McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

Professor James J. Barkocy

Corporate Financial Management

“There are three kinds of

people: the ones that can

count and the ones that

can’t.”

Net Present Value

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

Net Present Value - Present value of cash

flows minus initial investments.

2

Net Present Value

Example

Suppose we can invest $350,000 today and receive $400,000 in one year. What is our increase in value given a 7% expected return?

This is NPV

Profit = -350,000 +400,000

1.07= $23,832

Initial Investment

Added Value

$350,000

$23,832

3

Net Present Value

NPV = PV - required investment

NPV CC

r

t

t=

0

1( )

NPV CC

r

C

r

C

r

t

t=

0

1

1

2

21 1 1( ) ( )...

( )

4

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?

5

Net Present Value

Example - continued

0 1 2 3

$25,000$25,000$25,000

$450,000

$475,000

Present Value

23,364

21,836

387,741

$432,942

6

FV=450,000

PMT= 25,000

N=3

I=7

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?

7

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?

942,57$

)07.1(

000,475

)07.1(

000,25

)07.1(

000,25000,375

321

=

=

NPV

NPV

8

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.

9

Net Present ValueCalculating the NPV can be a laborious task. Fortunately,

financial calculators can perform this function easily.

HP-10B HP-12C

-375,000 CFj -375,000 g CF0

25,000 CFj 25,000 g CFj

25,000 CFj 25,000 g CFj

475,000 CFj 475,000 g CFj

7 i 7 i

NPV f NPV Both produce

NPV=57,941.95

10

The Net Present Value Rule

Net Present Value (NPV) =

Total PV of future CF’s - Initial Investment

Estimating NPV: 1. Estimate future cash flows: how much? and when?

2. Estimate discount rate

3. Estimate initial costs

Minimum Acceptance Criteria: Accept if NPV > 0

Ranking Criteria: Choose the highest NPV

11

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?

Year 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

Investment Timing

12

Equivalent Annual Annuity (Cost)

Equivalent Annual Annuity (Cost) - The payment per

period with the same present value as the cash flows.

Calculate the NPV of both projects.

Use NPV as your present value and find the

appropriate annuity payment.

13

Equivalent Annual Cost

Example

Given the following costs of operating two machines and a

10% cost of capital, select the lower cost machine using

equivalent annual cost method.

Year Annual

0 1 2 3 4 (N)PV@10% Cost

A -500 -120 -120 -120 -798.42 -321.05

B -600 -100 -100 -100 -100 -961.99 -289.28

14

Replacement Chain Method

NPV @10%= $-2,187.59

NPV @10%= $-1,971.08

0 1 2 3 4 5 6 7 8 9 10 11 12

-500 -120 -120 -120

-500 -120 -120 -120

-500 -120 -120 -120

-500 -120 -120 -120

-500 -120 -120 -620 -120 -120 -620 -120 -120 -620 -120 -120 -120

0 1 2 3 4 5 6 7 8 9 10 11 12

-600 -100 -100 -100 -100

-600 -100 -100 -100 -100

-600 -100 -100 -100 -100

-600 -100 -100 -100 -700 -100 -100 -100 -700 -100 -100 -100 -100

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Other Investment Criteria

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.

16

Internal Rate of ReturnExample

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?

321 )1(

000,475

)1(

000,25

)1(

000,25000,3750

IRRIRRIRR

=

IRR = 12.56%

17

Internal Rate of ReturnCalculating the IRR can be a laborious task. Fortunately,

financial calculators can perform this function easily.

HP-10B HP-12C

-375,000 CFj -375,000 g CF0

25,000 CFj 25,000 g CFj

25,000 CFj 25,000 g CFj

475,000 CFj 475,000 g CFj

{IRR/YR} f IRR

Both produce

IRR=12.56

18

-$60.00

-$40.00

-$20.00

$0.00

$20.00

$40.00

$60.00

$80.00

$100.00

$120.00

9% 19% 29% 39%

Discount rate

NP

V

NPV Payoff Profile

Discount Rate NPV

0% $100.00

4% $71.04

8% $47.32

12% $27.79

16% $11.65

20% -$1.74

24% -$12.88

28% -$22.17

32% -$29.93

36% -$36.43

40% -$41.86

If we graph NPV versus discount rate, we can see the

IRR as the x-axis intercept.

IRR = 19.44%

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The Internal Rate of Return (IRR) Rule

IRR: the discount that sets NPV to zero

Minimum Acceptance Criteria: Accept if the IRR exceeds the required return.

Ranking Criteria: Select alternative with the highest IRR

Disadvantages: Does not distinguish between investing and borrowing. IRR may not exist or there may be multiple IRR Problems with mutually exclusive investments

Reinvestment assumption: All future cash flows assumed reinvested at the IRR.

Advantages: Easy to understand and communicate

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Multiple IRRs

There are two IRRs for this project:

0 1 2 3

$200 $800

-$200 - $800

($120.00)

($100.00)

($80.00)

($60.00)

($40.00)

($20.00)

$0.00

$20.00

$40.00

$60.00

-50% 0% 50% 100% 150% 200%

NP

V

Discount rate

100% = IRR2

0% = IRR1

Which one

should we use?

21

The Timing Problem

($4,000.00)

($3,000.00)

($2,000.00)

($1,000.00)

$0.00

$1,000.00

$2,000.00

$3,000.00

$4,000.00

$5,000.00

10% 20% 30% 40%

Discount rate

NP

V

Project A

Project B

10.55% = crossover rate

16.04% = IRRA12.94% = IRRB

The preferred project in this case depends on the discount rate…

…not the IRR. 22

Calculating the Crossover Rate

Compute the IRR for either project “A-B” or

“B-A”Year Project A Project B Project A-B Project B-A

0 ($10,000) ($10,000) $0 $0

1 $10,000 $1,000 $9,000 ($9,000)

2 $1,000 $1,000 $0 $0

3 $1,000 $12,000 ($11,000) $11,000

($3,000.00)

($2,000.00)

($1,000.00)

$0.00

$1,000.00

$2,000.00

$3,000.00

0% 5% 10% 15% 20%

Discount rate

NP

V A-B

B-A

10.55% = IRR

23

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$

Internal Rate of ReturnExample

You have two proposals to choice between. The initial

proposal has a cash flow that is different than the revised

proposal. Using IRR, which do you prefer?

24

The Payback Period Rule

How long does it take the project to “pay back” its initial investment?

Payback Period = number of years to recover initial costs

Minimum Acceptance Criteria:

set by management

Ranking Criteria:

set by management

25

Payback Method

Example

The three projects below are available. The company accepts all

projects with a 2 year or less payback period. Show how this will

impact our investment decision.

Cash Flows

Prj. C0 C1 C2 C3 Payback NPV@10%

A -2000 +500 +1000 +10000 2+ +6,794

B -2000 +1000 +1000 0 2 - 264

C -2000 0 +2000 0 2 - 347

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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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Profitability

Project PV Investment NPV Index

L 4 3 1 1/3 = .33

M 6 5 1 1/5 = .20

N 10 7 3 3/7 = .43

O 8 6 2 2/6 = .33

P 5 4 1 1/4 = .25

Profitability Index

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