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..
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? Depends on the moment the payments are made. If they are made
continuously:
Negative Balance / Cash flow from the Break Even
Year
=
-2,000 / 3,000 =
When in the final year we break
even
.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.
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 (continuous
payment)
Net Present Value (NPV) - NPV is the final running total number. 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 -. It is a percentage, but NOT a simple rate of return!!
Year Cash flow

0
-15,000
1
+7,000
2
+6,000
3
+3,000
4
+2,000
5
+1,000
.
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. 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. 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 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%.
Cash Flow Times
=
Future Value
Note
of that years cash flow.
7000 X
(1+.1) 4 =
10249 compounded for 4 years
6000 X
(1+.1) 3 =
7986 compounded for 3 years
(1+.1)
2
=
3630 compounded for 2 years
2000 X
(1+.1)
1
=
2200 compounded for 1 years
1000 X
(1+.1)0 =
3000 X
TOTAL
1000
=
not compounded at all because
this is the final cash flow
25065 this is the Terminal Value
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