Financial statement that shows the firm’s cash receipts and cash payments over a period of time.
Cash available for distribution to investors after firm pays for new investments or additions to working capital. FCF = EBIT - taxes + depreciation - change in net working capital - capital expenditures
Any type of cash flows (whether they are equal, consecutive payments or irregular, unequal cash flows over time) are referred to as a stream of cash flows.
What is the future value of the stream of cash flows 3 years from now that pay $1200 now, $1400 in year 1 and $1000 in year 2? Interest rate is 8%.
PVs can be added together to evaluate multiple cash flows. PV= (c1/(1+r)1)+(C2/(1+r)2)+…
PVs can be added together to evaluate multiple cash flows. PV= (c1/(1+r)1)+(C2/(1+r)2)+…
Equally spaced level stream of cash flows for a limited period of time.
PV of Perpetuity Formula C = cash payment r = interest rate PV = C/R
In order to create an endowment, which pays $100,000 per year, forever, how much money must be set aside today in the rate of interest is 10%? PV = 100,000/0,10 = 1,000,000 $
If the first perpetuity payment will not be received until three years from today, how much money needs to be set aside today? PV = 1,000,000/(1+0,103) = 751.315 $
C = cash payment r = interest rate t = Number of years cash payment is received PV= C[(1/r) - 1/r(1+r)t]
The present value of $1 a year for each of t years. PVAF = [(1/r) - 1/r(1+r)t]
A level stream of payments starting immediately is known as annuity due. PV of an Annuity Due: (1+r) x PV of an Annuity FV of an Annuity Due: (1+r)t x PV of an Annuity
Value of payments, Implied interest rate for an annuity, Calculation of periodic payments; - Mortgage payment - Annual income from an investment payout - Future Value of annual payments
You plan to save $4,000 every year for 20 years and then retire.Given a 10% rate of interest, what will be the FV of your retirement account? FV = 4,000 [(1/0,10)- (1/0,10(1+0,10)20]*(1+0,10)20 FV = 229.100 $
•Identifying Cash Flows -Discount Cash Flows, Not Profits -Discount Incremental Cash Flows -Discount Nominal Cash Flows by the -Nominal Cost of Capitol -Separate Investment & Financing Decisions •Calculating Cash Flows
-Discount actual cash flows -Using accounting income, rather than cash flow, could lead to erroneous decisions.
A project costs $2,000 and is expected to last 2 years, producing cash income of $1,500 and $500 respectively. The cost of the project can be depreciated at $1,000 per year. Given a 10% required return, compare the NPV using cash flow to the NPV using accounting income.
- Discount incremental cash flows - Include All Indirect Effects - Forget Sunk Costs - Include Opportunity Costs - Recognize the Investment in Working Capital - Beware of Allocated Overhead Costs - Remember Shutdown Cash Flows
Ask yourself this question Would the cash flow still exist if the Project does not exist? If yes, do not include it in your analysis. If no, include it.
-When valuing a project, ignore how the project is financed. -Following the logic from incremental analysis ask yourself the following Question: Is the project existence dependent on the financing? If no, you must separate financing and investment decisions.
- Think of cash flows as coming from three elements Total cash flow = + cash flows from capital investments + cash flows from changes in working capital + operating cash flows - Cash Flow from Capital Investments Almost every project requires some sort of initial investment. This is often capitalized from an accounting perspective. In finance, the investment represents a negative cash flow
Operating cash flow = + Revenue - Costs - Taxes Methods of Handling Depreciation • Method l: Dollars in Minus Dollars Out • Method 2: Adjusted Accounting Profits • Method 3: Add Back Depreciation Tax Shield