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Description: CHAP 7

Texte:
Net present value (NPV): difference between the present value of cash inflows and the present value of cash outflows over a period of time.
Cost of capital: the rate of return that could have been earned by putting the same money into a different investment with equal risk
rate of return required to persuade the investor to make a given investment
discount rate for a project’s future cash flow
Internal rate of return (IRR): the interest rate that sets the NPV equal to zero

NPV rule (in general): When making an investment decision, take the alternative with the highest NPV. Choosing this alternative is equivalent to receiving its NPV in cash today.

NPR rule (stand-alone project): compare the project’s NPV to zero (the NPV of doing nothing) and accept the project if its NPV is positive.

Consider a take-it-or-leave-it investment decision involving a single, stand-alone project for Fredrick’s Feed and Farm (FFF).
The project costs $250 million and is expected to generate cash flows of $35 million per year, starting at the end of the first year and lasting forever.

The NPV of the project is calculated as:
NPV = -250 +35/r
The NPV is dependent on the discount rate.

You are considering opening a new plant. The plant will cost $100 million upfront. After that, it is expected to produce profits of $30 million at the end of every year. The cash flows are expected to last forever. Calculate the NPV of this investment opportunity if your cost of capital is 8%. Should you make the investment?

Solution:

NPV = –100 + 30/8% = $275 million.
Yes, make the investment.

Your firm is considering the launch of a new product, the XJ5. The upfront development cost is $10 million, and you expect to earn a cash flow of $3 million per year for the next five years. Plot the NPV profile for this project for discount rates of 0%, 5%, 10%, 15%, 20%, 25%, and 30%. For what range of discount rates is the project attractive?

Sometimes alternative investment rules may give the same answer as the NPV rule, but at other times they may disagree.
When the rules conflict, the NPV decision rule should be followed.

Internal Rate of Return (IRR) Investment Rule
Take any investment where the IRR exceeds the cost of capital. Turn down any investment whose IRR is less than the cost of capital.

The IRR Investment Rule will give the same answer as the NPV rule in many, but not all, situations.
In general, the IRR rule works for a stand-alone project if all of the project’s negative cash flows precede its positive cash flows.
In Figure 7.1, whenever the cost of capital is below the IRR of 14%, the project has a positive NPV, and you should undertake the investment.

You are considering investing in a start-up company. The founder asked you for $200,000 today and you expect to get $1,000,000 in nine years. Given the riskiness of the investment opportunity, your cost of capital is 20%. What is the NPV of the investment opportunity? Should you undertake the investment opportunity?
Calculate the IRR and use it to determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged.

Solution
NPV= (1,000,000/1.2^9) - 200,000 =
IRR= (1000000/200000)^1/9 -1
Do not take the project.
A drop in the cost of capital of just 20 – 19.58 = 0.42% would change the decision.

OpenSeas, Inc. is evaluating the purchase of a new cruise ship. The ship would cost $500 million, and would operate for 20 years. OpenSeas expects annual cash flows from operating the ship to be $70 million (at the end of each year) and its cost of capital is 12%.
a. Calculate NPV.
b. Calculate the IRR.
c. Is the purchase attractive based on these estimates?
d. How far off could OpenSeas’ cost of capital be before your purchase decision would change?

NPV= -500 + 70/0,12 (1 - 1/(1 + 0,12)^20)
discount rate could be off by 0,72 before the investment decision would change

In other cases, the IRR rule may disagree with the NPV rule and thus be incorrect.
Situations where the IRR rule and NPV rule may be in conflict:
Delayed Investments
Nonexistent IRR
Multiple IRRs

Pitfall 1: Delayed Investments
Assume you have just retired as the CEO of a successful company. A major publisher has offered you a book deal. The publisher will pay you $1 million upfront if you agree to write a book about your experiences. You estimate that it will take three years to write the book. The time you spend writing will cause you to give up speaking engagements amounting to $500,000 per year. You estimate your opportunity cost to be 10%.

Pitfall 1: Delayed Investments
Should you accept the deal?
Calculate the IRR.
The IRR is greater than the cost of capital. Thus, the IRR rule indicates you should accept the deal.

Pitfall 1: Delayed Investments
Should you accept the deal?
Since the NPV is negative, the NPV rule indicates you should reject the deal.

1000000 - (500000/1,1^1) - (500000/1,1^2) - ...

When the benefits of an investment occur before the costs, the NPV is an increasing function of the discount rate.

Pitfall 2: Multiple IRRs
Suppose Star informs the publisher that it needs to sweeten the deal before he will accept it. The publisher offers $550,000 advance and $1,000,000 in four years when the book is published.
Should he accept or reject the new offer?

Pitfall 2: Multiple IRRs
The cash flows would now look like
The NPV is calculated as

formula = 550000 - 500000/1+r - 500000/(1+r)^2 ...

Pitfall 2: Multiple IRRs
By setting the NPV equal to zero and solving for r, we find the IRR. In this case, there are two IRRs: 7.164% and 33.673%. Because there is more than one IRR, the IRR rule cannot be applied.

Pitfall 2: Multiple IRRs
Between 7.164% and 33.673%, the book deal has a negative NPV. Since your opportunity cost of capital is 10%, you should reject the deal.

Pitfall 3: Nonexistent IRR
Finally, Star is able to get the publisher to increase his advance to $750,000, in addition to the $1 million when the book is published in four years. With these cash flows, no IRR exists; there is no discount rate that makes NPV equal to zero.

No IRR exists because the NPV is positive for all values of the discount rate. Thus the IRR rule cannot be used.

IRR Versus the IRR Rule
While the IRR rule has shortcomings for making investment decisions, the IRR itself remains useful. IRR measures the average return of the investment and the sensitivity of the NPV to any estimation error in the cost of capital.

The payback period is amount of time it takes to recover or pay back the initial investment. If the payback period is less than a pre-specified length of time, you accept the project. Otherwise, you reject the project.
The payback rule is used by many companies because of its simplicity.

Consider a take-it-or-leave-it investment decision involving a single, stand-alone project for Fredrick’s Feed and Farm (FFF). The project costs $250 million and is expected to generate cash flows of $35 million per year, starting at the end of the first year and lasting forever.

Problem
Projects A, B, and C each have an expected life of five years.
Given the initial cost and annual cash flow information below, what is the payback period for each project?
cost / cash flow

Pitfalls
Ignores the project’s cost of capital and time value of money.
Ignores cash flows after the payback period.
Relies on an ad hoc decision criterion.

Mutually Exclusive Projects
When you must choose only one project among several possible projects, the choice is mutually exclusive.
NPV Rule
Select the project with the highest NPV.
IRR Rule
Selecting the project with the highest IRR may lead to mistakes.

Mutually exclusive investments
Because the IRR is a measure of the expected return of investing in the project, you might be tempted to extend the IRR investment rule to the case of mutually exclusive projects by picking the project with the highest IRR.
Unfortunately, picking one project over another simply because it has a larger IRR can lead to mistakes.
In particular, when projects differ in their scale of investment, the timing of their cash flows, or their riskiness, then their IRRs cannot be meaningfully compared.

If a project’s size is doubled, its NPV will double. This is not the case with IRR. Thus, the IRR rule cannot be used to compare projects of different scales.

Another problem with the IRR is that it can be affected by changing the timing of the cash flows, even when the scale is the same.
IRR is a return, but the dollar value of earning a given return depends on how long the return is earned.
Consider again the coffee shop and the music store investment in Example 7.3. Both have the same initial scale and the same horizon. The coffee shop has a lower IRR, but a higher NPV because of its higher growth rate.

An IRR that is attractive for a safe project need not be attractive for a riskier project.
Consider the investment in the electronics store from Example 7.3. The IRR is higher than those of the other investment opportunities, yet the NPV is the lowest.
The higher cost of capital means a higher IRR is necessary to make the project attractive.

Incremental IRR Investment Rule
Apply the IRR rule to the difference between the cash flows of the two mutually exclusive alternatives (the increment to the cash flows of one investment over the other).

In Example7.4, we can see that despite its lower IRR, the major overhaul has a higher NPV at the cost of capital of 12%. Note also that the incremental IRR of 20% determines the crossover point or discount rate at which the optimal decision changes.

Shortcomings of the Incremental IRR Rule
The incremental IRR may not exist.
Multiple incremental IRRs could exist.
The fact that the IRR exceeds the cost of capital for both projects does not imply that either project has a positive NPV.
When individual projects have different costs of capital, it is not obvious which cost of capital the incremental IRR should be compared to.

Evaluation of Projects with Different Resource Constraints
Consider three possible projects with a $100 million budget constraint:
Table 7.1 Possible Projects for a $100 Million Budget

The profitability index can be used to identify the optimal combination of projects to undertake.

Profitability index= value created/resource consumed = NPV / resource consumed

From Table 7.1, we can see it is better to take projects II & III together and forgo project I.

In some situations the profitability Index does not give an accurate answer.
Suppose in Example 7.4 that NetIt has an additional small project with a NPV of only $120,000 that requires three engineers. The profitability index in this case is 0.1 2/ 3 = 0.04, so this project would appear at the bottom of the ranking. However, 3 of the 190 employees are not being used after the first four projects are selected. As a result, it would make sense to take on this project even though it would be ranked last.

With multiple resource constraints, the profitability index can break down completely.



[ Langue: fr - Auteur: lt (sup) ]

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