Corporate Finance

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VU
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?
=6
Net present value vs. Internal rate of return:
Independent vs. dependent projects
NPV and IRR methods are closely related because:
i)
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.
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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
0
1
2
3
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:
i)
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".
0
1
2
3
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
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= 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.
It ensures that the firm reaches an optimal scale of investment.
·  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.
0
1
2
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.
0
1
2
3
4
Project A
-100 120 -
-
-
Project B
-100 -
-
-
174
Assume k = 10%
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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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