Financial management: lecture 6

NPV and other Investment Criteria

Capital Budgeting Decisions

Financial management: lecture 6

Today’s agenda

Net Present Value (revisit) Other two investment rules

Financial management: lecture 6

Net Present Value rule (NPV)

NPV is the present value of a project minus its cost

If NPV is greater than zero, the firm should go ahead to invest; otherwise forget about this project

A hidden assumption: there is no budget constraint or money constraint.

Financial management: lecture 6

NPV (continue)

In other words:

Managers can 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 if there is no budget constraint.

Financial management: lecture 6

Net Present Value

NPV = PV - required investment

NPV CC

r

C

r

C

rt

t

01

12

21 1 1( ) ( )...

( )

Financial management: lecture 6

An Example

An oil well, if explored, can now produce 100,000 barrels per year. The well will produce forever, but production will decline by 4% per year. Oil prices, however, will increase by 2% per year. The discount rate is 8%. Suppose that the price of oil now is $14 for barrel.

If the cost of oil exploration is $12.8 million, do you want to take this project?

Financial management: lecture 6

Solution

Visualize the cash flow patterns C0=1.4, C1=1.37, C2=1.34, C3=1.31 What is the pattern of the cash flow?

• g=C1/C0 -1 =-0.0208=-2.1%

• PV( the project) =C0+C1/(r-g)=15

• NPV=PV( the project ) -12.8>0

What’s your decision?

Financial management: lecture 6

Two other investment rules

IRR rule Payback period rule

Financial management: lecture 6

IRR rule

Internal Rate of Return (IRR) – Single discount rate at which NPV = 0.

IRR rule - Invest in any project offering a IRR that is higher than the opportunity cost of capital or the discount rate.

Financial management: lecture 6

IRR rule

Example

You can purchase a building for $350,000. The investment will generate $16,000 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?

Financial management: lecture 6

Internal Rate of Return

Example

You can purchase a building for $350,000. The investment will generate $16,000 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?

0 350 00016 000

1

16 000

1

466 000

11 2 3

,

,

( )

,

( )

,

( )IRR IRR IRR

Financial management: lecture 6

Internal Rate of Return

Example

You can purchase a building for $350,000. The investment will generate $16,000 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?

0 350 00016 000

1

16 000

1

466 000

11 2 3

,

,

( )

,

( )

,

( )IRR IRR IRR

IRR = 12.96%

Financial management: lecture 6

Internal Rate of Return

-200

-150

-100

-50

0

50

100

150

200

0 5 10 15 20 25 30 35

Discount rate (%)

NP

V (

,000

s)

IRR=12.96%

Financial management: lecture 6

What’s wrong with IRR?

Pitfall 1 - Mutually Exclusive Projects IRR sometimes ignores the magnitude of the project. The following two projects illustrate that problem.

Example

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

Financial management: lecture 6

Internal Rate of Return (1)

Example

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

Project C0 C1 C2 C3 IRR NPV@7%

H -350 400 14.29% 24,000$ I -350 16 16 466 12.96% 59,000$

Financial management: lecture 6

Internal Rate of Return

%29.14

0)1(

400350

1

IRR

IRRNPV

%96.12

0)1(

466

)1(

16

)1(

16350

321

IRR

IRRIRRIRRNPV

Financial management: lecture 6

What’s wrong with IRR (2)?

Pitfall 2 - Lending or Borrowing?

Example

project C0 C1 IRR (%) NPV at 10%

J

K

-100 +150 +50 +$36.4

+100 -150 +50 -$36.4

Financial management: lecture 6

What’s wrong with IRR (3)?

Pitfall 3 - Multiple Rates of Return Certain cash flows can generate NPV=0 at two

different discount rates. The following cash flow generates NPV=0 at both (-

50%) and 15.2%. Example

• A project costs $1000 and produces a cash flow of $800 in year 1, a cash flow of $150 every year from year 2 to year 5, and a cash flow of -150 in year 6.

Financial management: lecture 6

Payback period rule

Payback period is the number of periods such that 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 rule.

Financial management: lecture 6

Payback period rule

The following example shows that all the three projects have a payback period of 2. If the payback period used by the firm is 2, the firm can take project C and lose money.

Cash Flows

Prj. C0 C1 C2 C3 Payback NPV@10%

A -2000 +1000 +1000 +10000 2 7,429

B -2000 +1000 +1000 0 2 -264C -2000 0 +2000 0 2 - 347