# Discounted Cash Flow (notes)

The following is taken from Wikipedia.

**Background**

Using DCF analysis to compute the NPV takes as input cash flows and a discount rate and gives as output a price; the opposite process – taking cash flows and a price and inferring a discount rate, is called the yield.

**Definitions**

FV = DPV * (1+i)^n

DPV = FV/(1+i)^n = FV * (1-d)^n

DPV: discounted present value

FV: future cash flow; nominal value of cache flow in future

i: interest rate

d: discount rate { i/(1+i) } ; interest rate subtracted from BoY; rather than added at end of year

n: time in years before future cash flow

Summing multiple cash flows:

DPV = SUM{t=0..N} of { FV[t]/(1+i)^t }

**An Example**

“John Doe buys a house for $100,000. Three years later, he expects to be able to sell this house for $150,000.”

“the 3-year US Treasury Note rate is 5% per annum.”

“Using the DPV formula (FV=$150,000, i=0.05, n=3), that means that the value of $150,000 received in three years actually has a present value of $129,576 (rounded off).”

“Subtracting the purchase price of the house ($100,000) from the present value results in the net present value [(NPV)] of the whole transaction, which would be $29,576…”

“Another way of looking at the deal as the excess return achieved (over the risk-free rate) is (14.5%-5.0%)/(100%+5%) or approximately 9.0% (still very respectable). (As a check, 1.050 x 1.090 = 1.145 approximately.)”