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It would seem the partnership has not paid the expenses and therefore can not deduct them

hope your buddy also has a dedicated space for the business because he is subject to the home office rules 

so it comes down to what you agree to.

 

here are your options

a) Deduct the cost as an unreimbursed partner expense (UPE), or
b) Get reimbursement from your partnership via an accountable plan 

 

a) Unreimbursed Partner Expense
As a partner in a partnership, you generally can’t deduct any of the partnership expenses on your individual tax return—the partnership should pay for and deduct its own business expenses.

But if your partnership agreement or business policy forces you to pay for the expense out of pocket with no reimbursement available, then you can deduct the business expense in full on your individual tax return as Unreimbursed Partner Expenses (through the partnership K-1). Turbotax allows this. note the need for a partnership agreement or business policy which should be in writing and signed by both partners. 

Because the UPE is a trade or business expense, it also reduces your self-employment tax. You can deduct your full home-office expense even when the partnership has a tax loss for the year. Use Form 8829 to calculate the amount (but don’t include it with your tax return). 

b) Accountable Reimbursement Plan
The other option for realizing your home-office deduction is to have your partnership reimburse you for your home-office expenses under an accountable plan. This should be in writing 

When your partnership does this, the reimbursement is tax-free to you, the partner, and tax-deductible to the partnership, which reduces your share of the taxable net income from the partnership.
Here are the steps to obtaining the reimbursement:

a) Each of you uses Form 8829 (including depreciation)  to calculate the amount this can be done annually but the partnership can not deduct the reimbursement until it is actually paid to the partners. reimbursement can be as frequent as you agree to. 
b) Each submits the reimbursement request with appropriate documentation within the time frame required by your partnership’s accountable plan policy.
c) the partnership issues the reimbursement check 

 

if you each want to bear your own expenses the UPE option is probably the best choice. 

 

each of you will need to keep track of the depreciation taken because if you sell your homes at a gain, the depreciation taken must be recaptured before the home sale exclusion can be applied. the tax basis of your home is reduced by the depreciation deduction.