Present Value, Inflation, and Discounting

 

 

Miranda

 

The present value concept captures the time value of money by adjusting through compounding and discounting cash flows to reflect the increased value of money when invested.  The present value of a cash flow reflects in today’s terms, the value of future cash flows adjusted for the cost of capital.  In essence, the time value of money reflects the fact that money in hand today is more valuable than an identical amount of money received in the future and that benefits and costs are worth more if they are realized earlier.  Since money today can earn interest, all costs must be adjusted to reflect the inflation rate and then discounted to reflect their present value.  The time value of money reflects the idea that a dollar in hand today is worth more than a dollar in the future, even after making adjustments for inflation.  

 

 

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Steps for Calculating the Present Value of an Investment

 

The present value of an investment is calculated from the

time series of projected cash flows using discount rates

specified in the OMB Circular A-94, Appendix B2   (http://www.whitehouse.gov/omb/circulars/a094/a094.html).  

To estimate net present value (Cost Estimating Application), future

benefits and costs must be discounted.  Discount factors can be

reflected in real* or nominal terms as defined by OMB Circular A-94 Appendix C.  The discount rate used depends on the type of dollars

to be adjusted:

 

Discounting translates projected cash flows into present value terms using

specified discount factors.  As illustrated in Exhibit 6-6, the discount factor is equal to 1/(1+ i)n or (1+ i)-n where i is the interest rate and n is the number of years from the date of initiation for the project.  

 

Real Discount Rates—Adjusted to eliminate the effects of expected inflation  and used to discount Constant Year dollars or real benefits and costs.  A real discount rate can be approximated by subtracting expected inflation from a nominal discount rate.

 

Nominal Discount Rates—Reflect expected inflation and used to discount Then Year (inflated) dollars or nominal benefits and costs.

 

* in this case, “real” indicates that the effects of general inflation have been removed

 

Exhibit 6-6: Compounding and Discounting

 

Exhibit 6-6:  Compounding and Discounting

 

Exhibit 6-7 provides an example of how discounting is applied.

 

 

Examples

If cost is the only deciding factor, which investment should the organization invest in?

 

 

Year1

Year2

Year3

Year4

Year5

  Total

Project A Cost

$100

$100

$100

$100

$100

$500

Project B Cost

$500

$  ---

$  ---

$  --

$  --

$500

Project C Cost

$  ---

$  ---

$  ---

$  --

$500

$500

The organization should invest in the project with the lowest discounted cost stream.  In the example below, Project C has the lowest cost in terms of present value.  For example, you need $500 today for Project B.  Alternatively, you could put $449 in a bank today and receive the $500 you need in year 5 for Project C.  Economists contend you are better off with Project C because you can do something else with the $51 you did not put in the bank.

 

 

Year 1

Year 2

Year 3

Year 4

Year 5

Total

Program Year

0

1

2

3

4

 

Discount Factor

1.0000

0.9737

0.9481

0.9232

0.8989

Project A PV Cost

$100

$ 97

$ 95

$ 92

$ 90

$474

Project B PV Cost

$500

$  ---

$  ---

$  ---

$  ---

$500

Project C PV Cost

$  ---

$  ---

$  ---

$  ---

$449

$449

 

Exhibit 6-7: Discounting Example

 

There are generally two methods used to account for the inflation in a cost estimate.  One method is based on the Gross Domestic Product (GDP) rate, which is given in the yearly “Budget of the United States Government.”  For FY04, the inflator factor, which uses the increase in the GDP deflator to calculate the inflation rate is provided in the Summary Table section (http://www.whitehouse.gov/omb/budget/fy2004/pdf/budget.pdf, Table S12- Comparison on Economic Assumptions).  The other method calculates inflation as follows:

 

 

Inflation = (1 + Inflation Rate) ^ Year

 

 

Exhibit 6-8 is an example of how this formula is applied:

 

Exhibit 6 - 8: Applying the Inflation Rate

 

 

 

Exhibit 6-8:  Applying the Inflation Rate

 

To determine the present value of money, a discount rate must be applied to costs already adjusted for inflation.  There are two different types of discount rates:

 

1. Real Discount Rate is adjusted to eliminate the effects of expected inflation  and used to discount constant year dollars or real benefits or costs.  

 

 

Nominal Discount Rate

– Expected Inflation Rate

 

= Real Discount Rate

 

 

 

2. A Nominal Discount Rate is one adjusted to reflect inflation used to discount Then Year dollars or nominal benefits and costs. The formula used to apply the discount rate to calculate the present value is:

 

 

The Discount Process = 1/(1+Discount Rate)^Year

 

 

 

 

2 OMB Circular A-94 provides specific guidance on the discount rates to be used in evaluating Federal

programs whose benefits and costs are distributed over time.