Price Implied Expectations Analysis

  1. Disclaimer
  2. Why you Should Care about Mastering Market Implied Expectations in Stock Price
  3. Primer on Valuation
  4. Introducing Price Implied Expectations Analysis
  5. The Model
  6. Components of the Model

I wrote this article for colleagues with non-finance backgrounds at Shopify after the management announced a new compensation plan that would afford the company’s employees the agency to choose a percentage compensation allocation between stock and cash. The write-up and the accompanying model were my attempt to teach how to analyze stock price using Mauboussin’s expectations investing and to help decide if there are upsides to accepting stock instead of cash.

Outline of the Article

  • Disclaimer
  • Why you should care about Mastering Market Implied Expectations in Stock Price
  • Primer on Valuation
  • Introducing Price Implied Expectations Analysis
  • The Model
  • Components of the Model


  1. This article and the accompanying model are for information purposes and are not investment advice.
  2. I used Shopify in my Price Implied Expectations (PIE) model. However, I have no opinion on the fair value of the company’s stock price.

Why you Should Care about Mastering Market Implied Expectations in Stock Price

Employees in publicly traded companies such as Shopify that are partly compensated via stock grants are investors. The financial market aggregates a substantial amount of information based on the current conditions and future potential of a traded company in its stock price. Hence, it is beneficial to be able to deduce implied expectations that are embedded in stock price and to analyze if those expectations can be met or surpassed.

Let’s consider a publicly-traded company with the following properties to explain the concept of deducing market-implied expectations and its importance.

Name of the publicly traded firm = Company ABC

Total number of outstanding shares = 100 shares

Cost of Capital (CoC) of the firm = 10%

Most probable Free Cash Flow (FCF) growth rate of the firm forever = 5%

Most probable FCF a year from now = $10,000

With the data we have on ABC, we could use the “Gordon formula” (given below) to estimate the stockholder value and consequently, the fair price of the company’s per-unit share.


EV = Shareholder value/Market Cap

FCF = Free cash flow a year from now.

r = Opportunity cost of capital (CoC)

g = Sustained growth rate to perpetuity

By plugging in the available data in the Gordon formula, the derived fair value of ABC’s share price is $2,000.

While the computed fair price of ABC’s stock is $2,000, its shares could actually trade at a price that is markedly different from the fair value.

Now, imagine that ABC’s stock is trading at $10,000 per share on Wealthsimple and other stock trading platforms and I have an offer from the company with $20,000 in stock compensation. If I decide to take up the offer, at the current trading price, I would get 2 shares. But would getting 2 shares be a fair deal for me? It is a hard question to answer but with the principle of price implied market expectations analysis, I could deduce the market’s assumptions embedded in the stock price of $10,000 and subject the derived data to a viability test.

Previously, the Gordon formula was used to obtain ABC’s fair value stock price. But in this instance, we already have the price of the company’s shares traded on exchanges, so we want to work backward to derive an input that the market has used with the formula to arrive at a price of $10,000 per share.

CoC is data that is determined by the market. So, let’s assume there is a consensus that it is 10%. Let’s also assume that ABC’s management forecasted in their last earnings call that their FCF a year from now would be $10,000. With all the data we have now, the only variable that is missing in the Gordon formula is g — growth rate.

If we rearrange the expression above and solve for g, we would get 9%.

With the realization that the market has assumed a growth rate of 9% for ABC, what would be expected from me is to check the viability of ABC to grow at 9% forever. This requires an understanding of the firm’s historical performance, analyzing industry structure and Company ABC’s competitive positioning, reviewing the quality of the management team, etc. After, my analysis, if I realize that there is absolutely no way that ABC would grow at 9% in the future, should I still proceed to accept the 2 shares for stock compensation of $20,000 when I know the price is overvalued? That is another difficult question to answer but here are a few points to consider:

  1. The market can misprice the intrinsic value (stock price) of a company and the mispricing could go on for a long time. At $10,000 per share, the market assumed a growth rate of 9%. Market could decide tomorrow that the growth rate will be 9.5% forever, and this would further push up the stock price. So, if I accept 2 shares with 1 year vesting period, the share price could keep soaring and it is also possible that the Market will realize they’ve been aggressive in estimating the growth of the company thereby resulting in re-evaluation of the company’s stock price at 5% growth rate before my vesting period expires. If this happens, and the stock price drops to $2,000, I would be left with $4,000 after a year. That is a massive 80% loss from $20,000.
  2. Let’s be frank. The management of a company whose stock is priced very higher than what fundamentals can sustain won’t go out there and do things to purposely sabotage the price. It is actually great for a company and its existing investors to issue shares when its price is high. If ABC’s shares were being traded at $2,000 and I am getting $20,000 worth of stock compensation at that price point, I would get 10 shares. But at $10,000 per share, I only get 2. The lesser the shares that are issued, the better for the company.
  3. As I previously noted, the financial market can be irrational for a long period of time. So, I could take up the 2 shares from Company ABC at $10,000 and it could go higher before I am eligible to sell. But, if I understand that the market-implied expectations in a stock price are too aggressive, I could go back to renegotiate my compensation structure with ABC. I could ask for more cash compensation, or I could negotiate for higher stock compensation. For example, if I am able to get ABC to give me $40,000 in stocks, at $10,000 per share, I would get 4 shares. If the market reprices the share to $2,000 per unit, I would have $8,000. That is still better than having $4,000 if I only got 2 shares.
  4. There is always a chance that a company whose stock price is fairly valued today can trade lower tomorrow at another price point that is also a fair value of the stock. Scroll back up to check all the inputs we used to get ABC’s share at $2,000. If all the variables are kept constant and r (the cost of capital, CoC) increases to 15%, ABC’s share price will drop to $1,000 per unit. The cost of capital could increase when Fed raises rates to combat inflation. The business is still well-positioned to grow at 5% but with a higher CoC, the stock price reduces. It could go the other way too. If CoC is lesser than 10%, then the stock price will increase. The takeaway here is that it is important to understand what is driving stock price variation. Is it aggressive market expectations or changes in macroeconomic factors such as interest rates? This knowledge could be helpful in deciding if you should buy, hold or sell a stock.

Primer on Valuation

The value of a financial asset such as a company’s market capitalization is the present value of all future ‘Free Cash Flow’ (FCF) that will be generated by the asset. So, if we have to value the market cap and consequently, the share price of Shopify today, we need to estimate Shopify’s FCF from next year to perpetuity. After projecting Shopify’s FCF for all its future years of existence, which is forever, we would then discount the cash flows by an appropriate cost of capital to get a value today.

In the illustration presented in the table above, 6 inputs or variables were needed to be able to arrive at FCF of $10 Million. If we are valuing Shopify today, we would need to forecast what those inputs would be from next year till perpetuity. The complexity of forecasting FCF forever should be quite apparent by now. Imagine someone asking you to give a projection of how fast Shopify’s revenue would grow from “Year 2250 to Year 2251”. To overcome the complexity of FCF estimation, the forecast period is broken down into 2 periods.

  1. Explicit period
  2. After explicit period

During the “Explicit forecast period” (EFP), the variables needed to derive FCF would have to be precisely stated every year. This period is also the high growth period where revenue could grow by 100% from Year 1 to Year 2 and then by 80% from Year 2 to Year 3. The EFP could be as short as 5 years or as long as 30 years.

After explicit forecast period” (AEFP) commences a year after EFP ends. In AEFP, we assume the company that is being valued is in a stable growth phase forever. With this assumption, we could then use the “Gordon formula” that I earlier introduced to derive the value of the company from the start of AEFP till perpetuity. So, for example, if Shopify has 10 years EFP, its AEFP would start in Year 11. And the only variables I would need at that point to calculate its value would be FCF in Year 11, the rate Shopify’s revenue is expected to grow forever, and the cost of capital.

So, in a nutshell, here is the simplified formula for deriving the market cap of Shopify assuming it is all equity financed and it has non-operating assets.

NOTE: It is not just enough to forecast FCF during both EFP and AEFP. The FCFs obtained must be discounted at the appropriate cost of capital.

Introducing Price Implied Expectations Analysis

Mauboussin and Rappaport are the pioneers of “Price Implied Expectations Analysis” (PIE). In PIE, instead of using forecasted FCFs discounted at an appropriate cost of capital to derive the market cap of a company, we work backward. We would have the market cap right off the bat and then we would try to estimate the variables that would yield the FCFs during EFP & AEFP, whose discounted values would sum up to the market cap we have. Then we subject the variables we extract from this reverse calculation to a viability test in order to see how plausible it is for the company to meet or surpass those derived values.

The focus of this article and the accompanying model is to provide a guide on the thought process and workflow to use a reverse DCF calculation to derive inputs for FCFs. It is the responsibility of investors to stress test those inputs and anticipate when the market will revise their expectations for the inputs.

In Mauboussin and Rappaport’s book, the authors used data from sophisticated investment research and financial firms such as Morningstar and Value line as well as aggregated analysts’ forecasts to derive the variables the market used to compute FCFs for Domino’s Pizza. Investment firms and equity analysts are good enough proxies for the market.

I don’t have access to data from the investment firms to incorporate into the model I developed but I used aggregate analysts’ forecasts for Shopify’s 5-year revenue growth rate and used projected operating margins to benchmark the value I used. I got the data I used from Tikr Terminal and I made up what I consider to be the rational sentiment of the markets for other inputs needed to obtain FCFs from aggregate and average industry data relevant to Shopify.

Anyone using the developed model would have the choice to select any values as inputs for deducing FCFs. Remember that the purpose of price implied expectation analysis is to be able to estimate inputs the market has decided on to price a stock. Hence, even in the absence of access to consensus data from investment research firms and analysts, one could still play around with the model, select a wide range of values, compare them to the company’s historical performance and do an analysis to see if the values are practicable and can be surpassed or not.

The Model

The model is hosted on Google Sheet — Price Implied Expectations Model

Components of the Model

The 5 worksheets in the Model in the order they are presented are:

  1. Historical Fin Statements 17–21
  2. Model Inputs
  3. Price Implied Expectations (The main model)
  4. Operating Cash, ROIIC, and Invested Capital
  5. Operating Taxes

The “Historical financial statements” worksheet basically presents Shopify’s published financial data from 2017–2021. The data were obtained from Shopify’s investor website and used to analyze Shopify’s past performance such as capital invested and returns made on those investments, past revenue growth rate etc. The data in this worksheet feed other worksheets of the model.

Model Inputs” is the worksheet where the variables required to produce FCFs are inputted. Some of the data on the sheet were obtained directly from Shopify’s financial statements, and others were obtained from financial data websites. The rest of the inputs are data we intend to extrapolate from Shopify’s stock price in order to test their viability as value drivers (such as revenue growth, after-tax operating margin, etc.). Data that were copied from external sources or hardcoded are formatted in blue while those that were computed and linked from other worksheets are in black.

Price Implied Expectations” worksheet is the core model where we use data from the ‘Model Inputs’ worksheet to derive FCFs for explicit and after explicit forecast period. Based on the inputs I used, Shopify’s explicit forecast period is ~ 8 years from 2021. This basically means that with my inputs’ assumption which I consider to mirror market expectations, Shopify has got just 8 years of fast growth after which the company will transition to a stable growth stage. If you think that is plausible and you agree with the value drivers (inputs used to generate FCFs), then Shopify is probably fairly valued. If you think some of the inputs understate Shopify’s fundamentals and you feel the company could have an explicit forecast period of 20, 30, or maybe 40 years, then the company is probably undervalued. That is an analysis you have to perform.

Businesses create value for their owners when they invest capital and earn returns that exceed a specific hurdle rate or percentage on those endeavors. In the “Operating Cash, ROIIC and Invested Capital” worksheet, I used data from Shopify’s historical financial statements to analyze Shopify’s past return on investments (ROI). Prior to getting the ROI, I needed to clean up the published financial statements. This is because Shopify complies with an accounting standard known as GAAP when publishing financial statements. However, the format that the statements are presented often commingle operating and non-operating data, and when we are valuing a firm, we want to focus on its day-to-day operation capacity. Non-operating assets of the firm are valued separately.

The “Operating Taxes” worksheet is an extension of the previous worksheet. The focus of the sheet was to separate the impacts of non-operating and financing activities on the tax obligations of Shopify.

I would be the first to admit that I am still student of Valuation and I intend to be a lifelong learner. So, if you’ve got any feedback for me, feel free to drop a comment and I am also happy to answer any questions.