Chapter 1: Investment decisions.

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But there are other criteria to decide whether is a good idea to take a project or not. Although the NPV rule is the most used method there are: the IRR rule, the payback rule, the book rate of return rule and the profitability index rule.

The IRR: an example

Asset value in two subsequent periods:

- AV0: 80m and AV1: 96.8m

- Return: ry = (96.8 – 80)/80 = 0.21 or 21%

Value in two non-subsequent periods:

- AV0: 80m and AV2: 96.8m

- Return --> Numerical method: find r such that Net Present Value (NPV) = 0

[pic 9]

The IRR Rule

The internal rate of return of a cash flow stream is the interest rate ry that makes the NPV of a project equal to 0. [pic 10]

IRR and NPV

The IRR rule take any investment opportunity where the IRR exceeds the opportunity cost of capital. And turn down any opportunity whose IRR is less than the opportunity cost of capital. The IRR rule is only guaranteed to work for a stand-alone project if all of the project’s negative cash flows precede its positive cash flows. If it is not the case, the IRR rule can lead to incorrect decisions.

The IRR has some pitfalls:

- There might be several IRRs or none.

- Ignores magnitude and cannot select among different projects.

- Even more problematic if our discount rates are not stable over time (with which one do we compare the cost of capital?)

Payback period and the payback rule

- The payback period is the number of periods (years) it takes before cumulative forecasted cash flow equals initial outlay.

- The payback rule says only to accept projects that “payback” in the desired time frame.

- This method is deficient, primarily because it ignores cash flows after payback period and the present value of future cash flows. Relies on an ad hoc decision: Which is the appropriate payback time?.

- This rule is typically used for small investment decisions. In such cases, the cost of making an incorrect decision might not be large enough to justify the time required to calculate de NPV.[pic 11]

Project Selection

If only one from a set of positive NPV projects can be selected, we should select that with the largest NPV. When resources are limited, the profitability index (PI) helps selecting among various project combinations and alternatives:

- PI = (NPV - C0 ) / ( -C0 ) = PV / ( -C0 )

- If resources are unlimited, we should select projects with PI>1.

When projects are mutually exclusive, the firm can only take on one of the projects even if many of them are attractive. Often this limitation is due to resource constraints. Then the firm must choose the best set of investments it can make given the resources it has available. Managers often work within a budget constraint that limits the amount of capital they may invest in a given period. The manager’s goal is to choose the projects that maximize the total NPV while staying within the budget.

Profitability Index

The profitability index measures the value created in terms of NPV per unit of resource consumed. After computing the profitability index, we can rank projects based on it. For it to be completely reliable, two conditions must be satisfied:

- The set of projects taken following the profitability index ranking completely exhausts the available resource.

- There is only a single relevant resource constraint.

PART C – Adjusting for Risk

Risky Cash Flows

Future cash flows should be from now on “expected cash flows”. Example: Expected cash flow of a project: CF=$100 per year for three years.

Discount rate needs to reflect risk of cash flows and therefore may need to be higher than the “risk-free” rate:

- Risk-free rate, rf = 6%,

- But discount rate might need to be r = 12%

- Risk premium here is rp = 6%, and more generally r = rf + rp

[pic 12]

How to compute the expected cash flows?

Expected cash flows may come from scenario analysis. For example, CF = $100 if:

- 200 in good scenario, 100 in medium one, and 0 in bad one.

- And all of these scenarios are equally likely (probability: 1/3 each).[pic 13]

Finding the discount rate

In theory, what should the discount rate be?

- The return one can receive on similar investments, i.e. bearing same risks!

- Often called “cost of capital” as it measures opportunity cost of funds.

How to compute the “cost of capital” of a project of a firm? Often start computing cost of capital for the firm as a whole (many projects have similar risk as the firm as a whole). If not, it is a good starting point that can be adjusted.

Estimating the firm’s cost of capital

First, suppose that firm is financed with equity only:

- Firm’s cost of capital = expected equity return (see next chapter).

- Estimated using Capital Asset Pricing model (CAPM) (see next chapter).

Second, incorporate the possibility that it has debt, so there is the need to take into account cost of debt as well as the cost of equity: We use weighted average cost of capital (WACC) (see next chapter) .

CAPITAL ASSET PRICING MODEL (CAMP)

The