Terminal Growth Rate
Is the rate at that a company is assumed to grow beyond forecasted cash flows
In short, it is the rate at that a company is assumed to grow beyond forecasted cash flows. This is particularly important because, when performing valuation analysis, we are dealing essentially with assumptions to project our cash flows.
However, since they are all assumptions, their uncertainty rises as we go further into the periods. So we can be reasonably sure of the range of revenue growth for the next quarter, for instance, but not sure about the growth five years from now.
为了考虑到我们预测的一定时期之外的这种不确定性，我们必须假设一个代表超过该特定日期的所有未来现金流量的价值。为此，我们可以假设公司将以一定金额出售，或者derive a terminal value。
Since that terminal value represents the future cash flows, it is also built upon assumptions. Those assumptions, however, are different from the ones that underlie our projections. While at the start of the model, we had a lot of assumptions to build up our cash flow projections. Now we are essentially dealing with only one.
这样做的原因是我们正在寻求单一数量而不是一系列现金流。
When we talk about cash flows, the main concern is how they will grow over time, so our main assumption will be the rate at which they will grow forever. We then use that rate to arrive at a figure that accounts for that growth变成永久性。
That rate is exactly our terminal growth rate.
Understanding terminal growth rate
When performing valuation analysis, we are concerned with cash flow estimates, as the company's value is directly linked to them. However, since these future cash flows are based on assumptions, they may get a little out of touch when we stretch the projections too far into the future.
Now, let's recap how a估值过程有效。可以通过两种主要方式完成：可比和内在估值。终端增长率与现金流的概念有关，这与内在估值有关。
We use a折扣现金流模型确定企业在内在估值分析中值得多少。其背后的理论是，资产值得未来的现金流量，其折扣价为现值。
因此，为了估算这些现金流，我们建立了诸如收入增长，存货周转率rates, operating profit margins, etc. They may be accurate, but they are still assumptions.
As we project our cash flows for future periods, we can only be so certain. There comes a time when our assumptions will hold no value due to the natural unpredictability of events.
The terminal growth rate arises from a flaw inherent to intrinsic valuations - the accuracy of the assumptions.
This is exactly where the idea of terminal value comes in. When our assumptions start to look imprecise due to being too distant, we must assume the company will generate a certain amount of cash to discount it to present value.
NOTE
In short, we need a value that represents the cash flows beyond that date.
面对这个问题时，分析师有两种选择：
- 使用可比的公司从那时起，倍数得出其终端值
- Use the growth rate using the perpetuity method.
The first method takes a comparable multiple to find what the company will be worth at a point in the future.
例如，假设我们采用EV/EBITDA多重8。0 times. Then, we would multiply this figure by the projected EBITDA figure and得出企业价值at the terminal date.
From this point onwards, both methods are the same. Once we have this value in hand, we then sum it to all the other forecasted cash flows and discount them to present value using anappropriate discount rate。
最终目标是相同的。两者之间的变化是我们如何达到终端价值及其理由。
在第一种方法中，我们使用了可比的估值技术，这可能与intrinsic value approach。
对于我们感兴趣的第二个，我们假设现金流的一定增长率超出了某个时间点，称为增长率。
Also, in the second method, we derive a rate at which the company will grow forever, so it is, at least in theory, based on fundamentals.
The growth rate approach is known as the perpetuity method, as it assumes the company will exist forever and grow at a constant rate.
The perpetuity method
The method is built upon Gordon's Growth Model. It is an economic model aimed at estimating thefair valueof a stock in the future, and it has two key assumptions.
- 股息被视为现金流量
- The company will exist forever and will grow at a constant rate.
It was originally conceived to be used with dividends, but it can also be used with free cash flows as long as we assume they are the same.
It takes three inputs: thefree cash flowto the firm of the last forecast, the discount rate, and the assumed growth rate.
The formula is as follows:
Terminal Value=FCFF*(1+ g)/(WACC - g)
Where g is the growth rate, we take the discount rate equal to the WACC.
Notice that the growth rate must be less than the WACC for the formula to work. The rationale behind it is that, in perpetuity, companies are not expected to grow more than their cost of capital. It just would not make sense because, in the long term, it would mean the company eventually becomes larger than the entire economy.
In simple terms, it means that a company just isn't supposed to grow more than the risk it carries to investors.
To estimate the growth rate, we must be conservative. We can take the GDP of a particular economy as a proxy for the same.
By taking the growth rate to be lower than the GDP projections, we assume the company will not outgrow the overall economy in the long run, which would be an absurd assumption.
一旦我们拥有终端价值数，我们就可以将其放在DCFand discount it to the present value as if it were just a regular cash flow.
Estimating the growth rate
假设我们正在进行公司的估值A。在我们所有的所有假设和计算中都进行了估计，我们估计未来5年的未来现金流量。现在，我们必须估算终端价值。
The key question here is:How would we estimate the growth rate?
To make a sound assumption, we must keep in mind that we estimate a growth rate for perpetuity. That is, if the company were to continue growing and expanding forever, obviously, in practice, that would never be the case.
Also, remember the theory behind the estimation. We estimate the terminal value simply because we need a value to bring to the present value beyond a point our initial assumptions would no longer be reliable.
Now, to make a sanity check on our growth rate assumption, there are two key rules we must follow:
- The growth rate has to be greater than thehistorical inflation rate
- The growth rate has to be less than the historical GDP growth rate
To understand why our assumption must be between these two macroeconomic rates, we must first understand their meaning.
Inflationis a measure of economic activity. Since many variables get factored into the inflation figure, its headline number is not accurate for certain sectors.
When the经济升温，价格上涨，通货膨胀也是如此。因此，我们可以将通货膨胀率理解为经济活动的衡量。
On the other hand,GDPis anindicator of economic growthand is the sum of the value-added from all the goods and services produced t in a given economy.
We want to be conservative and thoughtful in our estimation. To achieve that, we must consider our growth rate to be higher than the historical inflation and lower than the historicalGDP。
The reason why we assume the growth rate to be greater than the inflation rate is that we are estimating the nominal figure for terminal value. So we have to consider the inflation effect.
Breaking down the calculation
终值的公式考虑three things:
1. Free Cash Flow to the Firm
From a valuationperspective, this figure is obtained viafinancial modeling。It represents how much cash is available to all stakeholders (debt and equity holders) in the company irrespective of their position in the capital stack( net of taxes).
Since we want freecash flow for allstakeholders, we must subtract the营运资金expenses and capital expenditures from theEBIT图（税收净）。
We consider the tax expense based on theEBITfigure to account for the tax shield effect of taking on debt.
当公司承担债务时，他们可以推断出interest expense从税单。鉴于我们对所有利益相关者的核算感兴趣，因此我们必须从EBIT数字中折扣税额。这样，我们可以掌握税收的自由现金流网。
2. Discount Rate
It is the same rate that is used in thediscounted cash flow。Usually, it is theWACC。WACC是cost of capitalfor the business, and it is a weighted measure between thecost of debtand thecost of equity。We can further break it down into its two components:
- Cost of debt: It is how much the company has to pay its debt holders to guarantee debt financing. It is the yield on the company's outstanding debt.
- Cost of equity:股权代表返回investo的成本rs expect to obtain from acquiring the company's shares. It is closely related to theconcept of opportunity cost，并考虑到三个不同的因素。
- The risk-free rate: It is the floor rate for the cost of equity calculation. Any excess return investment may yield must be above the country's risk-free rate. Otherwise, it wouldn't make much sense to invest in a riskier asset class without having higher returns.
- Equity risk premium: The equity risk premium is the extra yield compared to the risk-free rate that investors will earn by investing in the company.
This can be understood in terms of a risk-reward equation; if an investor is purchasing a riskier stock than others, then the reward must also be higher to compensate for the risk taken.
- Beta: Beta essentially measures how the company performs relative to the market. It is derived from the concept of standard deviation in statistics.
In practice, investors use it to assess a company's stock volatility. A beta greater than 1 means the stock is comparatively more volatile than the market, and a beta lower than 1 means the stock is more stable than the market.
Putting it all together, we came up with the WACC, which is used as the discount rate.
3.增长率
增长率是终端价值的关键部分，因为它们与同一概念密切相关，即超过特定预测期的现金流量的价值。
查看终端值的公式，我们注意到增长率不得大于WACC。But why?
请记住，我们正在评估公司的增长到永久性。由于WACC是企业资金的成本，如果我们假设增长率高于它，我们将假设一个永恒arbitrage opportunity would被创建，这是没有意义的。
The internal rate of return (IRR) for the investment must be greater than the WACC for our allocation to make sense. The reason for this is rooted in the concept of risk and return.
A company will always try to ensure that the capital is allocated to generate a higher return than the cost of capital; otherwise, it will result in an unprofitable equation for the firm.
Shortcomings
终端价值有两种主要方法：exit multiplesand the growth model.
While multiples are a relative form of valuation, in practice, they are used much more frequently because they allow a simpler and quicker calculation. Most importantly, they rely on fewer assumptions than the growth model.
Assumptions are a big element l in financial valuation and can make or break a model. The quality of assumptions relies on a fundamental feature: the timeframe for which it stands for.短期假设比长期假设更可能是可靠的。
The shortcoming for the growth method lies exactly here, no matter how conservative our assumptions are, they are fundamentally compromised simply by being too far into the future.
常见问题解答
It depends. Mostly on the company, you are assessing and the industry it operates in. A general rule of thumb would be that industries in the growth stage can be modeled with a higher growth rate than mature ones.
Our main goal is to be conservative and not overstate the growth prospects. So if 2% is reasonably below an optimistic projection for the company, it should be fine.
The calculation for the终值using comparables multiples is much more quickly since all we need is to obtain the companies' comparables (which we can easily do online)
On the other hand, finding a reasonable assumption for the growth rate is not such a simple task because there are many factors involved and many other assumptions included. That is why it is the route usually taken by academics.
Remember, we need to stay conservative? That is one of the reasons. Keeping conservative and reasonable assumptions allow us to keep our projections within reach.
The key here is to be conservative to all variables. We don't fully understand how they will behave in the future, and as we gather more data about the company, we may be able to tweak our assumptions.
It is, especially if wetake the terminal valueby the multiple approaches.
这可能发生，因为多个估值是比较分析。这不取决于我们的假设。
因此，尽管我们最初的假设返回不准确的现金流量，但最终价值数字是可靠的，因为它是通过市场研究获得的。
假定通过市场研究的信息是可靠的，因为该分析是基于市场效率假设的。
它指出,如果市场,事实上,高效,they have already priced in the company's performance, then its multiples should be reliable for benchmarking between its peers.
Researched and authored by Lucas Amorim |LinkedIn
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