Citibank: basic of corporate finance
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5-20 INTRODUCTION TO CAPITAL BUDGETING
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Profitability Index (PI)
Cash inflow
PV / Cash
outflow PV
Another common tool for making investment decisions is the
profitability index (PI). The PI is the ratio between the present
value of the cash inflows and the present value of the cash
outflows. The formula is:
PI = PV / PV
CO
Where:
PI = Profitability index of an investment
PV = Present value of the cash inflows generated by the
investment
PV
CO
= Present value of the cash outflows required by the investment
If there is only one cash outflow at the beginning of the investment
(CF
0
), the formula may be expressed as:
PI = PV / CF
0
Example
For example, if an investment generates discounted cash flows of
$3,500 and requires an investment of $2,500, what is the
profitability index of the investment?
PI = PV / CF
0
PI = $3,500 / $2,500
PI = 1.40
PI greater than
one is
acceptable
An investment with a profitability index greater than one creates
shareholder value and should be considered. Investments with PIs less
than one should not be accepted. You can probably see the relationship
between the NPV and the PI – both methods use the same information.
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Often a company will analyze several possible projects and rank the
projects according to their profitability indices. This information
tells the analyst which investment will give the company the most
return for its investment. In an ideal world, all projects with PIs
greater than one would be accepted. However, limited funds and
resources require most companies to choose the most profitable
investment opportunities.
Can't compare
projects of
different size
The weakness of PI is that it cannot measure the investment value for
projects of differing sizes. This concern is especially important when
considering mutually exclusive projects – the acceptance of one
project may not allow for the acceptance of any other projects.
Example
For example, consider a $20 million dollar project with a profitability
index of 1.3 and an $8 million project with a PI of 1.5. If the company
had only $25 million with which to invest in projects, a decision based
only on PI would indicate the company should invest in the $8 million
project. However, due to its size, the $20 million dollar project would
actually create more value for shareholders.
Practice what you have learned about calculating the internal rate of return, the payback
period, and the profitability index of an investment by completing the Practice Exercise
that begins on page 5-23; then continue to the "Unit Summary" and "Progress Checks."
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PRACTICE EXERCISE 5.3
Directions: Calculate the answer to each question, then enter the correct answer.
Check your solution with the Answer Key on the next page.
6. An investment generates the following cash flows:
Year 1 $10,000
Year 2 $12,000
Year 3 $13,000
Year 4 $14,000
Year 5 $14,000
If the investment requires an initial cash flow of $35,000 and the investor's
required rate of return is 12%, what is the NPV of the project?
$_____________________
What is the profitability index of the project?
_____________________
Should the investment be accepted using the profitability index method of capital
budgeting?
_____a) Yes
_____b) No
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ANSWER KEY
6. An investment generates the following cash flows:
Year 1 $10,000
Year 2 $12,000
Year 3 $13,000
Year 4 $14,000
Year 5 $14,000
If the investment requires an initial cash flow of $35,000 and the investor's
required rate of return is 12%, what is the NPV of the project?
$9,589.27
Enter -$35,000 as CF
0
and the other cash flows as listed in the table.
Enter 12% as the discount rate.
Press the NPV key and you should get $9,589.27.
What is the profitability index of the project?
1.274
Calculate the PV of the cash flows – you should get $44,589.27.
You could also take the NPV you calculated in the last problem
and add back the initial investment of $35,000 to arrive at the
present value of the future cash flows.
PI = PV / CF
0
PI = $44,589.27 / 35,000
PI = 1.274
Should the investment be accepted using the profitability index method of capital
budgeting?
Yes – The investment should be accepted, because the PI is
greater than one.
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PRACTICE EXERCISE
(Continued)
7. What is the IRR of an investment paying $4,000 annually for three years when the
initial investment is $10,000?
_________%
8. Compute the payback period for the following cash flows, assuming an initial
investment of $40,000.
Year 1 $10,000
Year 2 $14,000
Year 3 $18,000
Year 4 $22,000
Year 5 $25,000
_____________________
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ANSWER KEY
7. What is the IRR of an investment paying $4,000 annually for three years when the
initial investment is $10,000?
9.7%
Enter -$10,000 as CF
0
and three cash flows of $4,000.
Press the IRR key and you should get 9.7%.
8. Compute the payback period for the following cash flows, assuming an initial
investment of $40,000.
2 years, 46 weeks
After 2 years: $10,000 + $14,000 = $24,000
3rd year: $40,000 - $24,000 = $16,000
The initial investment was $40,000; we need to figure out how
much of Year Three's cash flow is needed to reach $40,000.
$16,000 / $18,000 = 0.88888
0.88888 of Year Three's cash flow is needed.
0.88888 x 52 weeks = 46 weeks
2 years and 46 weeks is the payback period.
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UNIT SUMMARY
In this unit we have looked at some methodologies for making
capital budgeting decisions. Analysts use these techniques to
evaluate and select the best investment alternatives in order to
maximize shareholders' equity.
Nominal vs.
effective rates
Securities that pay interest more frequently than annually have a stated
interest rate that may differ from the rate that is actually earned from
the investment. The stated rate is referred to as the nominal rate, while
the actual interest earned translates into the effective rate. The nominal
rate includes an adjustment to the real interest rate to account for the
rate of inflation.
Net present
value
The net present value of an investment is the sum of all the discounted
cash flows minus the original investment.
T
NPV = Σ CF
t
[1 / (1 + R)]
t
– CF
0
t = 1
A positive NPV means that the investor paid less than the present
value for the stream of cash flows. A negative NPV means that the
investor paid more than the present value.
Internal rate of
return
The internal rate of return is the actual rate of return that is earned
on an investment. The objective of this methodology is to find the
discount rate (required rate of return) that will equate the present value
of the cash flows with the amount of the original investment.
T
O = Σ CF
t
[1 / (1 + R)]
t
– CF
0
t = 1
Inflation
The amount of cash inflows and outflows may change as a result of
inflation. Therefore, inflation should be considered when calculating
the NPV and the IRR.
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Payback period
The payback period is the length of time it takes to recover the initial
investment in a project. Some companies set a hurdle time for a
project and will invest only if the payback will occur within that time
frame.
Profitability
index
The ratio between the present value of cash inflows and the present
value of cash outflows is the profitability index (PI) of a project.
PI = PV / PV
CO
Comparing projects according to the size of return on investment is a
good indicator of where to invest – as long as all projects in the
comparison are approximately the same size.
You have completed Unit Five: Introduction to Capital Budgeting. Please complete
Progress Check 5 that begins on the next page to check your understanding of the
concepts presented in this unit. If you answer any questions incorrectly, we suggest that
you return to the text and review the appropriate section before continuing to Unit Six:
Corporate Valuation – Risk.
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4 PROGRESS CHECK 5
Directions: Select the one best answer for each question. Check your responses with
the Answer Key on the next page.
1. If an analyst compares the net present value of several projects, s/he will know which
project:
_____a) will yield the most profit.
_____b) has cash flows that will exceed the initial investment by the greatest
amount.
_____c) will recover the initial investment by the hurdle date.
_____d) will yield a return on investment equal to the hurdle rate.
2. An investor with a one-year bond is interested in the number of compounding periods
in the year because:
_____a) if the effective interest rate is compounded more frequently than on an
annual basis, the nominal interest rate will exceed the quoted interest
rate.
_____b) the present value of the bond equals the face value plus the compounded
quoted interest rate.
_____c) the nominal rate is a floating rate that may change from period to
period.
_____d) the more frequently the nominal interest rate is compounded, the
greater will be the effective interest rate.
3. If the internal rate of return (IRR) of a project is 35% and the hurdle rate is 42%, then:
_____a) the project should be considered. The hurdle rate includes a percentage
for risk, and anything below it is less risky.
_____b) the profit is 7%.
_____c) the project should be rejected because it will reduce the shareholder's
value.
_____d) we calculate the cost of funds before making an "invest / don't invest"
decision.
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