Contents
Time Value of Money
Annuities
Perpetuities
Kinds of Interest Rates
Future Value of an Uneven Cash flow
Probability Distribution
Standard Deviation
CAPM
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The Balance Sheet
Capital Budgeting
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Capital Budgeting

Payback, Discounted Payback, NPV, Profitability Index, IRR and MIRR are all capital budgeting decision methods.


Cash Flow- We are going to assume that the project we are considering approving has the following cash flow. Right now, in year zero we will spend 15,000 dollars on the project. Then for 5 years we will get money back as shown below.

Year Cash flow
0 -15,000
1 +7,000
2 +6,000
3 +3,000
4 +2,000
5 +1,000

Payback - When exactly do we get our money back, when does our project break even. Figuring this is easy. Take your calculator.

Year Cash flow Running Total  
0 -15,000 -15,000  
1 +7,000 -8,000 (so after the 1st year, the project has not yet broken even)
2 +6,000 -2,000 (so after the 2nd year, the project has not yet broken even)
3 +3,000 +1,000 (so the project breaks even sometime in the 3rd year)

But when, exactly? Well, at the beginning of the year we had still had a -2,000 balance, right? So do this.

Negative Balance / Cash flow from the Break Even Year = When in the final year we break even
-2,000 / 3,000 = .666

So we broke even 2/3 of the way through the 3rd year. So the total time required to payback the money we borrowed was 2.66 years.

Discounted Payback - is almost the same as payback, but before you figure it, you first discount your cash flows. You reduce the future payments by your cost of capital. Why? Because it is money you will get in the future, and will be less valuable than money today. (See Time Value of Money if you don't understand). For this example, let's say the cost of capital is 10%.

Year Cash flow Discounted Cash flow Running Total
0 -15,000 -15,000 -15,000
1 7,000 6,363 -8,637
2 6,000 4,959 -3,678
3 3,000 2,254 -1,424
4 2,000 1,366 -58
5 1,000 621 563

So we break even sometime in the 5th year. When?

Negative Balance / Cash flow from the Break Even Year = When in the final year we break even
-58 / 621 = .093

So using the Discounted Payback Method we break even after 4.093 years.


Net Present Value (NPV) - Once you understand discounted payback, NPV is so easy! NPV is the final running total number. That's it. In the example above the NPV is 563. That's all. You're done, baby. Basically NPV and Discounted Payback are the same idea, with slightly different answers. Discounted Payback is a period of time, and NPV is the final dollar amount you get by adding all the discounted cash flows together. If the NPV is positive, then approve the project. It shows that you are making more money on the investment than you are spending on your cost of capital. If NPV is negative, then do not approve the project because you are paying more in interest on the borrowed money than you are making from the project.

Profitability Index

Profitability Index equals NPV divided by Total Investment plus 1
PI = 563 / 15,000 + 1

So in our example, the PI = 1.0375. For every dollar borrowed and invested we get back $1.0375, or one dollar and 3 and one third cents. This profit is above and beyond our cost of capital.

Internal Rate of Return - IRR is the amount of profit you get by investing in a certain project. It is a percentage. An IRR of 10% means you make 10% profit per year on the money invested in the project. To determine the IRR, you need your good buddy, the financial calculator.

Year Cash flow
0 -15,000
1 +7,000
2 +6,000
3 +3,000
4 +2,000
5 +1,000

Enter these numbers and press these buttons.

-15000 g CFo
7000 g CFj
6000 g CFj
3000 g CFj
2000 g CFj
1000 g CFj
f IRR

After you enter these numbers the calculator will entertain you by blinking for a few seconds as it determines the IRR, in this case 12.02%. It's fun, isn't it!

Ah, yes, but there are problems.

  • Sometimes it gets confusing putting all the numbers in, especially if you have alternate between a lot of negative and positive numbers.
  • IRR assumes that the all cash flows from the project are invested back into the project. Sometimes, that simply isn't possible. Let's say you have a sailboat that you give rides on, and you charge people money for it. Well you have a large initial expense (the cost of the boat) but after that, you have almost no expenses, so there is no way to re-invest the money back into the project. Fortunately for you, there is the MIRR.

Modified Internal Rate of Return - MIRR - Is basically the same as the IRR, except it assumes that the revenue (cash flows) from the project are reinvested back into the company, and are compounded by the company's cost of capital, but are not directly invested back into the project from which they came.

WHAT?

OK, MIRR assumes that the revenue is not invested back into the same project, but is put back into the general "money fund" for the company, where it earns interest. We don't know exactly how much interest it will earn, so we use the company's cost of capital as a good guess.

Why use the Cost of Capital?

Because we know the company wouldn't do a project which earned profits below the cost of capital. That would be stupid. The company would lose money. Hopefully the company would do projects which earn much more than the cost of capital, but, to play it safe, we just use the cost of capital instead. (We also use this number because sometimes the cash flows in some years might be negative, and we would need to 'borrow'. That would be done at our cost of capital.)



How to get MIRR - OK, we've got these cash flows coming in, right? The money is going to be invested back into the company, and we assume it will then get at least the company's-cost-of-capital's interest on it. So we have to figure out the
future value (not the present value) of the sum of all the cash flows. This, by the way is called the Terminal Value. Assume, again, that the company's cost of capital is 10%. Here goes...

Cash Flow Times   = Future Value
of that years cash flow.
Note
7000 X (1+.1) 4 = 10249 compounded for 4 years
6000 X (1+.1) 3 = 7986 compounded for 3 years
3000 X (1+.1) 2 = 3630 compounded for 2 years
2000 X (1+.1) 1 = 2200 compounded for 1 years
1000 X (1+.1)0 = 1000 not compounded at all because
this is the final cash flow
TOTAL     = 25065 this is the Terminal Value

OK, now get our your financial calculator again. Do this.

-15000 g CFo
0 g CFj
0 g CFj
0 g CFj
0 g CFj
25065 g CFj
f IRR

Why all those zeros? Because the calculator needs to know how many years go by. But you don't enter the money from the sum of the cash flows until the end, until the last year. Is MIRR kind of weird? Yep. You have to understand that the cash flows are received from the project, and then get used by the company, and increase because the company makes profit on them, and then, in the end, all that money gets 'credited' back to the project. Anyhow, the final MIRR is 10.81%.

Decision Time- Do we approve the project? Well, let's review.

Decision Method Result Approve? Why?
Payback 2.66 years Yes well, cause we get our money back
Discounted Payback 4.195 years Yes because we get our money back, even after discounting our cost of capital.
NPV $500 Yes because NPV is positive (reject the project if NPV is negative)
Profitability Index 1.003 Yes cause we make money
IRR 12.02% Yes because the IRR is more than the cost of capital
MIRR 10.81% Yes because the MIRR is more than the cost of capital









About the author

Mark McCracken

Author: Mark McCracken is a corporate trainer and author living in Higashi Osaka, Japan. He is the author of thousands of online articles as well as the Business English textbook, "25 Business Skills in English".

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Mark McCracken , All Rights Reserved