Calculating Net Present Value Why do we need to know about the Present value? Allows us to talk about values in a common time period If I invest $2,000 now in a business and I receive $20,000 in 25 years is it fair to say I made $18,000 in profit? What else could you have done with that money?
Using Cash Flows Visual representation of all costs and benefits REMEMBER WHAT YEAR YOU ARE DISCOUNTING YOUR CASH FLOWS TOO! Deciding the most “economic” way to solve for Present Value Basic Discounting/Compounding Annuities Perpetuities Infinite Periodic Series
Basic Discounting:
B C n NPVn nn 1 1 i i
Used for a one time benefit or cost For example: I can expect to net $10,000 in 3 years for a small stand of trees I own. How much is that worth right now?
Annuity
in 1 1 V a 0 i1 i n ( )
Used when a benefit or cost occurs every (year, month, day, week) for a set amount of time. ***Must adjust the interest rate according to the time scale you are using! Example: I plan on saving $500 every year for 15 years. How much is that money worth in present value terms? (after about 35-40 years, you can use the perpetuity formula and receive almost the same answer…and perpetuity is soooo much easier to compute)
Perpetuity
V0
a i
Easiest method of all. Good approximation to use if you want to throw something off the top of your head Expected cost or revenue FOREVER!!!! For example: I just won Washington’s “Lucky for Life”. I’ll receive $1000 every week for the rest of my life. How much is that worth in present value terms?
Infinite Periodic Series
a V 0 n 1i 1
Used when you expect a consistent cost or benefit at a set period forever. FOR EXAMPLE: Every 3 years, I can harvest my Chinchilla fur and receive $5,000. I assume my Chinchilla’s will last forever.
These can be used in combination with each other as well! For example: Every 3 years the Phish tour comes to my hometown and I can earn $500 by charging “hippy” college students to park on my lot. Since Phish is always touring I can expect this revenue indefinitely. BUT, I have to pay $50 in taxes for my land every year. I can use the INFINITE PERIODIC SERIES to calculate my cash benefits in year 0 and the PERPETUITY to calculate my costs!
Now you try! What would I use to calculate THIS? The NRCS has helped negotiate with a farmer to allow 500 acres to go idle for the next ten years. In return they will pay him $8,000 a year to pick up a hobby. What is that worth to the farmer in present value terms?
“Sustainable management” of forestland near Moscow Mountain creates beneficial Elk habitat. Yearly revenues from hunting licenses will total $1,000. Since it’s sustainable it will go on forever.
Man oh man am I green! I am going to buy 5,000 acres of prime forestland and let it GROW WILD! The feds will allow me to defer my taxes so that I can pay them every 4 years a lump sum. ($2,500) But I expect when I die my kids will sell the land for as much as they can. Let’s say $8,000 an acre.
Basic Discounting
B C n NPVn nn 1 1 i i
Annutiy
in 1 1 V a 0 i1 i n ( )
Perpetuity
V0
a i
Infinite Periodic Series
a V 0 n 1i 1