rio 30% undervalued vs bhp?

I think we need to start looking at what Rio will be worth now it is pretty much de-risked. I'd love to see some more detailed comparison of Rio against other similar companies.

My calculations which follow suggest that Rio is undervalued compared with BHP by about 30% (for Aussie investors anyway).

Looking at Comsec (at median forecast earnings - probably about a month or two out of date) - the following comparison with BHP comes to mind. Obviously this is nowhere near perfect. DYOR, as I have not DMOR.

Co; SP; Forecast 30/6/10 per share; Implied Earnings yield
BHP; $38; 149.5c; 3.9%
RIO; $73; 485.6c; 6.6%
Rio (adj); $58; 318.4c; 5.5%
Rio (adj) have adjusted rio for 21 for 40 issue at $28 - sp will be 73+73+28=174/3=50. Earnings will be 485.6x40/61 = 318.4 ps - due to 21 for 40.

Without accounting for reduced interest costs, and the JV, Rio is valued at about 41% less than BHP. So I would expect Rio to make up some of that difference in discount.

However Rio is more highly geared than BHP. (From latest half reports)
Co; total assets; total liabilities; % debt; gross borrowings; finance costs; annualised int rate
BHP; 73.3; 33.6; 46%; $11.4b; $497m (half); 8.7%*
RIO; 88.5; 64.6; 73%; $39.4b; $219m (quarter); 2.2%* (adjust for 27.8b at 0.8%, leaves $163m I against $11.6b – rate of 5.6% on other money.)
RIO adj; 88.5; 49.4; 56%; $24.2b; n/a; Assume 5.6%

If we were to match the capital structure of each, by assuming that BHP could wake up one morning and adjust the balance sheet to be leveraged at 56% – the following would be the effect of this change:

Co; total assets; total liabilities; % debt; gross borrowings; finance costs; annualised int rate
BHP (now); 73.3; 33.6; 46%; $11.4b; $497m (half); 8.7%*
BHP (leveraged) 73.3; 41; 56%; $18.8b; $1.05b; 5.6% (assume same as RIO).

Co; SP; Forecast 30/6/10 per share; Implied Earnings yield
BHP now; $38; 149.5c; 3.9%
BHP (leveraged); $38, 158.7c; 4.2%

BHP (leveraged) Assumes BHP uses the extra $7.4B to buy back 5.8% of their shares – so have raised EPS by 5.8%, plus assume interest costs will be about the same with reduced interest costs making interest costs changes immaterial.

*** In the end my admittedly dodgy calcs suggest that BHP is priced at a 4.2% (now more leveraged) return to RIO’s adjusted 5.5%. So Rio could have a thirty one percent rise in shareprice (5.5%-4.2%=1.3%/4.2%=31%) for being de risked, all other factors being equal (Which I know they are not). ***

Some notes. Obvious factors not taken into account include:
There will need to be further demand for Rio to mop up the extra stock.
BHP and Rio have a different portfolio of assets, with different life expectancies etc.
BHP and RIO have different amounts of cash and other agreements and strategic plusses and minuses.
Rio got some super-cheap financing of the Alcan deal.
Different currencies and locations of assets etc.
The list goes on.

I’ve bought a stack of Rio stock so we’ll see what happens. Does anybody have any differing opinions? I'd love to be shown that I have made a big mistake in my back of the envelope calcs too, so I can get the story right!