Managerial Fin

14 Jun Managerial Fin

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

Chapter 8

Net Present Value and Other Investment Criteria

8- ‹#›

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

8- ‹#›

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

8- ‹#›

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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11

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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11

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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13

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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14

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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16

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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20

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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21

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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23

Internal Rate of Return

IRR=12.56%

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24

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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23

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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26

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

8- ‹#›

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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48

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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28

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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32

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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35

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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36

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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38

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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39

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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40

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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42

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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45

Equivalent Annual Annuity

Example (with a twist)

Select one of the two following projects, based on highest “equivalent annual annuity” (r = 9%).

Project C0 C1 C2 C3 C4 NPV EAA
A -15 4.9 5.2 5.9 6.2
B -20 8.1 8.7 10.4
2.82

2.78

.87

1.10

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47

Capital Budgeting Techniques

Criterion Definition Investment Rule Comments
Net present value (NPV) Present value of cash inflows minus present value of cash outflows Accept project if NPV is positive. For mutually exclusive projects, choose the one with the highest (positive) NPV. The “gold standard” of investment criteria. Only criterion necessarily consistent with maximizing the value of the firm. Provides appropriate rule for choosing among mutually exclusive investments. Only pitfall involves capital rationing, when one cannot accept all positive NPV projects.
Internal rate of return (IRR) The discount rate at which project NPR equals zero Accept project if IRR is greater than opportunity cost of capital. If used properly, results in same accept-reject decision as NPV in the absence of project interactions. However, beware of the following pitfalls: IRR cannot rank mutually exclusive projects—the project with higher IRR may have lower NPV. The simple IRR rule cannot be used in cases of multiple IRRs or an upward-sloping NPV profile.
Profitability index Ratio of net present value to initial investment Accept project if profitability index is greater than 0. In case of capital rationing, accept projects with highest profitability index. Results in same accept-reject decision as NPV in the absence of project interactions. Useful for ranking projects in case of capital rationing, but misleading in the presence of interactions. Cannot rank mutually exclusive projects.
Payback period Time until the sum of project cash flows equals the initial investment Accept project if payback period is less than some specified number of years. A quick and dirty rule of thumb, with several critical pitfalls. Ignores cash flows beyond the acceptable payback period. Ignores discounting. Tends to improperly reject long-lived projects.
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Capital Budgeting Techniques

8- ‹#›

55

4

$

10

1

60

50

Profit

.

.

+

=

=

–

832

,

373

PV

)

07

.

1

(

000

,

400

)

1

(

1

=

=

=

+

+

r

C

832

,

23

832

,

373

000

,

350

NPV

=

+

–

=

832

,

373

.07

1

400,000

PV

7%

at

$400,000

of

PV

1

=

+

=

=

C

143

,

357

.12

1

400,000

PV

12%

at

$400,000

of

PV

1

=

+

=

=

C

832

,

373

.07

1

400,000

PV

7%

at

$400,000

of

PV

1

=

+

=

=

C

143

,

357

.12

1

400,000

PV

12%

at

$400,000

of

PV

1

=

+

=

=

C

t

t

r

C

C

)

1

(

NPV

0

+

+

=

t

t

r

C

r

C

r

C

C

)

1

(

…

)

1

(

)

1

(

NPV

2

2

1

1

0

+

+

+

+

+

+

+

=

t

t

r

C

r

C

r

C

C

)

1

(

…

)

1

(

)

1

(

NPV

2

2

1

1

0

+

+

+

+

+

+

+

=

942

,

57

$

NPV

)

07

.

1

(

000

,

475

)

07

.

1

(

000

,

25

)

07

.

1

(

000

,

25

000

,

375

NPV

3

2

1

=

+

+

+

–

=

investment

investment

=

return

of

Rate

1

–

C

3

2

1

)

IRR

1

(

000

,

475

)

IRR

1

(

000

,

25

)

IRR

1

(

000

,

25

000

,

375

0

+

+

+

+

+

+

–

=

Calculating IRR by using a spreadsheet

YearCash FlowFormula

0(375,000.00) IRR = 12.56%=IRR(B4:B7)

125,000.00

225,000.00

3475,000.00

Sheet1
Calculating IRR by using a spreadsheet
Year Cash Flow Formula
0 (375,000.00) IRR = 12.56% =IRR(B4:B7)
1 25,000.00
2 25,000.00
3 475,000.00
Sheet2
Sheet3
%

29

.

14

0

)

IRR

1

(

400

350

NPV

1

=

=

+

+

–