Please show formula

This case deals with the capital budgeting techniques of Net Present Value (i.e. NPV) and Internal Rate of Return (i.e. IRR). In this case, students will compare two mutually exclusive projects using NPV and IRR, and choose the best project. They will learn about NPV and IRR methods and their advantages and disadvantages. Students will also learn the weakness of the IRR method when comparing two or more projects. Finally, they will evaluate the two projects assuming that the projects are independent projects rather than mutually exclusive ones. This is a hands-on experience for students who want to delve into project valuation.

Introduction

After graduating from an MBA Program on the East Coast, Michael Strahan had started working

for a mining company. His company is evaluating two projects: One of them requires a smaller

investment, and then will create a big, positive cash flow in the first year; and then smaller cash

flows after that. The second project is a relatively bigger project. It will require a larger cash

flow at the beginning, and then will bring in a relatively small cash flow in the first year. But,

this second project will create much larger cash flows in the years after that.

Michael has been given the task of evaluating these two projects and choosing the best one for

his company. Initially he thought that this would be an easy task for him. He would just try to

accurately predict the cash flows from the two projects and then evaluate them using some of the

capital budgeting techniques that he had learned when he was at school.

He visits Elizabeth, one of his colleagues, in order to clarify some issues that come to his mind.

Liz he said, I am tasked with evaluating two projects and then choosing the best one for our

company. I am really excited because it seems like this decision will have a big impact on our

companys bottom line. Could you help me a little bit?

Elizabeth has been working for the company for more than five years. She sure wants to help his

colleague. She says Sure, I can help you. Exactly what do you want to learn?

Michael sighs Elizabeth, when evaluating these two projects, I think I need to use some of the

capital budgeting techniques that we had learned at school. For example, we had Net Present

Value, Internal Rate of Return, Payback Period, and others. I am not sure which of these methods

to use.

Elizabeth responds I read somewhere that NPV and IRR are the most commonly used methods

to evaluate a project. The Payback Period has lots of disadvantages, so you shouldnt use that

one for sure.

Michael responds I dont know what the advantages and the disadvantages of each of these

methods. I guess, first, I need to get more information about them. But, if I remember correctly,

the Payback Period ignores the time value of money, so it is not good.

Elizabeth says And it also ignores the cash flows that come after the payback period. In other

words, if there is a very big positive cash flow that is expected to come sometime in the future,

the Payback method ignores that. So, it is kind of weak. There are also other weaknesses with

that method.

She adds IRR also has some weaknesses. I dont remember them, but you need to research. You

dont want to do something wrong here.

Michael responds I have read on the web that IRR has two main weaknesses. So, I guess I need

to learn about those weaknesses.

Thanks Liz for offering help. I am now starting to work on it. I think I will see you a few times

in the coming days!

Elizabeth responds No problem. I am here for help, 24/7.

NPV and IRR

Michaels boss told him that these are mutually exclusive projects (meaning that the company

will accept only one of them). Michael thought that going over some of his class notes may

refresh his memory. After scrambling through his notes, he noticed that he skipped the lecture

where the professor explained capital budgeting techniques. No problem he thought. I can

search the web to find some information on these so called mutually exclusive projects.

Michael has found some explanations for NPV and IRR on the internet. Michael finds a straightforward explanation of Net Present Value: The difference between the present value of the future cash flows from an investment and the amount of investment. Present value of the expected cash flows is computed by discounting them at the required rate of return.

The same source explains IRR as follows: commonly used as an NPV alternative. Calculations of IRR rely on the same formula as NPV does, except with slight adjustments. IRR calculations assume a neutral NPV (a value of zero) and one instead solves for the discount rate. The discount rate of an investment when NPV is zero is the investments IRR, essentially representing the projected rate of growth for that investment. Because IRR is necessarily annual it allows for the simplified comparison of a wide variety of types and lengths of investments.

The Decision

Michael has requested some help in estimating the

The expected cash flows for the two are:

Yr. Project 1 Project 2

0 - $20 million -$30 million (Initial cash outlay for each project)

1 + $12 million +$5 million

2 + $8 million +15 million

3 + $5 million +20 million

He knows that for similar projects, his company has a required return of 12%, and a cost of capital of 10% so he decides to use the 12% required rate of return in his calculations.

To impress his boss, he wants to do a detailed analysis. He wants to answer all of the following

questions:

1. He decides to use the IRR method first. He wants to see which project is better according

to the IRRs. Which project is the best using IRR?

2. Is IRR an acceptable method to compare two mutually exclusive projects?

3. Is NPV an acceptable method when comparing two mutually exclusive projects?

4. Later, he visits one of his colleagues and talks about his findings. His colleague

recommends him to check the NPVs also. He says O.K. Why not? Confirming my findings with the other method would be nice. What does he find? Do NPVs confirm his earlier findings?

5. Are both methods (i.e. NPV and IRR) good in these situations? What would you do?

According to your opinion, which project is better for this company?

6. Does IRR always choose the same project whether a firm has a high cost of capital or a

low cost of capital?

7. How about NPV? Does NPV always choose the same project whether a firm has a high

cost of capital or a low cost of capital?

8. Michael finds his results confusing so he decides to prepare the NPV Profiles for the two projects.

9. According to the NPV Profiles of the two projects, at which discount rate are these two projects equivalent?

10. Over what range of discount rates should we choose Project A? Project B?

11. If they were independent projects rather than mutually exclusive projects, what would we

do?