Perpetuity Valuation – Navigating the Infinity
Recent years have witnessed an astronomical rise in business acquisitions. The acquisition decision is primarily dependent on the cash flows that will be generated in the future. This future outlook is not limited to the next 5 or 10 years but extends to perpetuity.
Perpetuity in the context of valuation is defined as the present value of cash flows beyond the projected period. Terminal Value, or perpetuity, is primarily the highest contributor to fair value using the Discounted Cash Flow Approach and goes beyond the formula used to compute it.
This article aims to provide an intricate understanding and application of the perpetuity calculation.
How is Perpetuity an abyss in Valuations?
Profound means having an intellectual depth and insight or something that is difficult to fathom or understand. In the world of valuation, perpetuity is incredibly profound in the sense that the calculation of perpetuity is made for a future that is immeasurably deep unless we apply assumptions and make use of mathematical calculations to bring the perpetuity towards the present.
In a valuation exercise involving companies in the early stages of their growth or start-ups, perpetuity constitutes a substantial portion of the business valuation computed using the Discounted Cash Flow method. In most cases involving the valuation of start-ups, it can be more than 100% of the Enterprise Value through DCF.
Is the percentage normal? Yes, in the sense that most start-ups or early stage companies are spending heavily on software infrastructure, advertising, and customer acquisition for scaling the business, and cash flows from operations take a significant hit. The cash flows typically stabilise after 5-10 years of inception, the caveat being that the business is successful and hasn’t already shut down.
Future Maintainable Cash Flows
The main concept to observe in the analysis of perpetuity is that perpetuity is computed on the basis of future maintainable cash flows. Future maintainable cash flows are the cash flows that an entity believes it can generate on a sustainable basis.
The characteristics of future maintainable cash flows are:-
- The cash flows should be derived from a long-term perspective.
- The cash flows should be free from any anomalies or non-frequent changes in either revenue, costs or tax considerations.
- It is expected to grow at a stable rate which is known as the long-run growth rate. The long-run growth rate is typically less than the Gross Domestic Product (GDP) Growth Rate for the economy being operated in.
Future maintainable cash flows are generally plugged as either the free cash flows for the last year of the explicit period or computing the same after starting with revenue and subsequently making the adjustments for profit margins, depreciation, working capital and capital expenditure as per the long-term assumptions adopted by the valuer.
Sample calculation for Future Maintainable Cash Flows
| Particulars | Terminal Value (Amount in ₹) |
|---|---|
| Total Revenue (Excluding Other Non Operating Income) | 5,000.00 |
| EBITDA | 2,500.00 |
| Depreciation & Ammortisation Expenses | -50.00 |
| EBIT | 2,450.00 |
| Tax on EBIT | -750.00 |
| Net Operating Profit adjusted for Tax (NOPLAT) | 1,700.00 |
| Adjustments: | |
| Depreciation | 50.00 |
| Changes in Operating Working Capital | -450.00 |
| Capital Expenditure | -250.00 |
| Future Maintanable Free Cash Flows to Firm (FCFF) | 1,050.00 |
Calculation of Terminal Value
Terminal Value can be computed in multiple ways but it is specifically limited to the three approaches listed below:-
- Multiple Approach: Applying the earning or sales multiple to arrive at the terminal value
- Constant Growth Approach: Assuming that the cash flows will grow at a constant rate for perpetuity
- Liquidation Value Approach: Assuming Liquidation in the Terminal Year and estimating the Liquidation Value
The most widely used method of computing terminal value is on a going concern basis using the Stable Growth Approach in India as well as overseas. This is a plain vanilla approach which perfectly fits in standard valuations and only warrants a method change when the business to be valued doesn’t necessarily has a terminal value. For example, in case of a company entering into a joint venture for only 10 years, the perpetuity value of the JV will not be computed and cash flows for only 10 years will be taken into account for the purpose of valuation.
Formula and Interpretation of Terminal Value
1. Multiple Approach
In the Multiple Approach, terminal value (TV) is computed by applying a valuation multiple to the variables for arriving at the enterprise or equity value. The multiple is arrived at by analysis of comparable companies listed on the stock exchange or by looking at transaction multiples available in the market.
Inputs →
• EV/Sales Multiple: 10 Times
• Sales of the company after 5 years: ₹1,000
Computation: Terminal value = ₹1,000 × 10 = ₹10,000
Interpretation: The challenge of using the multiple approach is that the multiplier to be used is related to the terminal period. Obtaining forward looking multiples is a challenge in itself on the valuation date, and using the same as a plug in the terminal period is a near impossible task due to the limited availability of data. 1 Year and 2 Year Forward EBITDA/Sales Multiples, or PE Multiples, are not readily available for the Indian markets.
2. Constant Growth Approach
Constant or Stable Growth Approach is the assumption that the cash flows beyond the projected period will grow at a constant rate until perpetuity. Cash flows can be either Free Cash Flows to the firm or Free Cash Flows to Equity. Accordingly, the discount rate will be WACC or Cost of Equity Ke.
Where:
- FCFn is the Future Maintainable Free Cash Flows
- g is the long-term growth rate
- r is the required rate of return [WACC or Ke]
Inputs →
• Future Maintainable Cash Flows: ₹1,000
• WACC: 15.00 %
• Growth rate = 5.00 %
Computation:
TV = ₹1,000 × (1 + 5.00%) / (15.00% − 5.00%)
TV = ₹1,000 × (1.05) / (10.00%)
TV = ₹10,500
Interpretation: Constant Growth Approach has relatively simple calculations and is the most widely used method of computing terminal value. This is also the most manipulated approach since it can be used to reflect biases and ultimately used to arrive at the desired value.
3. Liquidation Approach
Liquidation value is the amount of proceeds available to the equity shareholders after the business ceases operations and settles the dues to its creditors, employees, statutory dues, as well as payments to debentureholders and preference shareholders. One way to estimate this is to assume the value that the assets remaining at the end of the projected period will fetch when sold and to deduct the payables from the proceeds. The value that emerges is the liquidation value.
Inputs →
• Book Value of assets: ₹1,000
• Book Value of debt and all payables: ₹500
• Estimated sale proceeds from liquidation: ₹800
• Estimated liabilities to be settled on liquidation: ₹600
Computation:
TV = ₹800 – ₹600
TV = ₹200
Interpretation: The estimation of Terminal Value using Liquidation Approach involves high level of professional judgement to arrive at the Liquidation Value. Further, this approach does not take into account the earning power of the assets and only considers the Liquidation Value. In order to counteract this, we can use alternative method by taking the expected cash flows generated by all the assets and discount the same to arrive at its present value. Estimating the cash flows from a group of assets employed by the business entity is a challenge in itself.
Growth Rate Considerations
Growth rate is also an important factor in calculation of as well as directly proportional to the terminal value. The higher the growth rate, the higher the terminal value and vice versa. Growth rate is ideally less than the forecasted GDP growth rate of the economy in which the company operates. For example-If the valuation is being done for computing the fair value of equity shares of a company situated in India, the value to be used is lower than India’s forecasted GDP growth rate as per the latest available government data.
It is absolutely critical that no arbitrary value is plugged in the growth rate for the terminal value as the output is magnified exponentially and the results would be distorted. The valuer has to exercise significant care that the growth rate taken is from credible government sources and there must be a proper explanation for taking the same among the growth rate available to the valuer.
An ideal way to consider the growth rate is that if the nominal growth rate is 6.3%, then the growth rate to be adopted by the valuer is in the range of 4-5% depending on the company and economic factors such as product offering of the company, elasticity of demand, Indian/global footprint and intellectual property or intangible available.
As per the World Bank’s forecast for the Financial Year 2023-24, the Real GDP Growth Rate is estimated to be ~6.3%. The summarised GDP Growth rates from FY 2019-20 to FY 2023-24 are presented below:-
| Indicator (percent y-o-y) | FY19/20 | FY20/21 | FY21/22 | FY22/23 | FY23/24 |
|---|---|---|---|---|---|
| Real GDP Growth, at constant market prices | 3.90% | -5.80% | 9.10% | 6.90% | 6.30% |
| Real GDP Growth, at constant factor prices | 3.90% | -4.20% | 8.80% | 6.60% | 6.30% |
Sensitivity Analysis
Sensitivity of terminal value is defined as the change in terminal value due to changes in independent inputs such as growth rate, discounting rate and operating margins. We can observe sensitivity of Terminal value to changes in Long-Term growth rate through the following example:-
• Future Maintainable Cash Flows: ₹1,000
• WACC: 15%
• Growth Rate1 = 6.00 %
• Growth Rate2 = 5.00 %
• Growth Rate3 = 4.00 %
Table 1: Sensitivity of Terminal Value to Long-Term Growth Rate
| Growth Rates | 6.00% | 5.00% | 4.00% |
|---|---|---|---|
| Terminal Value | 11,778 | 10,500 | 9,455 |
| % Change in TV [Keeping 6% as Base] | - | 10.85% | 19.73% |
As evident in the table 1 above, a 1% change in growth rate leads to a 10.85% change in the Terminal Value, and 2.00% change in the growth rate results in TV falling by 19.73%. Since the results are magnified based on inputs, even minor errors can tamper with the valuation results by a significant factor.
The more the growth rate skews towards the required rate of return, the higher the value of perpetuity.
Key Assumptions for a Stable Growth Rate
While applying Constant Growth Model for computation of Perpetuity, there are three main assumptions which need to be considered. These are as follows:-
1. Length of the High Growth Period
No business can earn abnormal economic profit in the long-run, and all firms will earn normal profit as market participants. There are growth spurts available to new companies due to technological innovation, unique product offerings, or cost effective inputs to production, but that ultimately invites new players into the markets, leading to competition and thereby wiping out excess profits from the market.
Therefore, any startup that survives the initial phases of its life cycle, will have 5 to 10 years of high growth period and will ultimately stabilise.
It is up to the management to decide for how long the high growth period will last and the valuer to undertake a litmus test to ensure that the assumptions are rational and the projections provided by the management are rooted in reality and not aspirational.
The growth spurt is also dependent on the existing market participants, the size of the company, and the historical growth rate of the company.
2. Characteristics of Stable Growing Companies
A company having a stable growth is fundamentally different from a company having a high growth and is growing annually by two to ten times year-on-year. The company with stable growth will have consistent order flow, be less risky, and have fewer working capital and capital expenditure requirements.
It is necessary to assume that once the company enters a constant growth phase, capital expenditure requirements will also reduce, along with working capital and operating margins.
Accordingly, the assumptions used in Terminal Value calculations have to be consistent with stable growth companies, and there should not be any misalignment.
3. Transition from a High Growth Period to Stable Growth
Depending on the projections provided by the management, the valuation can approach the following scenarios:-
- 1. Two-Stage Model: The Company maintains high growth for the projected period and changes to stable growth in the terminal period. This model is appropriate for companies growing at moderate pace and where the shift is not immediate.
- 2. Three-Stage Model: The Company projects a high growth phase for a period, and then has a transition phase wherein it slowly shifts towards stable growth levels. This model is appropriate for companies with very high growth patterns where the transition phase allows for gradual adjustment and flexibility.
- 3. N-Stage Model: Company’s characteristics change each year from the valuation date until the terminal period. This method is suitable for early stage start-ups or companies with negative margins since it allows for change on a yearly or periodic basis.
Survival of the Fittest
The underlying assumption for ascertaining the terminal value is that the company is a going concern with perpetual life. For start-ups and other risky ventures, survivability is never guaranteed. In that case, does it make sense to the valuer to consider the terminal value of high-risk businesses or operating models? The Liquidation approach will make more sense in these specific cases.
Another aspect of the survival issue is that the valuer can adjust the higher risk and survivability by increasing the cost of capital or building the survival risk into the Company Specific Risk Premium for equity risk. Thus, companies with a higher likelihood of failure will have higher discount rates and a lower cost of capital.
It should be taken into consideration that survival is not accounted for twice in the valuation exercise, once at the time of providing cash flows with a pessimistic bias and again by increasing the discount rate. Cash burn ratio is a good indicator to check whether cash flow issues will arise for a particular business.
Conclusion
Cash flows in the projected period are easy to compute, whereas, the terminal period cash flows are relatively difficult to conclude without making a few judgements and assumptions. There are three methods to compute Terminal Value being the Multiple Approach, Liquidation Approach and Constant Growth Approach.
All three approaches have their own set of advantages and limitations, with the constant growth approach being the most prevalent in the industry. Under the constant growth approach, we assume that the business will generate future maintainable cash flows till perpetuity with a constant growth rate.
Perpetuity is the main driving force in ascertaining the value of a business and can significantly influence investment and acquisition decisions. One must be aware of the risks involved, industry considerations, and financial sanity over each of the variables adopted in computing the perpetuity value. Further, perpetuity needs to be analysed in the context of new digital businesses with their own unique models and ways of generating cash flows. The valuation methodology needs to be adapted to take into account digital assets, financial regulations, and the risks involved.
References
- Closure in Valuation: Estimating Terminal Value by Aswath Damodaran
- Financial Valuation, Application and Models by James R. Hitchner
- Standards of Value: Theory and Applications by Jay E. Fishman, Shannon P. Pratt and William J. Morrison
- https://www.worldbank.org/en/news/press-release/2023/04/04/indian-economy-continues-to-show-resilience-amid-global-uncertainties