Suppose I offered to give you either $1000 in June 2006 or $150 every June for the next 10 years, starting in 2007. Which offer is worth more? How would you figure this out? The answer is: by calculating discounted cash flows.

Discounted Cash Flow or DCF analysis is one of the first things taught in finance class in an MBA program. It’s a natural consequence of the time value of money, which states essentially that a dollar today is not worth the same as a dollar in the future. Discounted Cash Flow analysis is most commonly used to value a project or company (or lottery payout, as in the simple example above) using a discount rate or weighted average cost of capital, also abbreviated as WACC. (Did I forget to mention finance is big on acronyms?)

Determining an appropriate discount rate or WACC can get complicated, so for now, we’ll just simplify it and call it a percentage rate that we use to “discount” future cash flows to the present. For example, if you earned $100 every year, you can imagine that the $100 you earn 10 years from now won’t be worth the same as the $100 you earn this year. Inflation, the return you could be getting on the $100 during that time, risk, all sorts of aspects can play into evaluating what $100 in 2016 is worth in 2006.

If you’re working in corporate finance, chances are Treasury or some other official department has dictated an “official” cost of capital to use in your analysis. On this site, when I calculate Experiments in Finance’s NPV each month, I choose to use an annual rate of 5% as my discount rate, remembering to change this to its the monthly equivalent rate since I’m calculating monthly cash flows. My reasoning is that the cash flows for this project aren’t large, and a comparable activity of similar risk might be to put the money in a saving’s account instead. This is one of those situations where finance is more like art than science. You could argue ’til you were blue in the face about what the “right” cost of capital to use should be, but in the end it may not matter too much, especially if you conduct a sensitivity analysis using different rates.

Let’s get back to talking about DCFs. Discounted cash flow analysis essentially takes the cash flows for each period and discounts them back to the current moment. So, suppose we have cash flows of $100 starting next year for the next 10 years, and our discount rate is 8%. Then what we’re calculating looks like the following:

DCF = $100/(1+0.08) + $100/(1+0.08)

DCF = $100/(1+0.08) + $100/(1+0.08)

^{2}+ $100/(1+0.08)^{3}+ … + $100/(1+0.08)^{10}(In this particular case, we’ve set a constant $100 per year as our cash flow. If we were receiving different amounts each year instead, say, $100 every year, except for $150 in year 2 and $1000 in year 10, then we’d simply plug in those amounts instead in their respective years.)

What you’re doing is essentially “bringing back” the future cash flow to the present time, using the discount rate of 8%. This means that the value of receiving $100 every year for 10 years isn’t $1000 but $671. In fact, receiving $100 at the end of this year isn’t the same as having the cash in your at the beginning of the year. It’s worth $100 less the amount you would have earned in interest had you had it at the beginning of the year. And the $100 you earn two years from now is worth $100 less the amount you would have earned in compound interest over the two years. And so on. This is why wise articles about how much you need to save for retirement often result in seemingly large amounts.

Getting back to our original example, it turns out that if you assume a discount rate (which might represent the constant interest rate you can earn on your money) of 8%, then having $1000 in your pocket now versus having $150 for the next 10 years is the same. But if you assume that you can only earn 5%, then the stream of income is a better deal ($130 per year is the breakeven).

Discounted cash flow analysis is the basis of many things in finance, including Net Present Value or NPV, bond prices, annuity pricing, and many more. NPV and DCF calculations are one of the most frequently used finance tools for valuation purposes. But, like everything else, they have their limitations and are simply tools. If your numbers aren’t accurate to begin with, adding and dividing them will only result in a worse answer. DCFs and NPVs are also pretty inflexible. If future earnings and cash flows are very uncertain, or management has the option of changing a project midway through, then this type of analysis may not be the best way to go. In those cases, Real options or Monte Carlo might be more complex but better tools to use.

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## Flexo

Excellent article! Thanks for putting it together.

## How to calculate net present value (NPV) | Experiments in Finance

[...] Corporate finance I’ve been meaning to write a bit about NPV after having discussed how to calculate discounted cash flows and using NPV to calculate the valuation of this site. Since I haven’t written about corpoate finance in a while, I thought this might be a good change of pace. [...]

## How to calculate an internal rate of return (IRR), and when not to use it | Experiments in Finance

[...] Calculating the internal rate of return (or IRR) of a project is one of the most popular methods that companies and managers use to determine whether a project is worth investing in. Now that I’ve covered a bit about NPVs and DCFs, it makes sense to go through what IRR is, how to use it, and why it’s not an ideal measurement. [...]

## pitre

Simple and clear – excellent article!! Thanks

## Michael Lawrence

I have a real world problem. Can you help me? I am due a percentage of rent receipts, payable February 1, every five years. A payment of 237K is due 2/1/08.

Using 2.5% rent increases per year (below average the past 20 years); the payment schedule looks like this: 2013 = 360k; 2018=512k, 2023=634k, 2028=750k, 2033=884k, 2038=1,039k, 2043=1,204k,

2048=1,396k. What is the present value?

Is this kind of income stream something I could use to pay for a house? How to best structure a deal that is fair to both sides?

Thank you for your kind assistance. I am in over my head on this.

## rey

how wacc is computed? What is the importance of WACC?

## shahida

Hi,

i just need to check whether it is appropriate to use terminal value for the year 12 onwards? or terminal value is only appropriate to use only after 5 years?

## Muhammad Jasim

Simple and clear…just the way I wanted for my exams.Thank you!

## Adriana

If I want to do a projection of how much an investment of $500/mo would be at 9% interest for 30 years, do I use annual or effective rate of return? Thanks — ap

## P.Devaraj

Excellent, very simple and specific in approach, even a non economist can understand. Thank you.

## Mohd Qasim

i want to know how to make formulas in MS-Excel sheet for IRR,NPV etc.

## Mumtaz Ahmed Tabassum

I subscribed as per requirement, but could not be able to download solve excel problems. any body can give me tip or solution….

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