PART 3: CAPITAL BUDGETING
solution; (2) multiple solutions; and (3) no real solution. The following examples illustrate the problems
with multiple IRRs and no real solution.Lending Versus Borrowing
A company establishes a hurdle rate of 20% for new investments. Consider two projects with cash flows
occurring at just two dates: now and one year from now.
The first project displays the familiar pattern
of an initial cash outflow followed by a cash
inflow. Most investment projects probably fit this
profile. But the second project begins with a cash
inflow followed by a cash outflow. What kinds
of projects in the real world follow this pattern?
Think of a company that is cutting timber. The
timber is cut and sold immediately at a profit, but when harvesting is complete, the company must re-
plant the forest at considerable expense. Similarly, consider an optional warranty sold with a new car. The
warranty seller receives payment up-front, but may have to pay claims later on.
Both projects described in the table have a 50% IRR, but are the two projects equally desirable?
It should be intuitive to you that project 1 is superior because it generates net cash inflows over time,
whereas project 2 generates net cash outflows. Indeed, the NPVs bear this out: project 1 generates a
positive $25 NPV, and project 2 yields a negative $25 NPV.
The problem we are confronting here is known as the lending-versus-borrowing problem. We can think
of project 1 as analogous to a loan. Cash flows out today in exchange for a larger amount of cash in one
year. When we lend money, a higher interest rate (or a higher internal rate of return) is preferable, other
things held constant. In contrast, project 2 is analogous to borrowing money. We receive cash up-front,
but have to pay back a larger amount later. When borrowing money, a lower interest rate (or a lower IRR)
is preferred, other factors held constant. Therefore, we can modify the internal rate of return decision
rule as follows:1 When projects have initial cash outflows and subsequent cash inflows, invest when the project IRR
exceeds the hurdle rate.2 When projects have initial cash inflows and subsequent cash outflows, invest when the project IRR
falls below the hurdle rate.Figure 9.6 illustrates this situation. The NPV of project 1 falls when the discount rate rises, as we would
expect. This means that, if the IRR exceeds the hurdle rate, the project’s NPV is positive, but if the IRR
falls below the hurdle rate, the NPV is negative. So in this case it makes sense to follow the usual rule of
accepting projects when the IRR exceeds the hurdle rate. In contrast, the NPV of project 2 actually rises
as the discount rate rises. This counterintuitive relationship holds because the company is essentially
borrowing money in project 2. The higher the rate at which the company discounts the amount it will
have to repay, the lower the present value of that payment and the higher the NPV of the project. In this
case, it makes sense to accept projects only when the IRR falls short of the company’s hurdle rate.Multiple IRRs
A second difficulty with the IRR method can occur when a project’s cash flows alternate between
negative and positive values – that is, when the project generates an alternating series of net cash inflows
and outflows. In that case, there may be more than one solution to the IRR equation.Project Cash flow
nowCash flow in
one year