Much has been said and written about the finances of Britain's most successful sporting institution, Rangers Football Club.

Speculation over the possibility of a second administration or likely direction of the share price has dominated Rangers based conversations in many a pub and many an internet forum.

Not all of these conversations are helpful when they are presented in public, through various media, with no factual substance. They can subsequently cause unnecessary, widespread alarm and subject the club to destabilising influences, such as supporter boycotts and police investigations.

The preferred way forward for all supporters should be to thoughtfully and objectively use the available information in Rangers' financial accounts to present a factual representation of our club's current business operations and forecast it's likely success going forward.

Mathematics can help us to analyse the prospect of a company entering bankruptcy.

On 25th December 2013, the following report was prepared, and posted on the Vanguard Bears forum, regarding the likelihood of Rangers going bankrupt:

--- START OF ANALYISIS ---

Rangers International Football Club (RIFC) has an Altman Z2-Score of 2.25; a statistical bankruptcy meter generated from a set of balance sheet ratios.

Q – Are liquid assets a significant proportion of the assets?

A – RISK

• Testing: Working Capital/Total Assets > 0.2375
• RIFC Details: Working Capital/Total Assets = 0.018

Q – Do reinvested earnings make up a significant portion of the assets?

A – SAFE

• Testing: Retained Earnings/Total Assets > -0.1355
• RIFC Details: Retained Earnings/Total Assets = 0.34

Q – Are the assets relatively productive in terms of earnings?

A – SAFE

• Testing: Earnings Before Interest and Taxes/Total Assets > -0.082
• RIFC Details: Earnings Before Interest and Taxes/Total Assets = 0.019

Q – Does firm value compare favourably to its liabilities?

A – RISK

• Testing: Market Value of Equity/Book Value of Total Liabilities > 1.439
• RIFC Details: Market Value of Equity/Book Value of Total Liabilities = 0.89

Regarding the Altman Z2-Score:

• Greater than 3.00 = good financial health.
• Less than 1.80 = a company is in the distress zone and is in serious financial trouble; the distress zone is 80-90% accurate in predicting bankruptcy.
• Rangers' score of 2.25 indicates it is not entirely safe from financial distress and investors should be cautious.

--- END OF ANALYSIS ---

The problem with supporters warning of the imminent arrival of another financial collapse at Rangers is that they have no statistical analysis to give credibility to their claims.

When the share price was at around 33p, it was my opinion, reached using mathematical evidence, that the likely intrinsic value of Rangers was closer to 25.67p. I made similar comments in October 2013 when the share price was around 43p.

The following analysis regarding an estimate of the true share price valuation of RIFC was also carried out in December:

--- START OF ANALYSIS ---

a) Discounted Cash Flow Valuation Method (forward looking growth model): 0p per share; 100% overvalued (due to negative cash flows that are not forecast to increase in the next 8 years).

This is based on the following inputs:

• The company's sustainable cash flow is -£12.61m (taken as the average between latest free cash flow (-£18.9m) and 3 year average free cash flow (which includes 2 years of £0 due to not having data for those years, making this valuation input more unreliable))
• Expected growth rate of cash flow of 0% for the next 8 years (3 year average cash flow growth, 5 year average cash flow growth, year 1 forecast earnings per share growth and year 2 forecast earnings per share growth are normally added as an input here but that data is not available for Rangers at this stage, making this valuation input more unreliable)
• The company should settle into a long term growth rate of 3% (if we don't have reliable forecasts, we default to normal inflation levels and that is what we've done here)
• Investors require a return of 15% for the risk they are taking (due to being a small cap company, 9% would be applicable to large cap companies)

b) Earnings Power Value Valuation Method (zero growth model based on current earnings): 25.67p per share; 23.4% overvalued.

This is based on the following inputs:

• Sustainable level of revenue is £19.11m (latest revenue; 3 year average revenue and 12 month rolling forecast revenue is normally included but we don't have these inputs for RIFC, making this valuation input more unreliable)
• Across the economic cycle, the operating margin in 7.8% (we normally take an average of a 5-10 year operating margin and a trailing 12 month operating margin but we don't have that data for RIFC, making this valuation input more unreliable)
• On average the company see £0m of 'exceptionals' (we normally deduct the long term average of non-recurring charges but we don't have this data for RIFC, making this valuation input more unreliable)
• 15% of historic selling, general and administrative expense has funded growth (typically 15% to 50% of this is added back to a company's Earnings Power Value to make up for the fact some of that expenditure went towards funding growth as opposed to maintaining the existing asset base; Earnings Power Value only takes into account current earnings and is a zero growth model; we don't have enough data for RIFC on this value so we assume the minimum standard of 15%)
• Each year, the company spends -£2.48m on maintenance capital expenditure (capex)  (maintenance capex can be calculated by subtracting growth capex from total capex; again, we don't have long term forecasts for this based on historical figures so we are largely estimating these on limited results from the previous earnings report)
• Investors require a return of 15% for the risk they are taking (due to being a small cap company, 9% would be applicable to large cap companies)

c) "Relative to Sector" Valuation Method: 92.51p per share; 176.2% undervalued

Based on the following inputs:

When we compare RIFC to the Hotels and Entertainment services sector, we have the following valuation ratios for RIFC:

• Price To Book Value: 0.39
• Price To Tangible Book Value: 0.57
• Enterprise Value To Earnings Before Interest, Tax, Depreciation and Amortisation: 3.14
• Enterprise Value To Operating Profit: 8.38
• Enterprise Value To Sales: 0.66

By comparison, we have the following corresponding valuation ratios for companies in the Hotels and Entertainment Services sector:

• Price To Book Value: 1.95
• Price To Tangible Book Value: 2.19
• Enterprise Value To Earnings Before Interest, Tax, Depreciation and Amortisation: 12.7
• Enterprise Value To Operating Profit: 18.3
• Enterprise Value To Sales: 2.10

The Relative To Sector Valuation Method compares RIFC's valuation against the median multiples of the company's sector peer group.

d) Net Current Asset Value Valuation Method: 0p per share; 100% overvalued

Based on the following inputs:

The company's current assets (long term assets are not included) are £16.5m

• Cash And Short Term Investments (trailing 12 months) £11.2m
• Total Receivables, Net £5.23m
• Total Inventory £0.085m
• Other Current Assets £0.000m

The company's total liabilities are £24.7m

• Total Current Liabilities £15.1m
• Minority Interests £0.25m
• Deferred Tax £7.82m
• Total Long Term Debt £0.96m
• Total Other Liabilities £0.52m

The shares outstanding are 65,095,856m

e) Net Working Capital Valuation Method: 0p per share; 100% overvalued

Based on the following inputs:

• The company's Cash and Short Term Investments are £11.2m
• The company's Inventory is £0.085m
• The company's Receivables are £5.23m
• The company's Total Liabilities are £24.7m
• The Shares Outstanding are 65,095,856m

f) Tangible Book Value Valuation Method: 59.1p; 76.4% undervalued

• The company's Book Value (total assets minus liabilities) is £56.9m
• The company's Intangible Assets are £18.4m
• The company's Goodwill is £0.000m
• The Shares Outstanding are 65,095,856m

--- END OF ANALYSIS ---

The following commentary from the 10th of January 2014 further explained the information provided on the 25th of December 2013.

--- START OF COMMENTARY ---

"As you can see there are only three valuation methods that assign a value greater than 0p to Rangers; Earnings Power Value, Tangible Book Value and Relative To Sector.

There are only two valuation methods that assign a share price that is higher than the current level of 28.5p. However, investors likely won't use these methods to value Rangers, and inform their investing decisions, for the following reasons, thus eliminating any mathematical reason to think that the current share price is cheap, based on an objective analysis of the company's financial results:

Relative To Sector is an unreliable valuation because it compares Rangers to the Hotels and Entertainment Services sector, based on how the stock is classified by the stock market. It would be better to only compare Rangers to other football clubs but there is a shortage of listed football clubs and the sample size would be too small to draw any conclusions.

The Tangible Book Value method is good at valuing the club's assets. However, value of assets is very different to the value of the business. If the assets are not generating sufficient income to make a profit, then investors lose confidence in the ability of those assets to generate future growth and profitable cash flows. As a result, the business is worth less to those that may seek to invest in it. If the company is liquidated due to large debts, the investors likely won't see the value of the assets they invested in because shareholders are below creditors in the capital structure of a business. Therefore, an investor does not invest on the basis of the book value of the assets of a company but rather the ability of those assets to generate a return on investment.

Now, the only method left that assigns a value to Rangers, and would be a realistic evaluation of the club's true worth as a business, in the opinion of investors (which is largely what dictates the share price), is the Earnings Power Value method. This valuation metric values the club based on current earnings and assumes no growth in the company (which can't be measured anyway due to negative cash flows). It is a realistic valuation because it makes no assumptions about future growth, which can be inaccurate, and is only an analysis of the present situation.

According to the Earnings Power Value method, Rangers is valued at 25.67p. Therefore, the current share price of 28.5p is close to being a fair valuation of Rangers.

Rather than speculating on boardroom battles and their subsequent effect on the share price, I have simply looked at the value of the business from an objective, mathematical view. In the long term, a company's share price will converge with its Intrinsic Value. It's just mathematics and market forces. The downwards movement in the share price of Rangers comes as no surprise to me."

---END OF COMMENTARY---

The best way to comment on the financial situation at Rangers is by working with the facts, not by letting unfounded allegations cloud your judgement.

History will show us which commentary - evidence based mathematics here on Vanguard Bears or the agenda-driven, emotional rhetoric from power-seeking, self-proclaimed fans' representatives - proved to be an accurate account of the financial picture at Rangers.

It is now the 7th of May 2014 - Rangers is still operating and the share price is 23.00p.