Finance 101: Net Present Value (NPV)

Present Value: Present value is the $ amount achieved by using the capital markets to transfer cash flow from other dates/events to today (the present).
For instance lets assume if a bank is giving you 10% interest per year, hence in order to receive $1.10 at the end of a year, you need to invest $1.00 today. Thus Present Value of $1.10 one year from now @ 10% interest rate is $1.00

Discount Factor: The factor which discounts the future cash flows to obtain their present value is known as Discount Factor.
For instance,
PV of $1.10 to be received next year = 1.10/1.10 = ‘discount factor’= 1/(1+r).
10% or 0.10 = r is called the 1-year ‘discount rate’ or ‘interest rate.

1. Now suppose you will receive $1.21 two year from today and interest rate for both year is same (10% per annum). In order to find the discount factor, we need to think about Present Value of $1.21 that is to be received 2 years from now. We can split the 2 years into 2 duration of 1 year and find the value at the begining of each year. Once we have value at the end of Year 1 we can get the Present Value.
2. Thus value of $1.21 (received at year 2), a year from now, i.e. at end of Year 1 = 1.21/(1+r). But we also know that the Present value of CF a year from now is CF/(1+r) or CF * Discount factor for 1 year.
3. Present value of the cash flow = Value of CF at year 1 * Discount Factor for 1 year, which is equal to (1.21/(1+r)*1/(1+r) = 1.21/(1+r)2. From this we can compute the discount factor for year 2 as 1/(1+r)2.

General For Cash Flow in period t, PV = CF/(1+r)t. -r is the per period interest rate and t is the number of periods.

• For Cash Flows in several periods, C1, C2, C3, ....

PV = C1/(1+r) + C2/(1+r)2 + C3/(1+r)3 + .........

NET PRESENT VALUE

NPV is the PV of all cash flows including the initial (out) flowof the investment, C0

NPV = Co+ C1/(1+r) + C2/(1+r)2 + C3/(1+r)3 + .........

With a capital market all investors can agree on the ranking of projects.

NPV Rule: Invest if NPV > 0

Equivalent rule: Invest if Present Value of future Cash flows > Co (Initial Cash outflow)