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

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?

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

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

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

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%

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

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

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

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

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

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

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

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

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?

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.

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

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

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%

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

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

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

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)

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 The sum of the four factors is called the Annuity Factor The Annuity Factor can be found on the PV Annuity Table

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

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

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?

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?

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.

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

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?

Build a Timeline 1000s X axis represents time in years

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

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

Practical Exercise

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

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

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

Practical Exercise

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