Capital Budgeting

There can be situations where analyzing the cash flows results in multiple IRR values. It is important to note that an IRR equation is a polynomial equation, which may have multiple solutions mathematically. While this is not unusual mathematically, it complicates commercial interpretation.

In general, when undertaking a replacement project involving existing equipment or facilities, the decision to invest is based on incremental cash flows. The relevant cash flows to consider are those generated with the new investment compared to those that would be generated without the investment.

To illustrate this concept, consider an example involving an old machine and a new machine intended to replace it.

First, we need to analyze the incremental upfront investment. If we replace the old machine with a new one, the investment will entail $1,200,000 for the new machine and an additional $100,000 in working capital, totaling $1,300,000.

We will sell the old machine at its current market value of $600,000. Since this exceeds the book value of the old machine, capital gains tax will be applicable. The cash inflow from the sale of the machine will be calculated as $800,000 minus 35% of the difference between $800,000 and $500,000.

Thus, the total initial outlay will be:

$1,300,000 - ($800,000 - 35% x ($800,000 - $500,000))

= $1,300,000 - $695,000

= $605,000.

The incremental cash flow for each of the 10 years is:

(Incremental revenue - Incremental operating cost - Incremental depreciation) × (1 - Tax Rate) + Incremental depreciation.

= ($600,000 - $400,000) - ($150,000 - $100,000) - ($120,000 - $50,000) × 65% + ($120,000 - $50,000)

= $122,000.

At the end of the project, the net post-tax cash flow must also be considered. The new machine will have a salvage value of $400,000, which is $200,000 more than the old machine's salvage value. This incremental cash will be subject to capital gains tax. Therefore, the total incremental cash flow at project termination will be:

Incremental Salvage Value + Return of Working Capital - Tax on Capital Gain

= ($400,000 - $200,000) + $100,000 - ($400,000 - $200,000) × 35%

= $230,000.

With all this information, we can calculate the NPV of these incremental cash flows. If the NPV is greater than zero, we should invest in the new machine; otherwise, we should continue using the old machine.

When comparing two mutually exclusive projects, the one with the higher NPV usually wins. However, this may not be the best choice if the projects have different lifespans and can be replaced or replicated. Projects that can't be replaced are 'one-shot' projects, while those that can be repeated are 'investment chains'.

There are two methods to compare mutually exclusive projects with unequal lives:

· Equivalent Annual Annuity Approach

· Least Common Multiple of Lives Approach

Consider two projects, A and B, which will be replaced after they wear out, but only one can be chosen. Their cash flows are shown below.

Project B appears more favorable based on both NCF and NPV. However, it is important to note that Project A generates an NPV of $56 in just two years, whereas Project B takes three years to generate an NPV of $66. This suggests that the funds generated from Project A could be reinvested in another opportunity for an additional year, potentially yielding a return greater than the three-year return of Project B.

To evaluate this scenario, we can consider the repetition of these projects over their respective periods – two years for Project A and three years for Project B. By aligning the timelines, we see that both projects can operate within a 6-year period (the least common multiple of their durations). Over six years, Project A can be executed three times, while Project B can be executed twice. Establishing this common timeframe allows us to reassess the cash flows and NPVs of the projects. The recalculated cash flows are illustrated in the table below.

Essentially, the initial outlay for Project A would be reinvested every two years, generating consistent cash flows. Similarly, for Project B, the initial investment would be made every three years, capturing the cyclical benefits.

The table demonstrates that project A's cash flow has been repeated three times, and the NPV is calculated based on the cash flow of all three sub-projects. The resulting NPV is $141. An alternative method to calculate the NPV involves assuming that project A generates three NPVs at the end of period 0, period 2, and period 4, and then calculating the present value of these three NPVs. This method will yield the same result as before.

After reviewing the NPV of project B and project D, it is determined that investing in these projects would result in a reduction of value by $170 million. Therefore, it is recommended to invest only in project A and project C, which would yield $280 million in NPV and save $200 million in capital. This saved amount can be allocated to other profitable ventures.

Consider another scenario where the company has a budget of $1000 million and is presented with four different projects, all with positive NPVs, as shown below.