Sample NPV Calculation

Following is a net present value calculation for a hypothetical timber management scenario.  In this example, site preparation and planting take place in year 0 (now).  A weed control treatment is conducted in year 1.  A precommercial thinning, yielding no revenue, takes place in year 15.  There is an annual administrative cost of $5.00 per acre per year.  A commercial thinning takes place during years 40 and 50 and the stand is clearcut at age 60.  All cash flows take place at the beginning of the year.  A real discount rate of 5% is used. 

Step 1. Discount all costs.

Activity Discounting Formula Present Value ($/acre)
Site Preparation
Planting
Weed Control 		−$50
−$100
−$50(1/1.05) 		−$50.00
−$100.00
−$29.29
Precommercial Thinning −$50(1.05)15 −$24.05
Annual
Administrative Cost 		−$5 { [(1.05)59−1] / [0.05(1.05)59] } + $5* −$99.38
Total Present
Value of Costs 		  −$302.72

*If uniform series of payments occurs at the beginning of each year then this formula is used:

V0 = a { [(1 + i)n − 1 -− 1] / [i(1 + i)n −1] } + a

Where:

  • a = periodically recurring cost or revenue at the beginning of each period
  • V0 = present value
  • n = number of periods (years)
  • i = interest rate

If these payments occurred at the end of each year, the formula would simply be changed to:

V0 = a { [(1 + i)n − 1] / [i(1 + i)n] }

Step 2. Discount all revenues.

Activity Discounting Formula Present Value ($/acre)
Thin at age 40 $500(1/1.05)40 $71.02
Thin at age 50 $1,500(1/1.05)50 $130.81
Clearcut $2,500(1/1.05)60 $133.84
Total Present Value of Revenues   $355.67

Step 3. Subtract discounted costs from discounted revenues.

Net Present Value = $355.67 − $302.72 =  $32.95

(From Rose et al, 1988)