discounted cash flow

Examples of discounted cash flow in the following topics:

• Discounted Cash Flow Approach

  • The discounted cash flow approach finds the value of an asset using its expected return and the present values of future cash flows.
  • The discounted cash flow (DCF) approach utilizes the time value of money concept to find the value of an asset.
  • -- FCFN+1 = future cash flow one year after the projection period. k = discount rate. g = assumed constant growth rate.
  • FCFN+1 = future cash flow one year after the projection period. k = discount rate. g = assumed constant growth rate.
  • Calculate the value of a project using the discounted cash flow approach

• Discounted Payback

  • Discounted payback period is the amount of time to cover the cost, by adding positive discounted cash flow coming from the profits of the project.
  • Assuming the discount rate is 10%, we would apply the following formula to each cash flow.
  • Discounted Cash Flow at 10%: Year 0: -2000, year 1: 909, year 2: 827, year 3: 1503.
  • The next step is to compute the cumulative discounted cash flow, by summing the discounted cash flow for each year.
  • Accumulated discounted cash flows: Year 0: -2000, year 1: -1091, year 2: -264, year 3: 1239.

• NPV Profiles

  • The NPV calculation involves discounting all cash flows to the present based on an assumed discount rate.
  • Thus, when discount rates are large, cash flows further in the future affect NPV less than when the rates are small.
  • Conversely, a low discount rate means that NPV is affected more by the cash flows that occur further in the future.
  • The NPV Profile assumes that all cash flows are discounted at the same rate.
  • A higher discount rate places more emphasis on earlier cash flows, which are generally the outflows.

• Present Value of Payments

  • The value of a bond is obtained by discounting the bond's expected cash flows to the present using an appropriate discount rate.
  • As with any security or capital investment, the theoretical fair value of a bond is the present value of the stream of cash flows it is expected to generate.
  • Therefore, the value of a bond is obtained by discounting the bond's expected cash flows to the present using an appropriate discount rate.
  • In practice, this discount rate is often determined by reference to similar instruments, provided that such instruments exist.
  • The formula for calculating a bond's price uses the basic present value (PV) formula for a given discount rate .

• Modified IRR

  • Where n is the number of equal periods at the end of which the cash flows occur (not the number of cash flows), PV is present value (at the beginning of the first period), and FV is future value (at the end of the last period).
  • The formula adds up the negative cash flows after discounting them to time zero using the external cost of capital, adds up the positive cash flows including the proceeds of reinvestment at the external reinvestment rate to the final period, and then works out what rate of return would cause the magnitude of the discounted negative cash flows at time zero to be equivalent to the future value of the positive cash flows at the final time period.
  • If an investment project is described by the sequence of cash flows: Year 0: -1000, year 1: -4000, year 2: 5000, year 3: 2000.
  • First, we calculate the present value of the negative cash flows (discounted at the finance rate): PV(negative cash flows, finance rate) = -1000 - 4000 *(1+10%)-1 = -4636.36.
  • Second, we calculate the future value of the positive cash flows (reinvested at the reinvestment rate): FV (positive cash flows, reinvestment rate) = 5000*(1+12%) +2000 = 7600.

• Cash Flow from Financing

  • One of the three main components of the cash flow statement is cash flow from financing.
  • Receiving the money is a positive cash flow because cash is flowing into the company, while each individual payment is a negative cash flow.
  • Extending credit is an investing activity, so all cash flows related to that loan fall under cash flows from investing activities, not financing activities.
  • For example, a company may issue a discount which is a financing expense.
  • However, because no cash changes hands, the discount does not appear on the cash flow statement.

• Defining NPV

  • In order to see whether the cash outflows are less than the cash inflows (i.e., the investment earns a positive return), the investor aggregates the cash flows.
  • Since cash flows occur over a period of time, the investor knows that due to the time value of money, each cash flow has a certain value today .
  • Thus, in order to sum the cash inflows and outflows, each cash flow must be discounted to a common point in time.
  • Also recall that PV is found by the formula $PV=\frac { FV }{ { (1+i) }^{ t } }$ where FV is the future value (size of each cash flow), i is the discount rate, and t is the number of periods between the present and future.
  • The PV of multiple cash flows is simply the sum of the PVs for each cash flow.

• Present Value, Multiple Flows

  • The PV of multiple cash flows is simply the sum of the present values of each individual cash flow.
  • The PV of multiple cash flows follows the same logic as the FV of multiple cash flows.
  • The PV of multiple cash flows is simply the sum of the present values of each individual cash flow .
  • Each cash flow must be discounted to the same point in time.
  • Unfortunately, if the cash flows do not fit the characteristics of an annuity, there isn't a simple way to find the PV of multiple cash flows: each cash flow much be discounted and then all of the PVs must be summed together.

• Calculating the Payback Period

  • Start by calculating Net Cash Flow for each year: Net Cash Flow Year 1 = Cash Inflow Year 1 - Cash Outflow Year 1.
  • Then Cumulative Cash Flow = (Net Cash Flow Year 1 + Net Cash Flow Year 2 + Net Cash Flow Year 3 ... etc.)
  • Some businesses modified this method by adding the time value of money to get the discounted payback period.
  • They discount the cash inflows of the project by a chosen discount rate (cost of capital), and then follow usual steps of calculating the payback period.
  • Then the cumulative positive cash flows are determined for each period.

• Calculating the NPV

  • The NPV is found by summing the present values of each individual cash flow.
  • Cash inflows (such as coupon payments or the repayment of principal on a bond) have a positive sign while cash outflows (such as the money used to purchase the investment) have a negative sign.
  • The accurate calculation of NPV relies on knowing the amount of each cash flow and when each will occur.
  • Since many people believe that it is appropriate to use higher discount rates to adjust for risk or other factors, they may choose to use a variable discount rate.
  • NPV is the sum of of the present values of all cash flows associated with a project.