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I can't answer for the foreign housing exclusion, but I can tell you how housing expenses would be calculated for the clergy housing allowance. I suspect the rules are similar.
For the period when you received free housing, your "cost" is the fair market value of the housing, and the taxable value is also the fair market value. For the period when you received a cash stipend, the value of the cash stipend is the cash, and the cost of housing is what you actually paid.
The calculation (over the course of a whole year) would look like this:
Report as cost | Report as value | ||
January | Free housing worth $1500/month | $1500 | $1500 |
Feb | Free housing worth $1500/month | $1500 | $1500 |
March | Free housing worth $1500/month | $1500 | $1500 |
Apr, May, June | Free housing worth $1500/month | $4500 | $4500 |
July | Cash stipend of $1500, actual cost was $2000 | $1500 | $2000 |
Aug | Cash stipend of $1500, actual cost was $1900 | $1500 | $1900 |
Sept | Cash stipend of $1500, actual cost was $1800 | $1500 | $1800 |
Oct | Cash stipend of $1500, actual cost was $1500 | $1500 | $1500 |
Nov | Cash stipend of $1500, actual cost was $1300 | $1500 | $1500 |
Dec | Cash stipend of $1500, actual cost was $1300 | $1500 | $1500 |
Total | $18,000 | $19,200 |
(For this example, I assume you are living in a hot country and your utilities were higher due to air conditioning. The example would be calculated the same if your actual cost varied for any other reason, such as changing utilities, various housing fees, insurance, rent increases, and so on.)
I hope that makes sense.