Capital Budgeting Decision Rules What real investments should firms make?

Alternative Rules in Use Today NPV IRR Profitability Index Payback Period Discounted Payback Period Accounting Rate of Return

NPV Analysis The recommended approach to any significant capital budgeting decision is NPV analysis. NPV = PV of the incremental benefits – PV of the incremental costs. When evaluating independent projects, take a project if and only if it has a positive NPV. When evaluating interdependent projects, take the feasible combination with the highest total NPV. The NPV rule appropriately accounts for the opportunity cost of capital and so ensures the project is more valuable than comparable alternatives available in the financial market.

Lockheed Tri-Star As an example of the use of NPV analysis we will use the Lockheed Tri-Star case. To examine the decision to invest in the Tri- Star project, we first need to forecast the cash flows associated with the Tri-Star project for a volume of 210 planes. Then we can ask: What is a valid estimate of the NPV of the Tri-Star project at a volume of 210 planes as of 1967.

Lockheed Tri-Star – Key Points Pre-production costs estimated at $900 million incurred between 1967 and Total of 210 planes delivered from Revenues of $16 million per unit, 25% of revenue received 2 years in advance of delivery. Production costs of $14 million (at 210 units could decline to $12.5 million at 300) from Discount rate of 10% per year.

Tri-Star Cash Flows 210 planes ( ) Planes per year = 210/6=35 Production Costs ( ) 35($14M)=$490M per year Don’t forget the preproduction costs of $900M Revenues ( ) Total Revenues 35($16M)=$560M per year Deposits=0.25($560M)=$140M (2 yrs in advance) Net Revenues=$560-$140=$420M on delivery

Tri-Star Cash Flows (210 Planes)

Tri-Star in 1967

Accounting Profits at 210 Production revenues are $16M per plane and production costs are $14M per plane. Profit is $2M per plane. 210×$2M = $420M production profits. $420M vs. $900M preproduction costs is breakeven? Suppose production cost is $12.5M per plane (learning curve hits early). Profit per plane is $3.5M. At 210 planes this is $735M production profit. Now take the extreme low-end of the $800M - $1B preproduction cost range. Suddenly you have “breakeven.” Smart huh?

Tri-Star NPV 1967 ($Millions) Units SoldAverage Unit Cost Accounting Profit NPV 323$12.25$311-$ $12.00$700-$12 400$11.75$800$42 500$11.00$1,600$441

Tri-Star Cash Flows 1970 (210 Planes)

1970 Tri-Star

Tri Star Post Mortem Accounting breakeven approximately 275 planes $16M - $12.5M = $3.5M per plane $3.5M  275 = $962M profit versus $960M in actual development costs known in 1970 This more realistic breakeven level announced subsequent to the guarantees being granted. NPV breakeven approximately 400 planes Total free world market demand for wide-body aircraft approximately 325 planes Optimistic estimate: total demand 775 and 40% of that is 310 Lockheed share price $64 Jan 1967 drops to $11 Jan 1971 ($64-$11)(11.3 Million shares)=-$599 Million Compare to -$584 Million NPV

Internal Rate of Return Definition: The discount rate that sets the NPV of a project to zero (essentially project YTM) is the project’s IRR. IRR asks: “What is the project’s rate of return?” Standard Rule: Accept a project if its IRR is greater than the appropriate market based discount rate, reject if it is less. Why does this make sense? For independent projects with “normal cash flow patterns” IRR and NPV give the same conclusions. IRR is completely internal to the project. To use the rule effectively we compare the IRR to a market rate.

IRR – “Normal” Cash Flow Pattern Consider the following stream of cash flows: Calculate the NPV at different discount rates until you find the discount rate where the NPV of this set of cash flows equals zero. That’s all you do to find IRR $1,000 $400

IRR – NPV Profile Diagram Evaluate the NPV at various discount rates: RateNPV 0 $ $ $157.4 At r = 9.7%, NPV = 0

The Merit to the IRR Approach The IRR (as with the YTM) is an approximation to the return generated over the life of a project on the initial investment. As with NPV, the IRR is based on incremental cash flows, does not ignore any cash flows, and (by comparison to the appropriate discount rate, r) take proper account of the time value of money and risk. In short, it can be useful.

Pitfalls of the IRR Approach Multiple IRRs There can be as many solutions to the IRR definition as there are changes of sign in the time ordered cash flow series. Consider: This can (and does) have two IRRs $100$230-$132

Pitfalls of IRR cont…

Mutually exclusive projects: IRR can lead to incorrect conclusions about the relative worth of projects. Ralph owns a warehouse he wants to fix up and use for one of two purposes: A. Store toxic waste. B. Store fresh produce. Let’s look at the cash flows, IRRs and NPVs.

Mutually Exclusive Projects and IRR

At low discount rates, B is better. At high discount rates, A is better. But A always has the higher IRR. A common mistake to make is choose A regardless of the discount rate. Simply choosing the project with the larger IRR would be justified only if the project cash flows could be reinvested at the IRR instead of the actual market rate, r, for the life of the project.

Summary of IRR vs. NPV IRR analysis can be misleading if you don’t fully understand its limitations. For individual projects with normal cash flows NPV and IRR provide the same conclusion. For projects with inflows followed by outlays, the decision rule for IRR must be reversed. For Multi-period projects with several changes in sign of the cash flows multiple IRRs exist. Must compute the NPVs to see what is appropriate decision rule. IRR can give conflicting signals relative to NPV when ranking projects. I recommend NPV analysis, using others as backup.

Profitability Index Definition: The present value of the cash flows that accrue after the initial outlay divided by the initial cash outlay. Rule: Take any/only the projects with a PI>1. The PI does a benefit/cost (bang for the buck) analysis. Any time the PV of the future benefits is larger than the current cost PI > 1. When this is true what is the NPV? Thus for independent projects the rules make exactly the same decision.

PI and Mutually Exclusive Projects Example: Project CF 0 CF 1 10% PI A-$1,000 $1,500 $ B-$10,000 $13,000 $1, Since you can only take one and not both the NPV rule says B, the PI rule would suggest A. Which is right? The projects are mutually exclusive so the NPV of one is an opportunity cost to the other. We must take B, in this respect A has a negative NPV. PI treats scale strangely. It measures the bang per buck invested. This is larger for A but since we invest more in B it will create more wealth for us.

Payback Period Rule Frequently used as a check on NPV analysis or by small firms or for small decisions. Payback period is defined as the number of years before the cumulative cash inflows equal the initial outlay. Provides a rough idea of how long invested capital is at risk. Example: A project has the following cash flows Year 0 Year 1 Year 2 Year 3 Year 4 -$10,000 $5,000 $3,000 $2,000 $1,000 The payback period is 3 years. Is that good or bad?

Payback Period Rule Frequently used as a check on NPV analysis or by small firms or for small decisions. Payback period is defined as the number of years before the cumulative cash inflows equal the initial outlay. Provides a rough idea of how long invested capital is at risk. Example: A project has the following cash flows Year 0 Year 1 Year 2 Year 3 Year 4 -$10,000 $5,000 $3,000 $2,000 $1,000,000 The payback period is 3 years. Is that good or bad?

Payback Period Rule An adjustment to the payback period rule that is sometimes made is to discount the cash flows and calculate the discounted payback period. This “new” rule continues to suffer from the problem of ignoring cash flows received after an arbitrary cutoff date. If this is true, why mess up the simplicity of the rule? Simplicity is its one virtue. At times the payback or discounted payback period may be valuable information but it is not often that this information alone makes for good decision- making.

Average Accounting Return Definition: The average net income after depreciation and taxes (before interest) divided by the average book value of the investment. Rule: If the AAR is above some cutoff take the project. This is essentially a measure of return on assets (ROA).

AAR Problems Doesn’t use cash flows but rather accounting numbers. Ignores the time value of money. Does not adjust for risk. Uses an arbitrarily specified cutoff rate.