For some ten years I have advised students in my entrepreneurship class to use a 40% discount rate in their lifetime value calculations. Every semester someone decides to take advice they found on the internet and use a much lower rate. It does seem like, of the advice given, mine is at the high end. For instance:

Since the contribution for customers paid in years further out in the future is less valuable than those paid in more recent years, it is important to discount these future cash flows to the company. Although the "ideal" discount rate factors in the beta to account for the riskiness of the cash flows, one can stick to a shorthand of using something like 10%.

— Eisenmann, T., "Business Model Analysis for Entrepreneurs," Harvard Business School note 9-812-096, October 24, 2014.

Tom and I agree that calculating things like LTV is important (he talks extensively about it in his excellent *Why Startups Fail*.) But I think his rate is way too low. Of all the suggested discount rates I have seen, all of them are too low. In fact, my suggestion of 40% is probably too low.

This may seem like a dumb thing to get worked up over, but it makes a difference. A hundred dollars ten years from now is worth $39 today if you discount it at 10% per year; it is worth about *$3.50*—less than one-tenth the amount—if you discount it at 40% per year. For things that last a long time the rate makes a huge difference. But even for customer lifetime value, where the average lifetime may be much shorter, say three years, that $100 is worth $75 at 10% but only $36 at 40%. If you use 10% instead of 40% you double the estimated value of a prospective customer. If this is a faulty assumption you will end up investing in marketing strategies that suck value out of your company.

So it’s important who you believe: me or the boffins at HBS.

Here’s the short answer: Your investors will expect a certain return on their investment in your company and, to meet that expectation, your discount rate must be *at least* as high as their expected return. That is, the rate you use inside the company—call this the **inside rate**—must be at least as high as your investors’ expected rate—call that the **outside** rate.

## IRRs and discount rates

Investors expect to make money from their investment in a company.

The dream of every investor is for the money coming out to be larger than the money going in: to have a gain on investment. If an investor puts $1 million into an company and gets $5 million out, they have a $4 million gain and the return on their investment (their ROI) is $4 million/$1 million = 400%.

Investors also care about the timing of when they get the money back, because a dollar today is worth more than a dollar tomorrow. They calculate the return on investment per year (or per any time period) to get something called the internal rate of return (the IRR).

Here are two example investments. The first invests $50 and returns $20 per year for ten years. The second invests $50 and returns $200 ten years from now but nothing until then. Both have the investment and return, and thus the same gain and ROI—($200-$50)/$50 = 300%—but the timing is different. The first has a 66% IRR because the money, on average, comes in sooner, and the second has an 17% IRR.

A higher IRR investment is a better investment. Investors try to find the highest IRR they can.^{1}

The same thinking applies when you run a company. Inside the black box are various projects that need money and the CEO has to allocate capital among them.

When a CEO is allocating capital, they want to choose the highest IRR projects they can find first. This is simple in theory and hard in practice. Estimating future cash flows is prone to error and subject to uncertainty; projects interact and can add value to each other; defining the scope of a project so all receipts and disbursements are included can be hard; etc. There are also other considerations than IRR, like the cash flow itself. A project may have a higher IRR but the cash won’t arrive for five years. These receipts might be needed to pay salaries before then. Despite these limitations, doing the work to figure out the expected IRR of projects is a useful tool in deciding how to allocate capital.

The amount of cash generated by the company can’t be more than the sum of the cash generated by the sum of its projects, so the IRR of the company as a whole can’t be more than the weighted average of the company’s projects.^{2} To generate a specific outside rate, the company’s projects must average at least that rate. The outside rate can be no greater than the average inside rate.

But this isn’t strict enough: if *any* project has a lower IRR than the outside rate it should not be funded. The owners of the company are better off if the company just gives that project’s money back to them. The company should not undertake any projects that they expect to have a lower IRR than the outside rate. The outside rate is the **hurdle rate** for any project: if the company does not expect the project to jump that hurdle, the project should be canned unless there are strategic reasons not to. (There are situations where a lower IRR project may be valuable to the company for learning or reputation or a million other reasons that are hard to quantify in a spreadsheet. Things like LTV are tools, not rules.)

The inside rate must be greater than the outside rate.

## An Aside on Operationalizing the Discount Rate

Instead of ranking projects by IRR, companies often instead find each project’s net present value (NPV) using the hurdle rate. That is, they discount the cash flows of the project back to today using the hurdle rate as the discount rate. If the resulting NPV is positive that means the IRR for that project is higher than the hurdle rate. If it is negative, the IRR is lower than the hurdle rate. It’s just math. The higher the NPV, the higher the IRR.

Here’s the first example above but using a discount rate of 40% to get the NPV.

The IRR of this example was 66%. Since this is greater than the 40% hurdle/discount rate, the NPV is positive.

Here’s the second example, also using a discount rate of 40%.

The IRR of this example was 17%. Since this is less than the 40% hurdle/discount rate, the NPV is negative. The company should reject this project.

Companies use NPV to rank projects instead of IRR because NPV is easier to work with. For instance, many investments can be separated into (i) a one-time, immediate spend and (ii) over-time receipts. Using the NPV makes it easier to compare the upfront with the ongoing. It’s easy to see in the second example that if you lower the upfront spend by a bit more than the negative NPV, the NPV would become positive and thus the project would have an IRR greater than 40%. This is impossible to intuit when you’re looking at a raw IRR number. Here’s the second example with the upfront spend lowered by $41.

## So, What is the Outside Rate?

In standard corporate finance, the outside rate is called the company’s cost of capital. It is the weighted average of the interest rate on the company’s debt and the expected return investors demand on equity financing. The interest rate is explicit: it’s in the debt contracts. The the cost of equity is implicit, it is usually calculated using the capital asset pricing model, the CAPM. This uses the variability of the company’s stock compared to the overall market (the *beta*) as a stand-in for risk and then uses the two known risk/return points—the risk-free rate and the risk of the entire market—to draw a line along which all other risk/rewards are found. Finding the point on the line that corresponds to the company’s beta yields the company’s cost of equity. The riskier the stock, the higher the rate demanded.

Most venture-backed companies are primarily equity-financed, so we can just use the cost of equity as the outside rate. But we aren’t going to use the CAPM to figure out what that rate is, for two reasons.

The first is that we don’t have a measure of risk to feed the formula. The equity of venture-backed companies is rarely traded, so it is impossible to get valid measurements of beta. Some analysts use betas of comparable public companies to estimate the betas of private companies, but this is sketchy. The trading of a public company’s stock reflects the view of a large pool if investors: many are buying or selling based on their assessment of that particular company’s systematic and idiosyncratic risk. That is, their views on the riskiness of the company result in its beta, not vice-versa. As an investor who doesn’t have a fundamental view of a company’s riskiness, you can assess the wisdom of that crowd by back-solving from the beta to the risk. But using that beta for an entirely different company only covers the systematic risk. Venture-backed companies are primarily idiosyncratic risk, so using some other company’s beta is a bad idea.

The second is that we have a much easier and more direct way of knowing the outside rate: just ask the investors. VCs are like companies in that *they* have an outside rate as well: what their LPs expect them to return. (Perhaps the LPs are motivated by CAPM in some way, perhaps they are not, but it doesn’t really matter for our purposes.) What matters is that VCs will not invest in companies they expect to return less than their outside rate.

Plenty of people have asked VCs what rate of return they must get from their investments. A report from KPMG nicely summarizes some results.^{}

These rates are high. Much higher than a CAPM analysis would indicate. David Skok ran the CAPM numbers and came up with a 20% rate, half the rate VCs actually use.

Failure-adjusted, these rates make sense. The historical return for venture to LPs is about 20% per year. This should reflect pretty closely the risk of investments in venture funds. To achieve a 20% IRR to LPs, venture funds must get a 25% IRR from their portfolio companies (the remaining 5% goes to the VCs themselves as carry: 5% is 20% of 25%.) If half the portfolio companies fail, and the remainder exit after six years, the successful companies must generate an ~40% IRR.

There are some economists who think VCs should not adjust their discount rates for the possibility of failure, they should instead adjust the expectations of return for the companies they invest in and use a non-adjusted discount rate. This argument is flawed: moving the numbers around in the spreadsheet does not change the amount the investor must receive *from the companies that succeed.* Since no one knows which companies will succeed and which will fail, the investor must *expect* the higher return from all of them.

## The Consequences of Ignoring the Discount Rate

If a company does not pay interest to a lender, there are legally enforceable consequences. But not meeting the return to equity expectation is different: these expectations were probably never discussed explicitly and they certainly aren’t mentioned in any contract.

But the price the venture investor paid was derived from assumptions about the company’s growth. And the company’s growth is generated by investing the investor’s money in projects that have a sufficiently high return. If the company’s internal investments don’t meet that return, the company grows more slowly than expected. This will certainly be noticed by the investor. It will also be noticed by any prospective investors in the next round. If the inside rate is lower than the hoped-for outside rate, the company will face either a management change or a disappointing next round. This, of course, does not *necessarily* happen. The idea that corporate projects must have an IRR that exceeds the hurdle rate is not a law etched in stone, as corporate finance textbooks would have it. If a CEO decides to proceed with a project that doesn’t beat the hurdle rate the corporate cops don’t coming screaming up on their damodarancycles and haul them away. But if the CEO either can’t find internal projects with a high-enough IRR or decides to back lower-IRR projects for some other reason, the resulting slow growth will cause problems with the VCs.

In the best case, CEOs will have plenty of projects to allocate capital to, and will choose the ones with the highest potential returns. This may mean the advice to use 10% or 20% as the discount rate makes no difference because there are enough 40%+ IRR projects to soak up all the money anyway. The danger of a too-low discount rate is when the startup has more uncertain prospects. If the CEO decides that projects with a 10% IRR are good enough to satisfy investors and stops looking for better returning projects, they will be surprised when their investors blame them for underperforming.

In theory. In reality this is a bit trickier. If someone promises you $101 tomorrow for $100 today, this is an extremely high annualized IRR. It’s a much higher IRR than someone promising you $500 a year from now for $100 today. But some investors may prefer the latter because they don’t expect they will get the former every day of the year, or perhaps ever again. The latter promises an absolute gain of $400. The former an absolute gain of only $1. If that $1 then just sits around for a year, that’s all the investor will get. In other words, it’s not a perfect market and you have to take that into account if you’re doing more than writing a blog post. ↩

Remember, this is a simple model: some projects don’t meet expectations and some beat them; sometimes the money isn’t returned to the investor but instead reinvested in projects; and some of the cash goes to pay for things that are necessary but don’t generate cash themselves—like perhaps accounting. ↩

The sources for KPMG’s numbers are:

- Plummer, JL, "QED Report on Venture Capital Financial Analysis." (Palo Alto: QED Research, Inc., 1987.)
- Scherlis, DR and Sahlman, WA, "A Method for Valuing High-Risk, Long Term, Investments: The Venture Capital Method", Harvard Business School Teaching Note 9-288-006. (Boston: Harvard Business School Publishing, 1989.)
- Sahlman, WA, Stevenson, HH, Bhide, AV, et al., "Financing Entrepreneurial Ventures, Business Fundamental Series." (Boston: Harvard Business School Publishing, 1998.)
- Damodaran, A., "Valuing Young, Start-up and Growth Companies: Estimation Issues and Valuation Challenges." (Stern School of Business, New York University, 2009.) ↩