Investment Decisions -Net Present Value and others-

Capital-Budgeting

The process of decision making with respect to investments in fixed assets that is, should a proposed project be accepted or rejected.

It is easier to evaluate profitable projects than to find them.

2

Source of Ideas for projects

Within the Firm: Typically, a firm has a research & development (R&D) department that searches for ways of improving existing products or finding new projects.

Other sources: Competition, Suppliers, Customers

3

Capital-Budgeting Decision Criteria

1. Net Present Value

2. Internal Rate of Return

3. Payback Period

4. Profitability Index

5. Capital Rationing

4

Net Present Value or NPV

NPV is equal to the present value of all future free cash flows less the investments initial outlay. It measures the net value of a project in todays dollars. NPV = FCF - Initial outlay

(1+k)n

Decision Rule:

If NPV > 0, accept If NPV < 0, reject

5

NPV Example

Example: Project with an initial cash outlay of $60,000 with following free cash flows for 5 years.

Yr FCF

Initial outlay -60,000

1 25,000

2 24,000

3 13,000

4 12,000

5 11,000

The firm has a 15% required rate of return.

6

NPV = - Initial outlay + FCF

(1+k)n

PV of FCF = $60,764

Subtracting the initial cash outlay of $60,000 leaves an NPV of $764.

Since NPV>0, project is feasible.

7

NPV in Excel

Input cash flows for initial outlay and inflows in cells A1 to A6

In cell A7 type the following formula:

=A1+npv(.15,a2:a6)

Excel will give the NPV = $764

8

NPV Trade-offs

Benefits

Considers cash flows, not profits

Considers all cash flows

Recognizes time value of money

By accepting only positive NPV projects, increases value of the firm

Drawbacks

Requires detailed long-term forecast of cash flows

NPV is considered to be the most theoretically correct criterion for evaluating capital-budgeting projects.

9

Internal Rate of Return or IRR

IRR is the discount rate that equates the present value of a projects future net cash flows with the projects initial cash outlay

Decision Rule:

If IRR > Required rate of return, accept

IF IRR < Required rate of return, reject

10

11

IRR and NPV

If NPV is positive, IRR will be greater than the required rate of return

If NPV is negative, IRR will be less than required rate of return

If NPV = 0, IRR is the required rate of return.

12

IRR Example

Initial Outlay: $3,817

Cash flows:

Yr.1=$1,000, Yr. 2=$2,000, Yr. 3=$3,000

Discount rate NPV

15% $4,356

20% $3,958

22% $3,817

IRR is 22% because the NPV equals the initial cash outlay

13

Payback Period

Number of years needed to recover the initial cash outlay of a capital-budgeting project

Decision Rule: Project feasible or desirable if the payback period is less than or equal to the firms maximum desired payback period.

14

Payback Period Example

Example: Project with an initial cash outlay of $20,000 with following free cash flows for 5 years.

15

YEAR CASH FLOW BALANCE

1 $ 8,000 ($ 12,000)

2 4,000 ( 8,000)

3 3,000 ( 5,000)

4 5,000 0

5 10,000 12,000

Payback is 4 years

Trade-offs

Benefits:

Uses cash flows rather than accounting profits

Easy to compute and understand

Useful for firms that have capital constraints

Drawbacks:

Ignores the time value of money and

Does not consider cash flows beyond the payback period.

16

Profitability Index (PI)

PI is the ratio of the present value of the future free cash flows to the initial outlay. It yields the same accept/reject decision as NPV.

PI = PV FCF/ Initial outlay

Decision Rule:

PI > 1 = accept

PI < 1 = reject

17

PI Example

A firm with a 10% required rate of return is considering investing in a new machine with an expected life of six years. The initial cash outlay is $50,000.

18

PI Example

FCF PVF @ 10% PV

Initial Outlay

-$50,000 1.000 -$50,000

Year 1 15,000 0.909 13,636

Year 2 8,000 0.826 6,612

Year 3 10,000 0.751 7,513

Year 4 12,000 0.683 8,196

Year 5 14,000 0.621 8,693

Year 6 16,000 0.564 9,032

19

PI Example

PI = ($13,636 + $6,612+$7,513 + $8,196 + $8,693+ $9,032) / $50,000

=$53,682/$50,000 = 1.0736 Project PI > 1, accept.

20

NPV and PI

When the present value of a projects free cash inflows are greater than the initial cash outlay, the project NPV will be positive. PI will also be greater than 1.

NPV and PI will always yield the same decision.

21

Capital Rationing

Capital Rationing

Capital rationing occurs when a limit is placed on the dollar size of the capital budget.

How to select: Select a set of projects with the highest NPVs subject to the capital constraint. Using NPV may preclude accepting the highest ranked project in terms of PI or IRR.

23

Ranking Problems

Size Disparity

Time Disparity

Unequal Life

24

Size Disparity This occurs when we examine mutually exclusive projects of unequal

size.

Example: Consider the following cash flows for one-year Project A and B, with required rates of return of 10%. Initial Outlay: A = $200 B = $1,500

Inflow: A = $300 B = $1,900

25

Size Disparity

26

Size Disparity

Which technique to use to select the better project?

Use NPV whenever there is size disparity. If there is no capital rationing, project with the largest NPV will be selected. When capital rationing exists, select set of projects with the largest NPV.

But, small companies uses in general IRR when capital rationing exists.

27

Time Disparity Problem

Time Disparity problems arise because of differing reinvestment assumptions made by the NPV and IRR decision criteria.

Cash flows reinvested at:

According to NPV: Required rate of return

According to IRR: IRR

28

Example: Consider two projects, A and B, with initial outlay of $1,000, cost of capital of 10%, and following cash flows in years 1, 2, and 3:

1 2 3

A: $100 $200 $2,000

B: $650 $650 $650

29

Time Disparity Problem

30

Time Disparity Problem

Project A Project B NPV 758.83 616.45 PI 1.759 1.616 IRR 35% 43%

Ranking Conflict: Using NPV, A is better Using IRR, B is better

Which technique to use to select the superior project?: Use NPV (especially in lease calculations)

31

Unequal Lives Problem

This occurs when we are comparing two mutually exclusive projects with different life spans.

To compare projects, we compute the Equivalent Annual Annuity (EAA)

32

Unequal Lives Problem

Example: If you have two projects, A and B, with equal investment of $1,000, required rate of return of 10%, and following cash flows in years 1-3 (for project A) and 1-6 (for project B)

Project A = $500 each in years 1-3

Project B = $300 each in years 1-6

33

Computing EAA

1. Calculate projects NPV:

A = $243.43 and B = $306.58

2. Calculate EAA = NPV/annual annuity factor

A = $97.89 B = $70.39

3. Project A is better

34