METHODS OF PROJECT EVALUATIONS 2

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Corporate Finance FIN 622

Lesson 10

METHODS OF PROJECT EVALUATIONS

The following topics will be discussed in this hand out.

Methods of Project evaluations:

Internal Rate of Return IRR

Associated topics to be covered:

NPV vs. IRR

Criticism of IRR

The Internal Rate of Return (IRR)

The IRR is the discount rate at which the NPV for a project equals zero. This rate means that the present

value of the cash inflows for the project would equal the present value of its outflows.

The IRR is the break-even discount rate.

The IRR is found by trial and error.

Where r = IRR

IRR of an annuity:

Where:

Q (n, r) is the discount factor

Io is the initial outlay

C is the uniform annual receipt (C1 = C2 =....= Cn).

Example:

What is the IRR of an equal annual income of $20 per annum which accrues for 7 years and costs $120?

Net present value vs. Internal rate of return:

Independent vs. dependent projects

NPV and IRR methods are closely related because:

both are time-adjusted measures of profitability, and

ii)

Their mathematical formulas are almost identical.

So, which method leads to an optimal decision: IRR or NPV?

a) NPV vs. IRR: Independent projects

Independent project: Selecting one project does not preclude the choosing of the other.

With conventional cash flows (-|+|+) no conflict in decision arises; in this case both NPV and IRR lead to

the same accept/reject decisions.

Mathematical proof: for a project to be acceptable, the NPV must be positive, i.e.

Similarly for the same project to be acceptable:

Where R is the IRR.

Since the numerators Ct are identical and positive in both instances:

* Implicitly/intuitively R must be greater than k (R > k);

* If NPV = 0 then R = k: the company is indifferent to such a project;

* Hence, IRR and NPV lead to the same decision in this case.

b) NPV vs. IRR: Dependent projects

NPV clashes with IRR where mutually exclusive projects exist.

Corporate Finance FIN 622

Example:

Agritex is considering building either a one-storey (Project A) or five-storey (Project B) block of offices on a

prime site. The following information is available:

Initial Investment Outlay Net Inflow at the Year End

Project A -9,500

11,500

Project B -15,000

18,000

Assume k = 10%, which project should Agritex undertake?

= $954.55

= $1,363.64

Both projects are of one-year duration:

IRRA:

$11,500 = $9,500 (1 +RA)

= 1.21-1

Therefore IRRA = 21%

IRRB:

$18,000 = $15,000(1 + RB)

= 1.2-1

Therefore IRRB = 20%

Decision:

Assuming that k = 10%, both projects are acceptable because:

NPVA and NPVB are both positive

IRRA > k AND IRRB > k

Which project is a "better option" for Agritex?

If we use the NPV method:

NPVB ($1,363.64) > NPVA ($954.55): Agritex should choose Project B.

If we use the IRR method:

IRRA (21%) > IRRB (20%): Agritex should choose Project A.

Differences in the scale of investment

NPV and IRR may give conflicting decisions where projects differ in their scale of investment. Example:

Years

Project A -2,500 1,500 1,500 1,500

Project B -14,000 7,000 7,000 7,000

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Assume k= 10%.

NPVA = $1,500 x PVFA at 10% for 3 years

= $1,500 x 2.487

= $3,730.50 - $2,500.00

= $1,230.50.

NPVB == $7,000 x PVFA at 10% for 3 years

= $7,000 x 2.487

= $17,409 - $14,000

= $3,409.00.

IRRA =

= 1.67.

Therefore IRRA = 36% (from the tables)

IRRB =

= 2.0

Therefore IRRB = 21%

Decision:

Conflicting, as:

· NPV prefers B to A

· IRR prefers A to B

NPV

IRR

Project A $ 3,730.50 36%

Project B $17,400.00 21%

To show why:

The NPV prefers B, the larger project, for a discount rate below 20%

ii)

The NPV is superior to the IRR

a) Use the incremental cash flow approach, "B minus A" approach

b) Choosing project B is tantamount to choosing a hypothetical project "B minus A".

Project B

- 14,000 7,000 7,000 7,000

Project A

- 2,500 1,500 1,500 1,500

"B minus A" - 11,500 5,500 5,500 5,500

IRR"B Minus A"

= 2.09

Corporate Finance FIN 622

= 20%

c) Choosing B is equivalent to: A + (B - A) = B

d) Choosing the bigger project B means choosing the smaller project A plus an additional outlay of

$11,500 of which $5,500 will be realized each year for the next 3 years.

e) The IRR"B minus A" on the incremental cash flow is 20%.

f) Given k of 10%, this is a profitable opportunity, therefore must be accepted.

g) But, if k were greater than the IRR (20%) on the incremental CF, then reject project.

h) At the point of intersection,

NPVA = NPVB or NPVA - NPVB = 0, i.e. indifferent to projects A and B.

i) If k = 20% (IRR of "B - A") the company should accept project A.

This justifies the use of NPV criterion.

Advantage of NPV:

It ensures that the firm reaches an optimal scale of investment.

Disadvantage of IRR:

· It expresses the return in a percentage form rather than in terms of absolute dollar returns, e.g. the

IRR will prefer 500% of $1 to 20% return on $100. However, most companies set their goals in

absolute terms and not in % terms, e.g. target sales figure of $2.5 million.

The timing of the cash flow

The IRR may give conflicting decisions where the timing of cash flows varies between the 2 projects.

Note that initial outlay Io is the same.

Project A

- 100 20

125.00

Project B

- 100 100

31.25

"A minus B" 0

- 80 88.15

Assume k = 10%

NPV IRR

Project A

17.3 20.0%

Project B

16.7 25.0%

"A minus B" 0.6

10.9%

IRR prefers B to A even though both projects have identical initial outlays. So, the decision is to accept A,

that is B + (A - B) = A.

The horizon problem

NPV and IRR rankings are contradictory. Project A earns $120 at the end of the first year while project B

earns $174 at the end of the fourth year.

Project A

-100 120 -

Project B

-100 -

174

Assume k = 10%

Corporate Finance FIN 622

NPV IRR

Project A 9

20%

Project B 19

15%

Decision:

NPV prefers B to A.

IRR prefers A to B.

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