Net present value vs internal rate of return

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 C_t 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:

IRR_A: 

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

= 1.21-1

therefore IRR_A = 21%

IRR_B: 

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

= 1.2-1

therefore IRR_B = 20%

Decision:

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

NPV_A and NPV_B are both positive
IRR_A > k AND IRR_B > k

Which project is a "better option" for Agritex?

If we use the NPV method:

NPV_B ($1,363.64) > NPV_A ($954.55): Agritex should choose Project B.

If we use the IRR method:

IRR_A (21%) > IRR_B (20%): Agritex should choose Project A. See figure 6.2.

Figure 6.2 NPV vs IRR: Dependent projects

Up to a discount rate of k_o: project B is superior to project A, therefore project B is preferred to project A.

Beyond the point k_o: 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.