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.
Figure 6.1 NPV vs IRR Independent projects
If cash flows are discounted at k1, NPV is positive and IRR > k1: accept project.
If cash flows are discounted at k2, NPV is negative and IRR < k2: reject the project.
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.
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. See figure 6.2.
Figure 6.2 NPV vs IRR: Dependent projects
Up to a discount rate of ko: project B is superior to project A, therefore project B is preferred to project A.
Beyond the point ko: project A is superior to project B, therefore project A is preferred to project B
The two methods do not rank the projects the same.
