Valuing TBR and RND without their crossholdings

In an effort to ascribe a value to TBR, I’ve been constantly running up against the cross-holdings with RND. Below is my attempt at bootstrapping a value to both companies (as both need to be done at the same time in order to see just TBR’s value).

TL;DR:

Fair market value of TBR and RND’s assets only at 30Jun16 and $1545/oz is estimated as $5.56/share and $2.05/share respectively, backed by $5.06/share and $0.94/share of real-world assets (i.e. not including the crossholdings).

Full Analysis

First, I want to determine the Asset Value of each company at the end of the FY (30Jun16), without the value of the crossholding on the books. I also want to account for the true value of the gold held by each company at current market prices (rather than the value of the gold held at cost), and make an allowance for business income tax as if the entire gold inventory was sold at market prices. Using A$1545/oz, and with reference to the TBR and RND 30Jun16 Annual Reports (references given to the TBR report so others can play along at home), we get:



This gives us the net physical asset positions of the companies, in the real world.

Then, we need to determine the relationship between the market value of each company, and the so-called “pure value” of each company – that is, what each company would be worth without the cross-holding in the sister company. To do this, we need to frame out two simultaneous equations, per the valuing methodology of Cyganksi (2004):

T₀ = the pure value of TBR
M_T = the total market value of TBR including the crossholding
R₀ = the pure value of RND
M_R = the total market value of RND including the crossholding

M_T = T₀ + ( 0.442 x R₀ )
M_R = R₀ + ( 0.263 x T₀ )

Note that the equations use 44.2% and 26.3% of the pure values, not the total market values – we are trying to strip out the crossholding in both directions at once.

Reducing these down gives two equations for each company’s pure value:
T₀ = ( M_T – 0.442 * M_R ) / ( 1 – ( 0.442 * 0.263 ) )
R₀ = ( M_R – 0.263 * M_T ) / ( 1 – ( 0.442 * 0.263 ) )

If we then say that the pure value of each company is equal to the Asset Value of each company calculated above (i.e. the real world net assets, remembering that this calculated figure is without the value assigned by the company to the crossholding in each annual report), then we can solve for the one pair of estimated total market capitalizations where the equations will hold true:



Within the assumptions of the model, and the gold price used for calculations, the only share prices which imply fair (asset only) value for each company given the crossholdings are $5.56/share for TBR, and $2.05/share for RND.

Some interesting conclusions then fall out from this analysis.

Firstly, TBR ascribes an incredibly low amount of asset value to its RND shares – only A$1.1m for owning nearly half of RND (page 50 of TBR annual report). RND’s shares in TBR are also given an asset value about half of their market value. I can’t for the life of me figure out how or why – the “fair value” explanatory note (pg. 61) in the TBR annual report is of no help.

Secondly, the crossholdings of each company artificially inflate the market value (and therefore share price) of both companies.

Without the value of the crossholdings on each set of books, the assets of each company total $252.8m + $56.8m = $309.6m. Yet the analysis implies the total fair market value for the companies is $277.9m + $123.3m = $401.2m! Where has this extra ~$92m of value come from? Quite simply, it is a mirage. But I don’t say this as a bad thing – whilst only $309.6m of combined assets exist in the real world, investors should be willing to pay $277.9m or $123.3m for either company. This is because when viewing just one company, the real assets plus the shares held in the sister company do equate to $277.9m or $123.3m (without accounting for the crossholding back the other direction).

This may seem counterintuitive at first, so I recommend reading this simple example to help wrap your head around it:
https://www.intelligentinvestor.com.au/2010/10/cross-shareholding-riddle-revealed

Thirdly, this artificial inflation of the market values due to the crossholdings affects RND much more than it does TBR. This is due to the smaller asset base, differing percentages crossheld, and much, much smaller book value ascribed to the RND shares by TBR, versus the TBR shares by RND:



Fourthly, this analysis assumes an efficient market, with TBR and RND trading for $5.56 and $2.05 per share (at 30Jun16 and A$1545/oz). This is the only point within the solution space where the companies’ pure capitalizations equal their calculated asset values. In the real world, the market is not efficient, and combined with the very opaque financial reporting and complex corporate structures of the TBR/RND group, all of the above analysis should be taken with a large grain of salt.

Fifthly, if you were looking at the value of their assets only, TBR seems fairly priced (note this analysis is for Jun16 and we are in Dec16, so some additions of gold to the two stockpiles in the past half year have not been accounted for), and RND is either priced too cheap or too expensive, depending on whether you view the two companies as a single entity (too expensive), or RND on its own (too cheap).

Sixthly, all of this analysis is only looking at the current value of net assets in the two companies’ books, and gives no value to the future earnings of the mines. This is obviously incorrect, and implies our conclusion in my fifth point above should be “both companies are wayyy too cheap”. Without delving too deep into the P/L statements, at 100,000 ounces per year between TBR/RND, and with TBR retaining 23% of credited gold after selling most for expenses, I estimate about 49 cents per share of added value (after tax) per year for TBR at A$1545/oz. How you choose to value this is up to you (e.g. a 15x PER implies an asset minus crossholding plus earnings value for TBR of $12+/share); other posters such as Worzel1 and Eshmun can probably give a better estimate of the value of future earnings than me.

Finally, trying to value the companies purely by looking at their gold stockpiles is a futile exercise, and is why I hate this bloody crossholding. We need to assess market capitalizations without the effect of the crossholdings, and talk in real assets (and liabilities and unrealized taxes) only. If we’re not referring to the market cap of the sister company when valuing either TBR or RND, our figures will never be spot on. Gold on hand for both companies at 30Jun16 was worth ~$260m (after tax at A$1545/oz) – trying to apportion it to either company, or saying the combined market caps are less or more than the value of gold on hand without an allowance for taxes etc. is never going to be correct.

I would love to hear all of your thoughts on all of the above. And again, I cannot overstate enough how much I hate this bloody crossholding.

- seboya

Cyganski, P. (2004), “Valuation of Entities with Cross-Shareholding Ownerships”, Business Valuation Review, 23(4), pp. 197-200.