1. Recommend Investment Course of Action Based on NPV Calculation
Intermediate Cost Analysis
and Management
2.4

2. You’ve just won a million dollars!
Should you take the lump sum payment of $679,500 now or 20 annual payments of $50,000?

3. Terminal Learning Objective
Action: Recommend Investment Course of Action Based on NPV Calculation
Condition: You are training to become an ACE with access to ICAM course handouts, readings, and spreadsheet tools and awareness of Operational Environment (OE)/Contemporary Operational Environment (COE) variables and actors
Standard: With at least 80% accuracy:
Identify and enter relevant report data to solve Net Present Value equations using macro enabled templates and make appropriate recommendation

4. What is Net Present Value
“Net” refers to the result of combining multiple values
Net Pay combines wages earned (+) and payroll tax deductions (-)
Net Change in Financial Position combines Revenues (+) and Costs (-)
Net Present Value (NPV) refers to the combination of multiple discounted cash flows
A positive NPV means that the PV of the cash inflows outweighs the PV of the outflows

5. Multiple Cash Flows
Today is Rebecca’s 16th birthday. Her inheritance is held in trust and will be paid in the following installments:
$20,000 on her 21st birthday
$40,000 on her 30th birthday
$60,000 on her 40th birthday
$100,000 on her 50th birthday
Assume a discount rate of 8%
Task: Calculate the NPV of Rebecca’s inheritance

6. Identify the Key Variables
Cash Flows
Time in Years
$20,000 Inflow
$40,000 Inflow
$60,000 Inflow
$100,000 Inflow
…in 5 years (21st birthday) …in 14 years (30th birthday) …in 24 years (40th birthday) …in 34 years (50th birthday)
Discount rate = 8%

7. Build a Timeline
$100K $ K
The timeline helps us to visualize the cash flows and gives us a “reality check“
$60K
$40K
$20K 5 14 24
X-Axis = number of Years

8. Multiply by the PV Factors
Cash Flow *
PV Factor (8%) =
Present Value
$20,000
0.6806
$40,000
0.3405
$60,000
0.1577
$100,000
0.0730
Total
The NPV of Rebecca’s inheritance is $43,994

9. Multiply by the PV Factors (Cont.)
Cash Flow *
PV Factor (8%) =
Present Value
$20,000
0.6806
$13,612
$40,000
0.3405
$60,000
0.1577
$100,000
0.0730
Total
The NPV of Rebecca’s inheritance is $43,994

10. Multiply by the PV Factors (Cont.)
Cash Flow *
PV Factor (8%) =
Present Value
$20,000
0.6806
$13,612
$40,000
0.3405
13,620
$60,000
0.1577
$100,000
0.0730
Total
The NPV of Rebecca’s inheritance is $43,994

11. Multiply by the PV Factors (Cont.)
Cash Flow *
PV Factor (8%) =
Present Value
$20,000
0.6806
$13,612
$40,000
0.3405
13,620
$60,000
0.1577
9,462
$100,000
0.0730
Total
The NPV of Rebecca’s inheritance is $43,994

12. Multiply by the PV Factors (Cont.)
Cash Flow *
PV Factor (8%) =
Present Value
$20,000
0.6806
$13,612
$40,000
0.3405
13,620
$60,000
0.1577
9,462
$100,000
0.0730
7,300
Total
The NPV of Rebecca’s inheritance is $43,994

13. Multiply by the PV Factors
Cash Flow *
PV Factor (8%) =
Present Value
$20,000
0.6806
$13,612
$40,000
0.3405
13,620
$60,000
0.1577
9,462
$100,000
0.0730
7,300
Total
$43,994
The NPV of Rebecca’s inheritance is $43,994

14. Comparing the Cash Flows
$100K $ K
The red bars represent the Present Value of the
Future Cash Flows
$60K
$40K
$20K
$13.6K
$13.6K
$9.5K
$7.3K 5 14 24
X-Axis = number of Years

15. Questions to Think About
What would happen to the Present Value of Rebecca’s inheritance if she assumed a 6% discount rate? A 12% discount rate?
Rebecca has found a company that will pay her $40,000 cash now if she signs over her inheritance. What should she do?
What factors should she consider?
Rebecca has found a company that will pay her $40,000 cash now if she signs over her inheritance. What should she do?
What factors should she consider?

16. LSA #1 Check on Learning
Q1. How does the Net Present Value calculation differ from the calculation of the Present Value of a single cash flow? A1.
Q1. How does the Net Present Value calculation differ from the calculation of the Present Value of a single cash flow?
A1. The first steps are the same: identify the key variables (cash flows, number of periods, discount rate), build a timeline. Then, multiply the cash flows by there respective factors. The main difference is that there are multiple cash flows so once each has been converted to its present value, they must be summed up.

17. LSA #1 Summary
During this lesson, we first discussed understanding Net Present Value (NPV) and calculated NPV with a given graphed scenario

18. Equal Cash Flow Example
A machine may be purchased with four annual installments of $20,000. The discount rate is 4%.
Task: Calculate the NPV of this course of action

19. Identify the Key Variables
Cash Flows
Time in Years
$20,000 outflow
…in 1 year …in 2 years …in 3 years …in 4 years
Discount rate = 4%

20. Cash Outflows for Installment payments
Build a Timeline
X-Axis = number of Years $ K
Cash Outflows for Installment payments
-$20
-$20
-$20
-$20 $ K

21. Multiply by the PV Factors
Year
Cash Flow *
PV Factor (4%) =
Present Value 1
-20,000
0.962
-19,231 2
0.925
-18,491 3
0.889
-17,780 4
0.855
-17,096
Total:
-$72,598
The NPV of the Course of action is -$72,598

22. Annuity = Equal Cash Flows
Year
Cash Flow
PV Factor 4%
PV of Cash Flow 1
-20,000 *
0.962 =
-19,231 2
0.925
-18,491 3
0.889
-17,780 4
0.855
-17,096
An Annuity is a series of equal cash flows over equal time periods
The four equal installment payments qualify as an Annuity
This simplifies the calculation

23. Cash Flow * (PV Factor1 + PV Factor2)
Algebra of an Annuity
Essentially the NPV formula is:
(Cash Flow1 * PV Factor 1) +
(Cash Flow2 * PV Factor2)
and so on….
If the cash flows are equal, the will factor out and this becomes:
Cash Flow * (PV Factor1 + PV Factor2)

24. Annuity = Equal Cash Flows
Year
Cash Flow
PV Factor 4%
PV of Cash Flow 1
-20,000 * =
-19,231 2
-18,491 3
-17,780 4
-17,096 =
The sum of the four factors is called the Annuity Factor
The Annuity Factor can be found on the PV Annuity Table

25. Using the PV Annuity Table
The PV Annuity factor on the table is equal to the sum of the PV factors for a single cash flow for Year 1 through Year 4

26. Annuity = Equal Cash Flows
Year
Cash Flow
PV Factor 4%
PV of Cash Flow 1
-20,000 *
0.962 =
-19,231 2
0.925
-18,491 3
0.889
-17,780 4
0.855
-17,096
3.630
-$72,600
The PV of an Annuity is equal to:
Cash flow* PV Annuity Factor

27. Make a Recommendation
Another course of action is available: Pay $70,000 cash for the machine today
Which course of action should we take?
What if the discount rate is 2%? What if it is 6%?
What other factors might be considered?

28. Make a Recommendation
Another course of action is available: Pay $70,000 cash for the machine today
Which course of action should we take?
What if the discount rate is 2%? What if it is 6%?
What other factors might be considered?

29. LSA #2 Check on Learning
Q1. What is an annuity? A1. Q2. How does an annuity simplify the NPV calculation? A2.
Q1. What is an annuity?
A1. A stream of equal cash flows over equal time periods.
Q2. How does an annuity simplify the NPV calculation?
A2. It permits us to use the annuity factor from the PV annuity table. Then we only have to do a single calculation instead of one for each cash flow.

30. LSA #2 Summary
During this lesson, we discussed calculating Net Present Value and talked about the steps needed in order to make the necessary recommendation

31. Net Present Value
Reengineering a business process in your unit will cost $1 million now but will save an estimated $400,000 per year for the next three years.
Assuming a discount rate of 10%, what is the NPV of this course of action?

32. Build a Timeline
1000s
X axis represents time in years

33. Using the PV Annuity Table
-Initial Investment +( Cash Flow *Annuity Factor) = NPV
-1,000,000 +( 400,000*2.487) = -5,200

34. Should we proceed with Reengineering?
NPV is negative, so we should not proceed
The present value of the benefits to be received in the future is less than the initial investment
What if the discount rate is 8%?
-Initial Investment + Cash Flow (Savings) *Annuity Factor = NPV
-1,000,000 + (400,000*2.577) = 30,800

35. Practical Exercise

36. Calculate NPV Spreadsheet
Use the NPV Annuity tab when cash flows are equal
© Dale R. Geiger 2011

37. The spreadsheet calculates NPV and generates the timeline graph
Screenshots
Enter the key variables for consecutive time periods in the Cash Flow I tab
The spreadsheet calculates NPV and generates the timeline graph
© Dale R. Geiger 2011

38. If cash flows are non-consecutive like Rebecca’s inheritance, use the Cash Flow II tab
© Dale R. Geiger 2011

39. Practical Exercise

40. TLO Summary
Action: Recommend Investment Course of Action Based on NPV Calculation
Condition: You are training to become an ACE with access to ICAM course handouts, readings, and spreadsheet tools and awareness of Operational Environment (OE)/Contemporary Operational Environment (COE) variables and actors
Standard: With at least 80% accuracy:
Identify and enter relevant report data to solve Net Present Value equations using macro enabled templates and make appropriate recommendation