Online tutorials for calculating DCF (Discounted Cash Flow)?
"Here's a link to an online calculator employing the Discounted Cash Flow method:  Discounted Cash Flows Calculator.  Description: This calculator finds the fair value   of a stock investment the   theoretically correct way, as the   present value of future earnings. You   can find company earnings via the box   below.   [...] They also provide a link to the following relevant article:  Investment Valuation: A Little Theory.  Excerpt: A company is valuable to stockholders   for the same reason that a bond is   valuable to bondholders: both are   expected to generate cash for years   into the future. Company profits are   more volatile than bond coupons, but   as an investor your task is the same   in both cases: make a reasonable   prediction about future earnings, and   then ""discount"" them by calculating   how much they are worth today. (And   then you don't buy unless you can get   a purchase price that's less than the   sum of these present values, to make   sure ownership will be worth the   headache.)   [...]" "Check out Professor Damodaran's website: http://pages.stern.nyu.edu/~adamodar/ . Tons of good stuff there to get you started. If you want more depth, he's written what is widely considered the bible on the subject of valuation: ""Investment Valuation"". DCF is very well suited to stock analysis. One doesn't need to know, or forecast the future stock price to use it. In fact, it's the opposite. Business fundamentals are forecasted to estimate the sum total of future cash flows from the company, discounted back to the present. Divide that by shares outstanding, and you have the value of the stock. The key is to remember that DCF calculations are very sensitive to inputs. Be conservative in your estimates of future revenue growth, earnings margins, and capital investment. I usually develop three forecasts: pessimistic, neutral, optimistic. This delivers a range of value instead of a false-precision single number. This may seem odd: I find the DCF invaluable, but for the process, not so much the result. The input sensitivity requires careful work, and while a range of value is useful, the real benefit comes from being required to answer the questions to build the forecast. It provides a framework to analyze a business. You're just trying to properly fill in the boxes, estimate the unguessable. To do so, you pore through the financials. Skimming, reading with a purpose. In the end you come away with a fairly deep understanding of the business, how they make money, why they'll continue to make money, etc." what do you mean exactly?  Do you have a future target price and projected future dividend payments and you want the present value (time discounted price) of those? Edit: The DCF formula is difficult to use for stocks because the future price is unknown.  It is more applicable to fixed-income instruments like coupon bonds.  You could use it but you need to predict / speculate a future price for the stock. You are better off using the standard stock analysis stuff: Learn Stock Basics - How To Read A Stock Table/Quote The P/E ratio and the Dividend yield are the two most important.  The good P/E ratio for a mature company would be around 20.  For smaller and growing companies, a higher P/E ratio is acceptable.  The dividend yield is important because it tells you how much your shares grow even if the stock price stays unchanged for the year. HTH
I thought it was such a useful suggestion that I went ahead and created them. I'm sure you're not the only one who could derive some benefit from them, I know I will. http://www.investy.com/tools When I have some additional time, I will add the option for grace-periods, but for now I wanted to get them up so you could use the calculations as-is from the article. Enjoy. (Disclosure: I'm the founder of the site they are hosted on and I wrote the code for the calculators) Happy to help.   I always recommend you try and solve these types of problems by hand over financial calculators so that you can get a feel for how terms in the equation relate to one another. That's important while you're studying/learning.  But for work--by all means you should use the fastest method, which is probably excel. Many good sources on YouTube that you can find easily once you know what to look for.  Start following the stock market, present value / future value, annuities &amp; perpetuities, bonds, financial ratios, balance sheets and P&amp;L statements, ROI, ROA, ROE, cash flows, net present value and IRR, forecasting, Monte Carlo simulation (heavy on stats but useful in finance), the list goes on.  If you can find a cheap textbook, it'll help with the concepts.  Investopedia is sometimes useful in learning concepts but not really on application.  Khan Academy is a good YouTube channel.  The Intelligent Investor is a good foundational book for investing.  There are several good case studies on Harvard Business Review to practice with.  I've found that case studies are most helpful in learning how to apply concept and think outside the box.  Discover how you can apply it to aspects of your everyday life.  Finance is a great profession to pursue.  Good luck on your studies! You could create your own spreadsheet of Cash Flows and use the XIRR function in Excel: The formula is: Stop with all the stupid big words. You sound really pretentious. Just learn your 3 statements from accounting coach and learn statement analysis from streetofwalls.  If you're interested into valuation, streetofwalls is a good primer for DCF/public comps/M&amp;A comps/scenario analysis (LBO), but if you want to literally build out the model, Joshua Rosenbaum's investment banking valuation book is great. Everyone in banking I know used it to learn valuation The quant aspect '''''. This is the kind of math I was wondering if it existed, but now it sounds like it is much more  complex in reality then optimizing by evaluating different cost of capital. Thank you for sharing "First, don't use Yahoo's mangling of the XBRL data to do financial analysis.  Get it from the horse's mouth: http://www.sec.gov/edgar/searchedgar/companysearch.html Search for Facebook, select the latest 10-Q, and look at the income statement on pg. 6 (helpfully linked in the table of contents).  This is what humans do. When you do this, you see that Yahoo omitted FB's (admittedly trivial) interest expense.  I've seen much worse errors. If you're trying to scrape Yahoo... well do what you must.  You'll do better getting the XBRL data straight from EDGAR and mangling it yourself, but there's a learning curve, and if you're trying to compare lots of companies there's a problem of mapping everybody to a common chart of accounts. Second, assuming you're not using FCF as a valuation metric (which has got some problems)... you don't want to exclude interest expense from the calculation of free cash flow.  This becomes significant for heavily indebted firms. You might as well just start from net income and adjust from there... which, as it happens, is exactly the approach taken by the normal ""indirect"" form of the statement of cash flows.  That's what this statement is for.  Essentially you want to take cash flow from operations and subtract capital expenditures (from the cash flow from investments section).  It's not an encouraging sign that Yahoo's lines on the cash flow statement don't sum to the totals. As far as definitions go... working capital is not assets - liabilities, it is current assets - current liabilities.  Furthermore, you want to calculate changes in working capital, i.e. the difference in net current assets from the previous quarter.  What you're doing here is subtracting the company's accumulated equity capital from a single quarter's operating results, which is why you're getting an insane result that in no way resembles what appears in the statement of cash flows.  Also you seem to be using the numbers for the wrong quarter - 2014q4 instead of 2015q3. I can't figure out where you're getting your depreciation number from, but the statement of cash flows shows they booked $486M in depreciation for 2015q3; your number is high. FB doesn't have negative FCF." I feel like IRR is the tool you want to use for this, then you can look at your output and determine if it's higher than what your discount rate is likely to be.  Similarly, you can just do a traditional NPV analysis and then examine the sensitivity by changing the discount rate. If you're safely in profitable territory then you're probably fine despite not knowing the discount rate. The IRR is the Discount Rate r* that makes Net Present Value NPV(r*)==0. What this boils down to is two ways of making the same kind of profitability calculation.  You can choose a project with NPV(10%)>0, or you can choose based on IRR>10%, and the idea is you get to the same set of projects.  That's if everything is well behaved mathematically. But that's not the end of this story of finance, math, and alphabet soup. For investments that have multiple positive and negative cash flows, finding that r* becomes solving for the roots of a polynomial in r*, so that there can be multiple roots.  Usually people use the lowest positive root but really it only makes sense for projects where NPV(r)>0 for r<r* and NPV(r)<0 for r>r*.   To try to help with your understanding, you can evaluate a real estate project with r=10%, find the sum future discounted cash flows, which is the NPV, and do the project if NPV>0.   Or, you can take the future cash flows of a project, find the NPV as a function of the rate r, and find r* where NPV(r*)==0. That r* is the IRR.  If IRR=r*>10% and the NPV function is well behaved as above, you can also do the project. When we don't have to worry about multiple roots, the preceding two paragraphs will select the same identical sets of projects as meeting the 10% return requirement. "By the sounds of things, you're not asking for a single formula but how to do the analysis... And for the record you're focusing on the wrong thing. You should be focusing on how much it costs to own your car during that time period, not your total equity.  Formulas:  I'm not sure how well you understand the nuts and bolts of the finance behind your question, (you may just be a pro and really want a consolidated equation to do this in one go.) So at the risk of over-specifying, I'll err on the side of starting at the very beginning. Any financial loan analysis is built on 5 items: (1) # of periods, (2) Present Value, (3) Future Value, (4) Payments, and (5) interest rate.  These are usually referred to in spreadsheet software as NPER, PV, FV, PMT, and Rate. Each one has its own Excel/google docs function where you can calculate one as a function of the other 4. I'll use those going forward and spare you the 'real math' equations.  Layout: If I were trying to solve your problem I would start by setting up the spreadsheet  up with column A as ""Period"". I would put this label in cell A2 and then starting from cell A3 as ""0"" and going to ""N"". 5 year loans will give you the highest purchase value w lowest payments, so n=60 months... but you also said 48 months so do whatever you want.  Then I would set up two tables side-by-side with 7 columns each. (Yes, seven.) Starting in C2, label the cells/columns as: ""Rate"", ""Car Value"", ""Loan Balance"", ""Payment"", ""Paid to Interest"", ""Principal"", and ""Accumulated Equity"". Then select and copy cells C2:I2 as the next set of column headers beginning in K2. (I usually skip a column to leave space because I'm OCD like that :) ) Numbers: Now you need to set up your initial set of numbers for each table. We'll do the older car in the left hand table and the newer one on the right. Let's say your rate is 5% APR. Put that in cell C1 (not C3). Then in cell C3 type =C$1/12. Car Value $12,000 in Cell D3. Then type ""Down Payment"" in cell E1 and put 10% in cell D1. And last, in cell E3 put the formula =D3*(1-D$1). This should leave you with a value for the first month in the Rate, Car Value, and Loan Balance columns. Now select C1:E3 and paste those to the right hand table. The only thing you will need to change is the ""Car Value"" to $20,000. As a check, you should have .0042 / 12,000 / 10,800 on the left and then .0042 / 20,000 / 18,000 on the right.  Formulas again: This is where spreadsheets become amazing. If we set up the right formulas, you can copy and paste them and do this very complicated analysis very quickly.  Payment The excel formula for Payment is =PMT(Rate, NPER, PV, FV). FV is usually zero. So in cell F3, type the formula =PMT(C3, 60, E3, 0). Obviously if you're really doing a 48 month (4 year) loan then you'll need to change the 60 to 48. You should be able to copy the result from cell F3 to N3 and the formula will update itself.  For the 60 months, I'm showing the 12K car/10.8K loan has a pmt of $203.81. The 20K/18K loan has a pmt of 339.68.  Interest The easiest way to calculate the interest is as =E3*C3. That's (Outstanding Loan Balance) x (Periodic Interest Rate). Put this in cell G4, since you don't actually owe any interest at Period 0.  Principal If you pay PMT each month and X goes to interest, then the amount to principal is ""PMT - X"". So in H4 type =-F3 - G3. The 'minus' in front of F3 is because excel's PMT function returns a negative amount. If you want to, feel free to type ""=-PMT(...)"" for the formula that's actually in F3. It's your call.  I get 159 for the amount to principal in period 1.  Accumulated Equity As I mentioned in the comment, your ""Equity"" comes from your initial Loan-to-Value and the accumulated principal payments. So the formula in this cell should reflect that. There are a variety of ways to do this... the easiest is just to compare your car's expected value to your loan balance every time. In cell I3, type =(D3-E3). That's your initial equity in the car before making any payments. Copy that cell and paste it to I4. You'll see it updates to =(D4-E3) automatically. (Right now that is zero... those cells are empty, but we're getting there) The important thing is that as JB King pointed out, your equity is a function of accumulated principal AND equity, which depreciates. This approach handles those both.  Finishing up the copy-and-paste formulas I know this is long, but we're almost done.  Rate // Period 1 In cell C4 type =C3.  Payment // Period 1 In cell F4 type =F3.  Loan Balance // Period 1 In cell E4 type =E3-H4. Your loan balance at the end of period is reduced by the principal you paid. I get 10,641.  Car Value // Period 1 This will vary depending on how you want to handle depreciation. If you ignore it, you're making a major error and it's not worth doing this entire analysis...  just buy the prettiest car and move on with life. But you also don't have to get it scientifically accurate. Go to someplace like edmunds.com and look up a ballpark. I'm using 4% depreciation per year for the old (12K) car and 7% for the newer car. However, I pulled those out of my ass so figure out what's a better ballpark.  In G1 type ""Depreciation"" and then put 4% in H1. In O1 type ""Depreciation"" and then 7% in P1. Now, in cell D4, put the formula =D3 * (1-(H$1/12)).  Paste formulas to flesh out table As a check, your row 4 should read 1 / .0042 / 11,960 / 10,641 / 203.81 / 45 / 159 / 1,319. If so, you're great. Copy cells C4:I4 and paste them into K4:Q4.  These will update to be .0042 / 19,883 / 17,735 / 339.68 / 75 / 265 / 2,148.  If you've got that, then copy C4:Q4 and paste it to C5:C63. You've built a full amortization table for your two hypothetical loans. Congratulations.  Making your decision I'm not going to tell you what to decide, but I'll give you a better idea of what to look at. I would personally make the decision based on total cost to own during that time period, plus a bit of ""x-factor"" for which car I really liked.  Look at Period 24, in columns I and Q. These are your 'equities' in each car. If you built the sheet using my made-up numbers, then you get ""Old Car Equity"" as 4,276. ""New Car Equity"" is 6,046. If you're only looking at most equity, you might make a poor financial decision.  The real value you should consider is the cost to own the car (not necessarily operate it) during that time... Total Cost = (Ending Equity) - (Payment x 24) - (Upfront Cash).  For your 'old' car, that's (4,276) - (203.81 * 24) - (1,200) = -1,815.75 For the 'new' car, that's (6,046) - (339.68 * 24) - (2,000) = -4,106.07.  Is one good or bad? Up to you to decide. There are excel formulas like ""CUMPRINC"" that can consolidate some of the table mechanics, but I assumed that if you're here asking you would have gotten stuck running some of those.  Here's the spreadsheet: https://docs.google.com/spreadsheet/ccc?key=0Ah0weE0QX65vdHpCNVpwUzlfYjlTY2VrNllXOS1CWUE#gid=1" E&amp;P can be valid throug Net Present Value methods, on a field-by-field basis. As no field is ever-lasting, and there Are not an unlimited number of fields, perpetuity-formulaes Are shitty.  FCFF on a per-field basis with WC and Capex, with a definite lifetime.  Thank you for the compliment. Does it teach anything else other than the DCF approach?  I've already learned that in on of my financing courses. I'm more interested in the more exotic valuation techniques, and how to use and weigh multiple techniques for valuation. "To calculate the balance (not just principal) remaining, type into your favorite spreadsheet program: It is important that the periods for ""Periods"" and ""Rate"" match up.  If you use your annual rate with quarterly periods, you will get a horribly wrong answer. So, if you invest $1000 today, expect 6% interest per year (0.5% interest per month), withdraw $10 at the end of each month, and want to know what your investment balance will be 2 years (24 months) from now, you would type: And you would get a result of $872.84. Or, to compute it manually, use the formula found here by poster uart:   This is often taught in high-school here as a application of geomentric series. The derivation goes like this.  Using the notation :  r = 1 + interest_rate_per_term_as_decimal p = present value a = payment per term eot1 denotes the FV at end of term 1 etc.  eot1: rp + a   eot2: r(rp + a) + a = r^2p + ra + a   eot3: r(r^2p + ra + a) + a = r^3p + r^2a + ra + a ...   eotn: r^np + (r^(n-1) + r^(n-2) + ... 1)a = p r^n + a (r^n - 1)/(r-1)  That is, FV = p r^n + a (r^n - 1)/(r-1).   This is precisely what exel [sic] computes for the case of payments made at the end of each term (payment type = 0). It's easy enough to repeat the calculations as above for the case of payments made at the beginning of each term. This won't work for changing interest rates or changing withdrawal amounts.  For something like that, it would be better for you (if you don't want online calculators) to set up a table in a spreadsheet so you can adjust different periods manually." "Both models understand that the value of a company is the sum total of all cashflows in the future, discounted back to the present. They vary in their definition of ""cash"". The Gordon Growth model uses dividends as a proxy for cashflow, under the assumption that this is the only true cash received by shareholders. (In theory, counting cash is meaningless if there's no eventual end-game where the accumulated cash is divvied up amongst the owners.) The Gordon model is best used to value companies that have an established, reliable dividend. The company should be stable, and the payout ratio high. GG will underestimate the value of firms that consistently maintain a low payout ratio, and instead accumulate cash. There are multiple DCF models. A firm valuation measures all cash available to both equity and debt holders. A traditional equity valuation measures all cash that can be claimed by shareholders. While the latter seems most intuitive and pertinent to a shareholder, the former is very good at showing what a company can do regardless of their choice of capital structure. A small add-on to a firm valuation is the concept of EVA, or economic value add, where the return on capital (all capital -- both debt and equity) is compared to the blended cost of capital. The DCF model is more flexible (optimistic?) than the Gordon in its approach to cash. The approach can be applied to many types of companies, at every stage in their maturity, even if they don't pay a dividend. A simplistic, or single-stage DCF is similar to the Gordon. The assumption is that the company is fully mature, growing at a rate perhaps just slightly above inflation, forever. For younger companies a multi-stage DCF can be employed, where you forecast fairly confident numbers for the next 3-5 years, then 3-5 years beyond that the forecast is less certain, but assumed to be slowing growth, and a generally maturing, stabilizing company. And then the steady-state stage is tacked on to the end. You'll want to check out Professor Aswath Damodaran's website: http://pages.stern.nyu.edu/~adamodar/ . He addresses all this and so much more, and has a big pile of spreadsheets freely downloadable to get you started. I also highly recommend his book ""Investment Valuation"". It's the bible on the topic." **Using your Time Value of Money functions on your calculator**   N = 3x2 = 6   PV = -914   PMT = (.16 x 1000)/2 = 80   FV = 1000    Compute I/Y  Or     **Step by step calculations**   1) Compute the PV of **(FV of Bond)**1000 in **(3x2)**6 periods at **(16%/2)**8% with no payments   2) Compute the PV of an Annuity of **(.16/2x1000)**$80 payments over **(3x2)**6 periods with an interest rate of **(16%/2)**8% and 0 Future Value   3) Combine the values from Steps 1 and 2