Slides 2 4 recommend investment course of action based on NP

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Recommend Investment Course of Action Based on NPV Calculation

© Dale R Geiger 2011 1

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

© 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

Multiple Cash Flows

is held in trust and will be paid in the following installments:

• $20,000 on her 21 st birthday

• $40,000 on her 30 th birthday

• $60,000 on her 40 th birthday

• $100,000 on her 50 th birthday

• Assume a discount rate of 8%

• Task: Calculate the NPV of Rebecca’s inheritance

© Dale R Geiger 2011 5

Identify the Key Variables

…in 5 years (21 st birthday)

…in 14 years (30 th birthday)

…in 24 years (40 th birthday)

…in 34 years (50 th birthday)

Discount rate = 8%

Build a Timeline

$

X-Axis = number of Years

The timeline helps us to visualize the cash flows and gives us a “reality check“

$20K

$40K

$60K

$100K K

© Dale R Geiger 2011 7

Multiply by the PV Factors

Cash Flow * PV Factor (8%) = Present Value

Multiply by the PV Factors

Cash Flow * PV Factor (8%) = Present Value

Multiply by the PV Factors

Cash Flow * PV Factor (8%) = Present Value

Multiply by the PV Factors

Cash Flow * PV Factor (8%) = Present Value

Multiply by the PV Factors

Cash Flow * PV Factor (8%) = Present Value

Multiply by the PV Factors

Cash Flow * PV Factor (8%) = Present Value

Comparing the Cash Flows

$

X-Axis = number of Years

The red bars represent the Present Value of the Future Cash Flows

$20K

$40K

$60K

$100K K

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?

© Dale R Geiger 2011 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?

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

Build a Timeline

X-Axis = number of Years

Cash Outflows for Installment payments

Multiply by the PV Factors

Year Cash Flow * PV Factor (4%) = Present Value

Annuity = Equal Cash Flows

Year Cash Flow PV Factor 4% PV of Cash Flow

Algebra of an Annuity

• Essentially the NPV formula is:

(Cash Flow1 * PV Factor 1)

+ (Cash Flow2 * PV Factor2)

Annuity = Equal Cash Flows

Year Cash Flow PV Factor 4% PV of Cash Flow

• 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

© Dale R Geiger 2011 25

Annuity = Equal Cash Flows

Year Cash Flow PV Factor 4% PV of Cash Flow

• 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?

© 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?

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

X axis represents time in years

1000s

© 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

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

Calculate NPV Spreadsheet

© Dale R Geiger 2011 35

Use the NPV Annuity tab when cash flows are equal

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 37

If cash flows are non-consecutive like

Rebecca’s inheritance, use the Cash Flow II tab

Practical Exercise