How does using $100 cash to pay back a $40 loan affect the 3 financial statements? Assume a 10% tax rate.

Ok so cash is down by $94 (u add back the tax shield)
Loans payable is down by $40
So by A = L + SE, SE has to go down by $54
On the income statement, there is an interest expense of $60, so pretax income is down $60. With the tax shield, net income is only down by $54
On the CFS, net income is down by $54 but I don't know what to do after this. Do you add interest expense back? But that wouldn't make net change in cash to be down by $94.
Let me know if I'm right or wrong, and any clarification is appreciated.

 
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Not sure if this question makes much sense. The way you worded it, cash would be down $40 (and show up on CFS as debt repayment) and on the BS cash would be down by $40 and liabilities would be down by $40 (equity unchanged). 
 

Tax rate only comes into effect if the questions incorporates interest expense, etc. Are you remembering the question correctly? And yes, cash interest expense  only shows up on the P&L

 

And how is cash only down by $40? You're using cash to pay back both the principal amount and the interest incurred from it.

 

On IS, $60 in interest expense, assuming 10% tax rate, NI goes down by $54.

On CFS, NI down by $54, CFF down by $40 due to principal repayment, cash down by $94.

On BS, on asset side, cash down by $94. On liabilities side, debt down by $40 due to principal repayment. On equity side, SE down by $54 due to fall in NI.

A down by $94 = L down by $40 + E down by $54 ($94)

 

So in the CFS, you don't do anything with interest expense?

 

No because the net income that flows into the cash flow statement was already reduced by the interest expense on the income statement. You don’t add back interest expense because it was an actual outflow of cash and reduced your net income. Cash from financing recognizes the $40 principal pay down as -40 (note only payments of principal recognized here). That leads to -54 NI + (-40 principal payment) = -94 change in cash

 

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