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

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: FM Leaders in a classroom environment working as a member of a small group, using doctrinal and administrative publications, self-study exercises, personal experiences, practical exercises, handouts, and discussion
Standard: With at least 80% accuracy (70% for international Learners) you must:
Describe Net Present Value
Calculate present value of an annuity
Recommend course of action using Net Present Value

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
$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

9. 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

10. 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

11. 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?
Q1. What would happen to the Present Value of Rebecca’s inheritance if she assumed a 6% discount rate? A 12% discount rate?
It is not necessary to re-work the calculation with the new discount rates. Learners should understand and be able to verbalize that the higher discount rate of 12% will decrease the net present value, while the lower interest rate of 6% will increase the NPV.
Q2. Rebecca has found a company that will pay her $40,000 cash now if she signs over her inheritance. What should she do?
Since the cash offer is less than the NPV of the inheritance at 8%, this is a not good deal for Rebecca. However, if she were to assume a discount rate of 12%, which would decrease the NPV of her inheritance, this offer would probably be attractive.
Q3. What factors should she consider?
Are there alternative investment courses of action that might bring a return greater than 8%? If so, she could take the money now and invest it and achieve even greater future cash flows. She might also want to consider her expected lifespan. The average 16 year old can’t imagine living to be 50 years old, but most of them will. If she has serious health problems, however, she may not live to collect all of her inheritance, and may need the cash now for medical bills.

12. 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 their 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.

13. LSA #1 Summary
We discussed how Net Present Value (NPV) uses multiple cash flows and the Present Value (PV) factor to solve for the sum. We then applied this by solving an activity.

14. 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

15. 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%

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

17. 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

18. 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

19. 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, they will factor out and this becomes:
Cash Flow * (PV Factor1 + PV Factor2)

20. 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

21. 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

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
3.630
-$72,600
The PV of an Annuity is equal to:
Cash flow* PV Annuity Factor

23. 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?

24. LSA #2 Check on Learning Q1. What is an annuity?
Q2. How does an annuity simplify the NPV calculation?
Q1. What is an annuity?
A1. An annuity is 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.
A2.

25. LSA #2 Summary
We discussed what an annuity was and how it simplified the NPV calculation by creating one calculation for all cash flows.

26. 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?

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

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

29. 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*2.577 = 30,800

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

31. 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

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

33. LSA #3 Check on Learning Q1. What does Net Present Value represent?
Q2. How can it be used to evaluate investments in property, plant and equipment?
A2.
Show Slide #33: LSA#3 Check on Learning
Facilitator’s Note: Ask the following Questions; (Facilitate discussion on answers given)
Q. What does Net Present Value represent?
A. It represents the sum of all of the discounted cash flows, whether positive or negative, over the life of the investment being evaluated
Q. How can it be used to evaluate investments in property, plant and equipment?
A. Most investments in property, plant, or equipment require a large up-front investment. The Net Present Value allows us to evaluate that initial cost, in today’s dollars, against the future cash flows, which will be realized in discounted dollars.

34. LSA #3 Summary
We applied the NPV calculation to various examples by calculating the PV of an annuity. We then were able to recommend if a Course of Action was favorable by having a positive NPV.

35. TLO Summary
Action: Recommend Investment Course of Action Based on NPV Calculation
Condition: FM Leaders in a classroom environment working as a member of a small group, using doctrinal and administrative publications, self-study exercises, personal experiences, practical exercises, handouts, and discussion
Standard: With at least 80% accuracy (70% for international Learners) you must:
Describe Net Present Value
Calculate present value of an annuity
Recommend course of action using Net Present Value

36. Practical Exercise