harvesting of trees

By doing so, you defer the receipt of the cash flow, yet increase the cash flow

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Investment Timing

Example

You may purchase a computer anytime within the next five years. While the computer will save your company money, the cost of computers continues to decline. If your cost of capital is 10% and given the data listed below, when should you purchase the computer?

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Investment Timing

Example

You may purchase a computer anytime within the next five years. While the computer will save your company money, the cost of computers continues to decline. If your cost of capital is 10% and given the data listed below, when should you purchase the computer?

Time Cost PV Savings NPV at Purchase NPV Today

0 50 70 20 20.0

1 45 70 25 22.7

2 40 70 30 24.8

3 36 70 34 Date to purchase 25.5

4 33 70 37 25.3

5 31 70 39 24.2

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Equivalent Annual Annuity

Equivalent Annual Annuity – The cash flow per period with the same present value as the cost of buying and operating a machine

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Equivalent Annual Annuity

Example

Given the following costs of operating two machines and a 6% cost of capital, select the lower cost machine using equivalent annual annuity method.

Costs ($ thousands)

Year: 0 1 2 3 PV @ 6% EAA

Machine I -15 -4 -4 -4 -25.69 -9.61

Machine J -10 -6 -6 -21.00 -11.45

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