# Recommend Investment Course of Action Based on NPV Recommend Investment Course of Action Based on NPV Calculation Dale R. Geiger 2011 1 Youve just won a million dollars! Should you take the lump sum payment of \$679,500 now or 20 annual payments of \$50,000? Dale R. Geiger 2011 2 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 Dale R. Geiger 2011 3 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

Dale R. Geiger 2011 4 Multiple Cash Flows Today is Rebeccas 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 Rebeccas inheritance Dale R. Geiger 2011 5

Identify the Key Variables Cash Flows Time in Years 1. 2. 3. 4. in 5 years (21st birthday) in 14 years (30th birthday) in 24 years (40th birthday) in 34 years (50th birthday) \$20,000 Inflow \$40,000 Inflow \$60,000 Inflow \$100,000 Inflow Discount rate = 8% Dale R. Geiger 2011

6 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 Dale R. Geiger 2011

7 Multiply by the PV Factors Cash Flow * PV Factor (8%) = \$20,000 * 0.6806 = \$40,000 * 0.3405

= \$60,000 * 0.1577 = \$100,000 * 0.0730 = Present Value Total The NPV of Rebeccas inheritance is \$43,994

Dale R. Geiger 2011 8 Multiply by the PV Factors Cash Flow * PV Factor (8%) = \$20,000 * 0.6806 = \$40,000

* 0.3405 = \$60,000 * 0.1577 = \$100,000 * 0.0730 = Present Value \$13,612

Total The NPV of Rebeccas inheritance is \$43,994 Dale R. Geiger 2011 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 =

\$100,000 * 0.0730 = Total The NPV of Rebeccas inheritance is \$43,994 Dale R. Geiger 2011 10 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 = Total The NPV of Rebeccas inheritance is \$43,994 Dale R. Geiger 2011 11

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 Rebeccas inheritance is \$43,994 Dale R. Geiger 2011 12 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 Rebeccas inheritance is \$43,994 Dale R. Geiger 2011 13

Comparing the Cash Flows \$ \$100K K The red bars represent the Present Value of the Future Cash Flows \$60K \$40K \$20K \$13.6K 5 \$13.6K 14 \$9.5K \$7.3K

24 X-Axis = number of Years Dale R. Geiger 2011 14 Questions to Think About What would happen to the Present Value of Rebeccas 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? Dale R. Geiger 2011 15 Questions to Think About What would happen to the Present Value of Rebeccas 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? Dale R. Geiger 2011 16 Check on Learning How does the Net Present Value calculation differ from the calculation of the Present Value of a single cash flow? Dale R. Geiger 2011 17 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

Dale R. Geiger 2011 18 Identify the Key Variables Cash Flows Time in Years 1. 2. 3. 4. in 1 year in 2 years in 3 years in 4 years \$20,000 outflow \$20,000 outflow \$20,000 outflow \$20,000 outflow

Discount rate = 4% Dale R. Geiger 2011 19 Build a Timeline X-Axis = number of Years \$ K Cash Outflows for Installment payments -\$20 \$ -\$20 -\$20 -\$20

K Dale R. Geiger 2011 20 Multiply by the PV Factors Year Cash Flow 1 2 3 4 -20,000 -20,000 -20,000 -20,000 * PV Factor (4%) * *

* * = Present Value 0.962 = 0.925 = 0.889 = 0.855 = Total: -19,231 -18,491 -17,780 -17,096 -\$72,598 The NPV of the Course of action is -\$72,598 Dale R. Geiger 2011 21

Annuity = Equal Cash Flows Year Cash Flow 1 -20,000 2 -20,000 3 -20,000 4 -20,000 * * * * PV Factor 4% 0.962 0.925 0.889 0.855 = =

= = PV of Cash Flow -19,231 -18,491 -17,780 -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 Dale R. Geiger 2011 22 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) Dale R. Geiger 2011 23 Annuity = Equal Cash Flows Year Cash Flow 1 -20,000 2 -20,000 3 -20,000 4 -20,000 * * * * PV Factor 4%

+ 0.962 + 0.925 + 0.889 + 0.855 = 3.630 = = = = PV of Cash Flow -19,231 -18,491 -17,780 -17,096 The sum of the four factors is called the Annuity Factor The Annuity Factor can be found on the PV Annuity Table Dale R. Geiger 2011 24

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 Dale R. Geiger 2011 25 Annuity = Equal Cash Flows Year Cash Flow 1 -20,000 2 -20,000 3 -20,000 4 -20,000 -20,000 * * *

* * PV Factor 4% 0.962 0.925 0.889 0.855 3.630 = = = = = PV of Cash Flow -19,231 -18,491 -17,780 -17,096 -\$72,600 The PV of an Annuity is equal to:

Cash flow* PV Annuity Factor Dale R. Geiger 2011 26 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? Dale R. Geiger 2011 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? Dale R. Geiger 2011 28 Check on Learning What is an annuity? How does an annuity simplify the NPV calculation? Dale R. Geiger 2011 29 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? Dale R. Geiger 2011

30 Build a Timeline 1000s X axis represents time in years Dale R. Geiger 2011 31 Using the PV Annuity Table -Initial Investment +( Cash Flow *Annuity Factor) = NPV -1,000,000 +( 400,000*2.487) = -5,200 Dale R. Geiger 2011 32 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 Dale R. Geiger 2011 33 Practical Exercise Dale R. Geiger 2011 34 Calculate NPV Spreadsheet Use the NPV Annuity tab when cash flows are equal Dale R. Geiger 2011 35

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 36 If cash flows are non-consecutive like Rebeccas inheritance, use the Cash Flow II tab Dale R. Geiger 2011 37 Practical Exercise Dale R. Geiger 2011 38