Crossword Genius

Cost of being twice disheartened when about to start (8)

Ross

I believe the answer is:

twopence

I'm a little stuck... Click here to teach me more about this clue!

'cost of' is the definition.
The definition and answer can be both related to property as well as being singular nouns.
Perhaps there's an association between them I don't understand?

'twice disheartened when about to start' is the wordplay.
'disheartened' suggests removing the centre.
'when about' indicates putting letters inside.
'to start' becomes 'open' (opening is a kind of starting).
'twice' with its middle removed is 'twce'.
'twce' going around 'open' is 'TWOPENCE'.

'being' acts as a link.

Can you help me to learn more?

(Other definitions for twopence that I've seen before include "bit of history" , "Penny plain, - coloured" , "Low-value coin" , "Not much money" , "very little bread" .)

I've seen this clue in the Evening Standard.
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