All the cash costs of constructing a building are shown in the balance sheet as an asset, and this is amortised over its useful life to the profit and loss account with an annual cost of amortisation. So you make a building for 40 million with a useful life of 40 years, say, 1 million will be a cost in the profit and loss account each year.
The financing of the building only appears in the balance sheet, either as increased equity or a loan, the only thing that will impact profit and loss from the financing is an annual interest charge on any loans (zero financing cost for funding by equity).
Now, the Etihad Stadium is owned by the Council but it is leased on a long-term basis, pretty much over its useful life by the club, so accounting rules say it has to be treated as an owned asset: ie; the asset is shown at a calculated value in the balance sheet and amortised with an annual amortisation cost to the profit and loss account, and a calculated loan amount is included on the other side of the balance sheet as well, as a loan, with an annual interest charge included in costs in the profit and loss account.
Now, any improvements to the stadium financed by City will be added to the cost of the asset in the balance sheet and there will therefore be an increased amortisation charge (increase = cost of improvement over the number of remaining years of useful life) each year. Depending how the improvements are financed, there will either be an additional loan in the balance sheet with an annual interest charge to the profit and loss account, or increased equity with no profit and loss effect.
What was it you asked, again? I forgot where I was going with that ....