




















References




Net Present Value
(NPV)







































What is PV (present value)?



To better understand
NPV (Net Present Value), let's first look at what is present value (PV). PV
is the current worth of a future amount of money. "A dollar today is
worth more than a dollar tomorrow", this is referred to as the time
value of money. A given amount of money today has different (usually higher
or equal) buying power than the same amount of money in the future. In
finance and investment, PV is used to evaluate the future cash flows.



PV formula






















PV =

Ct















(1 + i)ᵗ
































What is discount rate?



Discount rate is a
key factor to calculate present value of future cash flows properly. The
higher the discount rate, the lower the present value of the future cash
flows. Typically 7%  10% is a good range for most projects in today’s market
conditions.





















What is Net Present Value (NPV) and how to
calculate NPV?



NPV is the sum of
the present value (PV) of the future individual cash flows (including in
flows and out flows) minus initial investment.





















NPV formula:























N

















NPV =

Ʃ


Ct

 Co













(1+i)ᵗ













t=1


































Let's see the example:



Let’s use NPV to
evaluate a 5years project: Initial investment at year 0 is $ 100,000;
discount rate is 7% annually. Annually profit from the end of the first year
to the end of the fifth year is:



· $20,000



· $30,000



· $30,000



· $30,000



· $25,000



At the end of third year, there is $5,000
maintenance expense.





















Then the PV of each year is:



· Year 0: 100,000



· Year 1: 20,000/(1+0.07) = 18,691.59



· Year 2: 30,000/(1+0.07)² = 26,203.16



· Year 3: 30,000/(1+0.07)³ – 5,000/(1+0.07)³ = 20,407.45



· Year 4: 30,000/(1+0.07)⁴ = 22,886.86



· Year 5: 25,000/(1+0.07)⁵ = 17,824.65



We get NPV by adding all PVs above from year 0 to
year 5.



NPV = 6,013.71





















NPV tells how much value an investment or project
will bring in.



If NPV > 0, the investment may be accepted.



If NPV < 0, the investment should be rejected.



Using NPV to
determine an investment is certainly not enough. IRR (Internal Rate of
Return) will tell you other variable over project economics. The rate of
return so should be used to compare different investments.


















