1. Chapter 9 Net Present Value and Other Investment Criteria
T9.1 Chapter Outline
Chapter 9 Net Present Value and Other Investment Criteria
Chapter Organization
9.1 Net Present Value
9.2 The Payback Rule
9.3 The Average Accounting Return
9.4 The Internal Rate of Return
9.5 The Profitability Index
9.6 The Practice of Capital Budgeting
9.7 Summary and Conclusions
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Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd.

2. Capital Budgeting
In Chapter 1 we defined capital budgeting as ‘the process of planning and managing a firm’s investment in fixed assets’
...probably the most or at least one of the most important issues in corporate finance.
Identifying investment opportunities which offer more value to the firm than their cost - the value of the future cash flows need to be greater than the investment required
estimating the size, timing and risk of future cash flows is the most challenging aspect of capital budgeting

3. Average Accounting Return - AAR
Investment Criteria
NPV - Net Present Value
the difference between an investment’s market value and its cost
Payback -
the length of time it takes to recover the initial investment
Discounted Payback
the length of time required for an investment’s discounted cash flows to equal its initial cost
Average Accounting Return - AAR
an investment’s average net income divided by its average book value
Internal Rate of Return
the discount rate that makes the NPV of an investment equal to zero

4. Investment Critieria cont’d
The Profitability Index- “PI’
‘The present value of an investment’s future cash flows divided by its initial cost
- also known as the benefit/cost or cost/benefit ratio

5. Assume you have the following information on Project X:
NPV Illustrated
Estimate future cash flows, calculate the PV of these cash flows and then compare to cost of project to arrive at NPV
Assume you have the following information on Project X:
Initial outlay -$1,100 Required return = 10%
Annual cash revenues and expenses are as follows:
Year Revenues Expenses
$1, $500
, ,000
Draw a time line and compute the NPV of project X.

6. NPV Illustrated (concluded)1 2
Initial outlay
($1,100)
Revenues $1,000
Expenses 500
Cash flow $500
Revenues $2,000
Expenses 1,000
Cash flow $1,000
– $1,100.00
+$181.00 1
$500 x
1.10 1
$1,000 x
1.10 2
NPV

7. Underpinnings of the NPV Rule
The foundation of the NPV approach:
The market value of the firm is based on the present value of the cash flows it is expected to generate;
Additional investments are “good” if the present value of the incremental expected cash flows exceeds their cost;
Thus, “good” projects are those which increase firm value - or, put another way, good projects are those projects that have positive NPVs!
Conclusion - Invest only in projects with positive NPV’s.

8. Net Present Value Profile
120
Year Cash flow
0 – $275
1 100
2 100
3 100
4 100
100 80 60 40 20
– 20
– 40
Discount rate 2% 6%
10%
14%
18%
22%
IRR

10. ‘length of time it takes to recover the initial investment’
Payback Rule
‘length of time it takes to recover the initial investment’
how long does the investment take before I recover my initial investment? - a break-even in an accounting sense but not in an economic sense
The Payback ‘Rule’ - an investment is considered acceptable if the payback is less than some pre specified time frame
shortcomings of the payback rule vs the NPV
ignores time value of money - simply adds up future cash flows
ignores risk differences - payback is calculated the same way for projects that are risky and ‘safe’ projects
determining the cut-off - what should the payback be??
Ignores the cash flows beyond the payback cut-off

11. Payback Rule Illustrated
Initial outlay -$1,000
Year Cash flow
1 $200
2 400
3 600
Accumulated
2 600
3 1,200
Payback period = 2 2/3 years

12. Payback - Incremental Well Case
Payback occurs after year 1
- about 1 year and two months

13. What are its shortcomings?
Discounted Payback
The same basic concept in how long does it take to recover the original investment but in this case the future cash flows are discounted.
‘the length of time it takes for an investment’s discounted cash flows to equal its initial cost.’
break-even in an economic sense – time value of money is considered
What are its shortcomings?
Cash flows beyond the cut-off point are ignored
the cut-off point still has to be arbitrarily established

14. Discounted Payback Illustrated
Initial outlay -$1,000
R = 10%
PV of
Year Cash flow Cash flow
1 $ $ 182
Accumulated
Year discounted cash flow
1 $ 182
2 513
3 1,039
4 1,244
Discounted payback period is just under 3 years

15. Ordinary and Discounted Payback (Table 9.3)
Cash Flow Accumulated Cash Flow
Year Undiscounted Discounted Undiscounted Discounted
1 $100 $89 $100 $89

16. Discounted Payback - Incremental Well Case
Using discounted cash
flows - payback takes
a few months longer

17. Average Accounting Return
‘An investment’s average net income divided by its average book value’ or
‘Some measure of average accounting profit/some measure of average accounting value’
....’a project is acceptable if its average accounting return exceeds a target average accounting return
Advantages
easy to calculate
readily available accounting information
What are its shortcomings?
Ignores time value of money - the average return does not differentiate between near term returns vs. Returns in the distant future
focuses on net income and book value instead of cash flow and market value

18. Average Accounting Return Illustrated
Average net income:
Year
Sales $440 $240 $160
Costs
Gross profit
Depreciation
Earnings before taxes
Taxes (25%)
Net income $105 $30 $0
Average net income = ($ )/3 = $45

19. Average Accounting Return Illustrated (concluded)
Average book value:
Initial investment = $240
Average investment = ($ )/2 = $120
(assuming st. line depreciation)
Average accounting return (AAR):
Average net income $45
AAR = = = 37.5%
Average book value $120

20. Return on Capital Employed/investment
Return on Capital Employed - (ROCE)
Ratio at a particular point in time
Earnings plus after tax interest on long term debt/average capital employed
Capital employed is total equity plus total long term debt including the current portion of long term debt
Return on Investment - (ROI)
similar to the ‘average accounting return’ -
average book value is the average investment

21. Internal Rate of Return or ‘IRR’
‘the discount rate that makes the NPV of an investment equal to zero’
- sometimes called the discounted cash flow or ‘DCF return’
The IRR ‘rule’ suggest that an investment is acceptable if the IRR exceeds the required return.
A viable alternative to the NPV model
Used extensively in practice - provides a return figure when analyzing investments as opposed to a $ figure
more difficult to calculate - requires trial and error

22. Internal Rate of Return Illustrated
Initial outlay = -$200
Year Cash flow
1 $ 50
2 100
3 150
Find the IRR such that NPV = 0
0 =
(1+IRR) (1+IRR) (1+IRR)3
200 =
(1+IRR) (1+IRR) (1+IRR)3

23. Internal Rate of Return Illustrated (concluded)
Trial and Error
Discount rates NPV
0% $100
5% 68
10% 41
15% 18
20% -2
IRR is just under 20% -- about 19.44%

24. Net Present Value Profile
120
Year Cash flow
0 – $275
1 100
2 100
3 100
4 100
100 80 60 40 20
– 20
– 40
Discount rate 2% 6%
10%
14%
18%
22%
IRR

25. IRR - Incremental Well Case
IRR for this incremental well
project is 63% - the discount
rate where the NPV is zero

26. Internal Rate of Return
What are the shortcomings of the IRR approach?
Non -conventional cash flows make the calculation much more difficult
Mutually exclusive Investments - meaning we can accept one project but not another that is under consideration

27. Multiple Rates of Return – a shortcoming
Assume you are considering a project for which the cash flows are as follows:
Year Cash flows
$252
,431
,035
,850
,000

28. Multiple Rates of Return (continued)
What’s the IRR? Find the rate at which the computed NPV = 0:
at 25.00%: NPV = _______
at 33.33%: NPV = _______
at 42.86%: NPV = _______
at 66.67%: NPV = _______

29. Multiple Rates of Return (continued)
What’s the IRR? Find the rate at which the computed NPV = 0:
at 25.00%: NPV =
at 33.33%: NPV =
at 42.86%: NPV =
at 66.67%: NPV =
Two questions:
1. What’s going on here?
2. How many IRRs can there be?

30. Multiple Rates of Return (concluded)
NPV
$0.06
$0.04
IRR = 1/4
$0.02
$0.00
($0.02)
IRR = 1/3
IRR = 2/3
IRR = 3/7
($0.04)
($0.06)
($0.08)
0.2
0.28
0.36
0.44
0.52
0.6
0.68
Discount rate

31. IRR, NPV, and Mutually Exclusive Projects
Net present value
Year
Project A: – $
Project B: – $
160
140
120
100 80 60 40
Crossover Point 20
– 20
– 40
– 60
– 80
– 100
Discount rate 2% 6%
10%
14%
18%
22%
26%
IRR A IRR B

32. Profitability Index - ‘PI’
‘The present value of an investment’s future cash flows divided by its initial cost’
measures ‘bang for the buck’ or the value created per dollar invested
Shortcomings
does not recognize total market value added (as does the NPV approach) - thus when comparing mutually exclusive investments it can lead to incorrect decisions

33. Profitability Index Illustrated
Now let’s go back to the initial example - we assumed the following information on Project X:
Initial outlay -$1,100 Required return = 10%
Annual cash benefits:
Year Cash flows
1 $ 500
,000
What’s the Profitability Index (PI)?

34. Profitability Index Illustrated (concluded)
Previously we found that the NPV of Project X is equal to:
($ ) - 1,100 = $1, ,100 = $
The PI = PV inflows/PV outlay = $1,281.00/1,100 =
This is a good project according to the PI rule……It’s a good project because the present value of the inflows exceeds the outlay.

35. Profitability Index- Incremental Well Case
What is the Profitablity Index if the firm has
a required rate of return of 15%?
PV of cash inflows at 15% = $694,442
$694,442/$300,000 = 2.31
....for every $1 invested, the project is returning $2.31
....a healthy return!!

36. Summary of Investment Criteria
I. Discounted cash flow criteria
A. Net present value (NPV). The NPV of an investment is the difference between its market value and its cost. The NPV rule is to take a project if its NPV is positive. NPV has no serious flaws; it is the preferred decision criterion.
B. Internal rate of return (IRR). The IRR is the discount rate that makes the estimated NPV of an investment equal to zero. The IRR rule is to take a project when its IRR exceeds the required return. When project cash flows are not conventional, there may be no IRR or there may be more than one.
C. Profitability index (PI). The PI, also called the benefit-cost ratio, is the ratio of present value to cost. The profitability index rule is to take an investment if the index exceeds 1.0. The PI measures the present value per dollar invested.

37. Summary of Investment Criteria (concluded)
II. Payback criteria
A. Payback period. The payback period is the length of time until the sum of an investment’s cash flows equals its cost. The payback period rule is to take a project if its payback period is less than some prespecified cutoff.
B. Discounted payback period. The discounted payback period is the length of time until the sum of an investment’s discounted cash flows equals its cost. The discounted payback period rule is to take an investment if the discounted payback is less than some prespecified cutoff.
III. Accounting criterion
A. Average accounting return (AAR). The AAR is a measure of accounting profit relative to book value. The AAR rule is to take an investment if its AAR exceeds a benchmark.

38. A few questions
1. Which of the capital budgeting techniques do account for both the time value of money and risk?
2. The change in firm value associated with investment in a project is measured by the project’s _____________ .
a. Payback period
b. Discounted payback period
c. Net present value
d. Internal rate of return
3. Why might one use several evaluation techniques to assess a given project?

39. A few questions
1. Which of the capital budgeting techniques do account for both the time value of money and risk?
Discounted payback period, NPV, IRR, and PI
2. The change in firm value associated with investment in a project is measured by the project’s Net present value.
3. Why might one use several evaluation techniques to assess a given project?
To measure different aspects of the project; e.g., the payback period measures liquidity, the NPV measures the change in firm value, and the IRR measures the rate of return on the initial outlay.

40. Year Cash Flows A Cash Flows B 0 -$30,000 -$45,000 1 15,000 5,000
Solution to Problem 9.3
Offshore Drilling Products, Inc. imposes a payback cutoff of 3 years for its international investment projects. If the company has the following two projects available, should they accept either of them?
Year Cash Flows A Cash Flows B
0 -$30,000 -$45,000
, ,000
, ,000
, ,000
, ,000

41. Solution to Problem 9.3 (concluded)
Project A:
Payback period = ($30, ,000)/10,000
= 2.50 years
Project B:
Payback period = ($45, ,000)/$250,000
= years
Project A’s payback period is 2.50 years and project B’s payback period is 3.04 years. Since the maximum acceptable payback period is 3 years, the firm should accept project A and reject project B.

42. Solution to Problem 9.7
A firm evaluates all of its projects by applying the IRR rule. If the required return is 18 percent, should the firm accept the following project?
Year Cash Flow
0 -$30,000
,000
2 0
,000

43. Solution of Problem 9.7 (concluded)
To find the IRR, set the NPV equal to 0 and solve for the discount rate:
NPV = 0 = -$30, $25,000/(1 + IRR)1 + $0/(1 + IRR) $15,000/(1 + IRR)3
At 18 percent, the computed NPV is ____.
So the IRR must be (greater/less) than 18 percent. How did you know?

44. Solution of Problem 9.7 (concluded)
To find the IRR, set the NPV equal to 0 and solve for the discount rate:
NPV = 0 = -$30, $25,000/(1 + IRR)1 + $0/(1 + IRR) $15,000/(1 + IRR)3
At 18 percent, the computed NPV is $316.
So the IRR must be greater than 18 percent. We know this because the computed NPV is positive.
By trial-and-error, we find that the IRR is percent.