Business Valuation 105 – Contingent Methods of Valuation

The Black and Scholes option pricing theory (OPT) offers a clue as to how the equity in a firm may be valued. Suppose we recognise the fact, that an equity investor in a geared firm with limited liability has a call option on the underlying assets of the firm. In that case, we have, potentially, a method for valuing the business.  

Conceptually this is an influential theory; the use of option pricing methodology in the valuation of a business creates difficulties in estimating the necessary input parameters into the model.  

Using the real options methodology, one approach is to simulate the future cash flows of a firm given realistic current conditions and estimates of the volatility of key input variables. 

With this, we can generate an overall estimate of the future volatility of the business and then using a specified set of assumptions about the terminal value of the company creates an option value for the business. This modelling approach has many refinements but essentially provides both methods and insights into the valuation of all firms that are financed partly by debt and, in particular, highly leveraged, fast-growing start-up companies.

The limits on the value

Traditionally, the value of the firm in the hands of its investors will have a lower limit equal to the break-up value of the firm, less all external claims on the business (the sum of its short and long term liabilities). Generally, it was argued that once the present value of the firm’s future cash flows (when discounted at the equity investors rate of return) falls below this value then it would be rational for the investors to cut their losses, liquidate the firm and salvage what value they could. However, this relatively simple analysis is tempered in the light of options theory. From an options theory perspective, the equity investors in a geared firm have a call option on the value of the firm’s assets over and above the value of the debt. If the value of the assets should fall below the value of the debt then given limited liability the equity investors could put the firm into members’ voluntary liquidation and walk away leaving the debt holders to bear the loss. Thus in a geared firm, the equity value of the business is the value of a call option on the firm’s net assets. In an ungeared firm, the option value does not exist. Thus the value of the firm to the equity investors is simply the present value of the net cash flows anticipated over the lifetime of the business.

This line of reasoning suggests that valuing a firm depends upon the existence of gearing and that the value of the firm is not simply the present value of its assets in current use minus the amount of its outstanding debt. 

If the firm is not geared, the critical numbers are: (i) the realisable value of its assets and (ii) the present value of the firm’s assets in continued use. The greater of these is its equity value. In the presence of gearing the critical numbers are: (i) the present value of the firm’s assets and (ii) the value of the firm’s outstanding debt. The value of the firm, in this case, will be the value of the option to continue in business.  

This perspective on the value of a firm suggests that the following variables are critical:

(i) The present value of the firm’s assets in use. Generally, the greater this value, the greater will be the value of a call on those assets at exercise.

(ii) The value of the outstanding debt (the exercise value of the firm) – generally the lower this value, the more valuable the call becomes until at the limit of zero leverage the call value equals the present value of the firm’s assets in use.

(iii) The term to maturity of the debt – the longer the time, the greater the value of the equity call. 

(iv) The risk-free rate of return used to discount the exercise value multiplied by the probability of exercise. Given the inverse relationship between exercise value and firm value, this would suggest that the higher the rate, the greater the call value. However, this is unlikely to be the case overall given that the present value of the firm’s assets (i) will be determined in part by the discount rate and that this in its turn is partly influenced by the risk-free rate.

(v) The expected volatility of the present value of the firm’s assets, which leads to the somewhat paradoxical result that the higher the uncertainty about future cash flows, the more valuable is the call option on those cash flows.

Valuing the firm as an option

In the more general valuation context, a firm’s equity should not be traded, or we may have reason to believe that the correct valuation is considerably different from that revealed by the share price.  

Schwartz and Moon (2000) developed a procedure for the contingent valuation of equities using option pricing and simulation methods. 

They used as their case study which at that time had been in business for just over three years. The company was still not profitable in the conventional sense but was growing its market and its revenues at a rapid rate. 

In March 1996 the quarterly sales of were $0.875 million. By September 1999 its sales had risen to $355.8 million. Here, in outline, is the procedure Schwartz and Moon followed:

A stochastic model was created of the firm’s revenue-generating process and its cost structure. This model contained a drift term which reflects the expected rate of growth in its revenues and a stochastic period reflecting the degree of uncertainty about that growth rate. The expenditure model reflected not only the company’s fixed and variable cost structure but also the impact of taxation upon the company’s profits. 

Refinements of this stochastic model included a mean-reverting process to the estimated long-run rate of revenue growth as well as a procedure for carrying forward losses for tax purposes from one period to the next.  

A bankruptcy condition was imposed were given a starting amount of cash bankruptcy was defined as the point when the amount of cash and other monetary assets reached zero.

A time horizon was defined for the simulation of the firm’s future cash flows, and a terminal value invoked. In their study, Schwartz and Moon, set the final value as ten times EBITDA. Another approach would be to take the net cash flow figure and to capitalise the following year’s projected earnings at the risk-free rate of return less the terminal growth rate of profits. However, the time horizon should be such that by that time, the equity holder’s option is so far into the money that there is zero default risk.  

A simulation is then undertaken to generate a large number of cash flow paths. In the simulated series of quarterly cash flows for Amazon assuming a starting revenue of £356million per quarter, a growth rate of 11 per cent a quarter and a starting volatility of revenues of 10 per cent per quarter. The factors were built-in, and the firm’s starting balance of cash resources available was assumed to be £200 million.

The key point to note is that a number of the price paths had been generated one of which shows default in period 5. Indeed, depending upon the software used, a model can be built which will permit many hundreds of such price paths to be generated. The model can be refined to reflect a wide range of different circumstances: different patterns of growth and the decline in growth as the firm matures, other cost structures, the correlation between variables, differing tax regimes and different initial conditions. From the simulation, the volatility of the cash-flow projection can then be determined, and the likely default in each time period determined. This volatility, expressed as the standard deviation of the company’s future cash flows, can then be adjusted to a continuous-time basis and a valuation of the options component of the company’s valuation determined.

The challenge with this approach of valuation lies in estimating the initial volatilities of the future revenue growth and, in later variants of the model, the volatilities of future costs. 

Nevertheless, the technique does offer a potential route for valuing companies that are in their early stages of growth and which rely upon substantial investment in intangible assets. 


Published by Mohamed Ebrahim, MBA, CeMap, MLIBF, MCSI

Mohamed Ebrahim Mohamed is an author of books related to Islamic Finance, Financial Reporting, Accountancy, and related topics. Mohamed, is currently based in Birmingham, West Midlands, England, United Kingdom and is a Co-founder, CEO and Director of a Start-up Everest Fin Edu Tech Limited. He utilises his training and experience of over 25 years to find funding solutions for individuals, businesses and property buyers, investors and developers especially for the SME'S. Mohamed, is a Senior Partner with Ace Associates LLP - Certified Public Accountants & CEO of Ace Financial Advisory Limited, he is a CPA Kenya and holds an MBA from The University of Manchester (UK) and B.A (Hons) from Manchester Metropolitan University, He has worked for over 25 years with firms in Kenya -Ernst & Young – Assurance Advisory Business Service & Tax Service lines, PKF Kenya Audit Senior, and Devani –Devani & Co. United Arab Emirates -Group Financial Controller - Credo Investments FZE. Canada – Mc Tavish & Co. CPA’s. A member Institute of Directors (Kenya) and Non-Executive Directors Association (UK). He served on the ICPAK Coast Branch, Executive Council as Secretary and CPD Convener (2013-15) and from May 2016 to May 2018. Vice-Chair May 2018 to June 2020. He was commended by ICPAK in June 2015 for his services to the Accounting profession by ICPAK. Furthermore, Mohamed Ebrahim was awarded a Fellowship of the Institute of Certified Public Accountants of Kenya on.11th December 2020. Educational & Professional details. Mohamed speaks English, Gujerati, Hindi, Urdu, Swahili. Born in an Indian immigrant family from Gujerat India, settled on the Swahili Coast of East Africa for four (4) generations, Bachelor of Arts (Hons) – Sustainable Performance Management Manchester Metropolitan University Master of Business Administration The University of Manchester – Manchester Business School Certified Islamic Finance Executive (CIFE) Advanced. Certified Islamic Finance Executive in Islamic Accounting Ethica Institute of Islamic Finance, Dubai, UAE. ACMA, CGMA, Member, Chartered Institute of Management Accountants and Association of International Certified Professional Accountants, registered as a CIMA Member in Practice. CPA, Practicing member Institute of Certified Public Accountants of Kenya FCFIP, Fellow Member -International Institute of Certified Forensic Investigation Professionals FCT, Fellow Member, Fellow Chartered Treasurer FFA – Fellow of the Institute of Financial Accountants MCIArb - Chartered Institute of Arbitrators, Full Member. MCSI: Member, Chartered Institute of Securities & Investments Institute of Internal Auditors - Member Currently, a Doctoral Student at the Edinburgh Business School, completed the Coursework stage, working on the doctoral thesis Interim Award - Post Graduate Certificate in Business Research methods Short Courses and MOOC’s • The World Bank Group's MOOC on Financing for Development. • Financial Markets an online non-credit course authorized by Yale University, facilitator being Professor Robert Shiller – 2013 recipient of Nobel Prize in Economic sciences • Principles of Valuation: Time Value of Money authorized by University of Michigan • Islamic Financial & Capital Markets -101 - & Structure and Trading of Sukuk102 – by Islamic Research and Training Institute • Islamic Finance & Banking 101 & 102 – Islamic Modes of Finance - by Islamic Research and Training Institute • University Teaching MOOC on Coursera by Hong Kong University. • Oxford Brookes University Business School – Online mentoring Course • ICPAK - Training of Trainers PRESENTATIONS AND PUBLICATIONS Professional Conference paper IICFIP 2014 Global Conference “Creating a Business Culture based on ethics” MBA Dissertation Risk Management in Islamic Financial Institutions Publications in Professional Journals The Accountant – Journal of the Institute of Certified Public Accountants of Kenya • Tax Reforms 1 – Time for a Flat Tax system in Kenya – February- March 2012 issue • Tax Reforms 2 – Specific Tax Simplification Reforms – April –May 2012 Issue • Risk Management in Islamic Financial Institutions – December-January 2013 issue Africa Islamic Finance Report (Volume 1 no, 2)- April- June 2016 • A case for Islamic Sharia Compliant Real Estate Investment Trust (Islamic REITS) in Kenya Others Islamic Home Financing

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