Uniform Series Present Worth (USPW)

The Uniform Series Present Worth (USPW) calculator computes the Uniform Series Present Worth factor based on the interest rate and number of cash flow periods.

INSTRUCTIONS: Enter the following:

• (i%) Interest rate
• (n) Number of cash flow periods

Uniform Series Present Worth (USPW):  The calculator returns the USPW factor as a real number.

The Math / Science

The USPW is a Discrete Compounding Discount Factor. This discount factor can be used to calculate the present worth of an annualized cash flow.  The formula for Uniform Series Present Worth is:

     `USPW =((1+i)^n-1)/(i(1+i)^n)`

where: 

• USPW is the Uniform Series Present Worth factor
• i is the interest rate
• n is the number of cash flow periods.

USPW EXAMPLE

If your company was going to invest some amount of money to produce revenue, you could compute the present value of that investment considering that expenses and and depreciation are deductible and the actual revenue from the investment will be taxed.

In this example we will assume annual expenses of $550 and a salvage value on the investment of $600.  So, if your company has 25,000 to invest for ten years, which you have estimated will bring in $3,700 per year, you can compute the real value of that investment to your company at a fixed rate of 9% as the sum of the following cost components:

First we calculate the USPW and Single Payment Present Worth (SPPW) for 9% interest rate and 10 years:

USPW[9%, 10 yrs] = 6.418

SPPW[9%, 10 yrs] = 0.4224

• Investment = $25,000
• Net Tax Revenue = $3,700, which is taxed at 49%.  Therefore the net value after taxes of the revenue is `$3,700 * USPW[9%, 10 yrs] * ( 1 - tax rate) = $3,700 * 6.418 * (1 - 0.49) = $3,700 * 6.418 * 0.51 = $12,110.77`
• Annual Expenses Not Deductible = $550 * USPW * (1 - 0.49) = $550 * 6.418 * 0.51 = $1,800.25
• Present Worth of Salvage  = $600 * SPPW  = $600 * 0.4224 = $253.44

So, PV = - (Investment) + Net Tax Revenue - Annual Expenses Not Deductible + Present Worth of Salvage

            = -$25,000 + $12,110.77 - $1,800.25 + $253.44

            = -$14,436.04

Present and Future Worth Calculators

• (SPCA) Single Payment Compound Amount Factor
• (USSF) Uniform Series Sinking Fund Factor 
• (SPPW) Single Payment Present Worth Factor
• (UGFW) Uniform Gradient Future Worth Factor 
• (UGPW) Uniform Gradient Present Worth Factor 
• (UGUS) Uniform Gradient Uniform Series Factor 
• (USCA) Uniform Series Compound Amount Factor 
• (USPW) Uniform Series Present Worth Factor 

REFERENCE
Lindeburg, Michael R (1992). Engineer In Training Reference Manual. Professional Publication, Inc. 8th Edition.