Slides recommend investment course of action

X-Axis = number of YearsThe timeline helps us to visualize the cash flows and gives us a “reality check“ The timeline helps us to visualize the cash flows and gives us a “reality check

Calculate Net Present Value

Principles of Cost Analysis and Management

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

handouts, and awareness of Operational Environment (OE)/Contemporary

Operational Environment (COE) variables and actors

• 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 Pay combines wages earned (+) and payroll tax deductions (-)

• Net Change in Financial Position combines Revenues (+) and Costs (-)

flows

outflows

Multiple Cash Flows

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

Identify the Key Variables

…in 5 years (21st birthday)

…in 14 years (30th birthday)

…in 24 years (40th birthday)

…in 34 years (50th birthday)

Discount rate = 8%

X-Axis = number of Years

The timeline helps us to visualize the cash flows and

gives us a “reality check“

The timeline helps us to visualize the cash flows and

gives us a “reality check“

$20K

$40K

$60K

$100K K

Multiply by the PV Factors

Multiply by the PV Factors

Multiply by the PV Factors

Multiply by the PV Factors

Multiply by the PV Factors

Multiply by the PV Factors

Comparing the Cash Flows

X-Axis = number of Years

The red bars represent the Present Value of the

Future Cash Flows

The red bars represent the Present Value of the

Future Cash Flows

$20K

$40K

$60K

$100K K

Questions to Think About

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?

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?

over her inheritance What should she do?

Check on Learning

Present Value of a single cash flow?

Equal Cash Flow Example

discount rate is 4%

Identify the Key Variables

X-Axis = number of Years

Cash Outflows for Installment

payments 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

1 -20,000 * 0.962 = -19,231

2 -20,000 * 0.925 = -18,491

3 -20,000 * 0.889 = -17,780

4 -20,000 * 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

Algebra of an Annuity

(Cash Flow1 * PV Factor 1)

+ (Cash Flow2 * PV Factor2)

and so on…

Cash Flow * (PV Factor1 + 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

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

• 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?

Check on Learning

Net Present Value

save an estimated $400,000 per year for the next three years

X axis represents time in years

1000s

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?

• The present value of the benefits to be received in the future is less than the initial investment

-Initial Investment + Cash Flow (Savings) *Annuity Factor = NPV

-1,000,000 + 400,000*2.577 = 30,800

Check on Learning

Practical Exercise

Calculate NPV Spreadsheet

Use the NPV Annuity tab when cash flows are

equal Use the NPV Annuity tab when cash flows are

equal

If cash flows are non-consecutive like Rebecca’s inheritance, use the Cash Flow II

tab

If cash flows are non-consecutive like Rebecca’s inheritance, use the Cash Flow II

tab

Practical Exercise