Ch - University of Kentucky



Ch.5 Why Net Present Value Leads to Better Investment Decisions than Other Criteria

A review of the basics

Net Present Value

The Payback Rule

The Internal Rate of Return

Profitability index

Net Present Value

The difference between the present value of all future cash inflows minus the cost of investment.

Accept a project if its NPV is positive.

Reject a project if its NPV is negative.

Ex) Find NPV of the following project using a discount rate of 12%

Initial outlay: $40,000

CF year1 = 15,000

CF year2 = 14,000

CF year3 = 13,000

NPV = 15,000(PVIF 12%,1) + 14,000(PVIF 12%,2) + 13,000(PVIF 12%,3) - 40,000

= -6,191

Do not take this project.

Ex) Find NPV of the following project using a discount rate of 12%

Initial outlay: $40,000

CF year1 = 15,000 CF year2 = 14,000 CF year3 = 13,000 CF year4 = 12,000 CF year5 = 11,000

NPV = 15,000(PVIF 12%,1) + 14,000(PVIF 12%,2) +

13,000(PVIF 12%,3) + 12,000(PVIF 12%,4)

+ 11,000(PVIF 12%,5) - 40,000

= $7,678

Accept this project.

Key features of NPV:

Recognizes the time value of money

Solely depends on the forecasted cash flows and the opportunity cost of capital

Since present values are all measured in today’s dollars, you can add them up

So, NPV (A+B) = NPV (A) + NPV (B)

Q) You are given a job to make a decision on project X, which is composed of three projects A, B, and C which have NPVs of +$50, -$20 and +$100, respectively. How would you go about making the decision about whether to accept or reject the project?

Why does the NPV rule work?

The market value of the firm is based on the present value of the cash flows it is expected to generate.

Additional investments are “good” if the present value of the increased expected cash flows exceeds their cost.

Thus, “good” projects are those which increase firm value - or, put another way, good projects are those projects that have positive NPVs!

Moral of the story: Invest only in projects with positive NPVs.

The Payback Rule

The payback is defined to be the amount of time until cash flows recover the cost of investment (counted in years).

It measures how quickly the project will return its original investment

Accept the project if calculated payback period is less than some prespecified number of years

EX) Initial outlay $10,000

Year Cash flow

1 $2,000

2 4,000

3 3,000

4 3,000

5 1,000

after three years the firm will have recaptured $9,000 on an initial investment of $10,000, leaving $1,000 of the initial investment to be recovered.

during the fourth year, a total of $3,000 will be returned from this investment.

Assuming it will flow into the firm at a constant rate over the year, it will take one-third of the year (1000/3000) to recover the remaining $1,000.

Thus, the payback period on this project is 3.33 years.

Suppose a firm’s maximum desired payback period is three years.

Then, calculated payback is more than the desired payback period. Reject this project.

Example

Examine the three projects and note the mistake we would make if we insisted on only taking projects with a payback period of 2 years or less.

Disadvantages of payback period:

1. Requires an arbitrary cutoff point.

2. Ignores cash flows beyond the cutoff date.

3. Gives equal weight to all cash flows before the cutoff date. From the previous example, the payback rule says that projects B and C are acceptable, but because C’s cash inflows occur earlier, C has the higher NPV at any discount rate.

4. Does not use use the time value of the money. Some companies discount the cash flows before they compute the payback. However, the discounted-payback rule still takes no account of any cash flows after the cutoff date.

Internal Rate of Return (IRR)

The discount rate that equates the present value of the project’s future cash flows with the project’s initial cash outlay.

Alternatively, the discount rate that makes NPV=0.

Accept the project if IRR > the required rate of return

Reject the project if IRR < the required rate of return.

The required rate of return(also called the discount rate) is the opportunity cost of investing in the project rather than in the capital market. In other words, instead of accepting a project, the firm can always give the cash to the shareholders an let them invest it in financial assets.

Therefore, the IRR rule says that accept investment opportunities offering rates of return in excess of their opportunity costs of capital.

The IRR must be calculated by trial and error, because there is no explicit solution except for even cash flows cases.

Initial outlay = $200

Year Cash flow

1 50

2 100

3 150

Find the IRR such that NPV = 0

50 100 150

0 = -200 + + +

(1+IRR)1 (1+IRR)2 (1+IRR)3

50 100 150

200 = + +

(1+IRR)1 (1+IRR)2 (1+IRR)3

Trial and Error

Discount rates NPV

0% $100

5% 68

10% 41

15% 18

19% 1.65

20% -2

IRR is between 19% and 20%. (using a financial calculator, it is 19.44%)

An easy case for finding IRR

Assume that a firm with a required rate of return of 10% is considering a project that involves an initial outlay of $45,555. If the investment is taken, the cash flows are expected to be $15,000 per year over the project’s four year life.

Find IRR for this example. This is an annuity problem, because we have an equal amount of money and a limited period.

Note that IRR is the discount rate that equates the present value of the project’s future cash flows with the project’s initial cash outlay.

Therefore, 45,555 = 15,000 (PVIFA r%, 4)

3.037 = (PVIFA r%, 4)

r = 12% = IRR

Since IRR > 10%, Accept the project

Ex) Initial investment: $275

1 100

2 100

3 100

4 100

275 = 100 (PVIFA r%, 4)

2.75 = (PVIFA r%, 4)

IRR = between 16% and 18%

Pitfall 1 - Lending or Borrowing?

With some cash flows (as noted below) the NPV of the project increases as the discount rate increases.

This is contrary to the normal relationship between NPV and discount rates. IRR method cannot distinguish between a borrowing project and a lending project.

In this case, IRR > Opportunity cost ;Accept or reject?

The only way to find the answer is to look at the NPV. Reject.

Pitfall 2 - 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%.

There can be as many different internal rates of return for a project as there are changes in the sign of the cash flows

Pitfall 3 - Mutually Exclusive Projects

Mutually exclusive investment decisions: a situation where taking one investment prevents the taking of another.

As noted below, both projects are good investments, but F has the higher NPV and is better.

Why? Remember, we are ultimately interested in creating value for the shareholders, so the option with the higher NPV is preferred, regardless of the relative values.

Therefore, projects cannot be ranked using their IRRs

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