I need some help from the math majors out there. The question of the week a couple of weeks ago concerned making charitable contributions and taking the tax deductions. For those not familiar with the US tax code, money paid to certain charities is deductible for income tax purposes, generally within the year paid.
The situation: I want to make a $1,000 charitable contribution in the first part of 2005 and I decide that I want to do this the last week of 2004. There exists some date in 2005 before which it makes sense for me to make the contribution on December 31, 2004 thereby getting the deduction earlier than if I had made it when planned. Positive and negative cash flows sounds like a problem for IRR (Internal Rate of Return) to me.
Some assumptions: I make 10% on my money and I pay a total tax rate of 33%. Also, I get a refund three months after year end.
I set up the cash flows and calced the IRR but didn’t get the expected results. I wanted to see if I could figure it out manually to help me find my error. Manually, I come up with April 30th, i.e. contributions I plan on making before April 30th should be made before the end of the year, and those after should be made when planned. My question is: Why don’t the IRRs equal when the cash flows from the manual method equal?
Column B – I make the payment on Dec 31st and get the refund on Mar 31st. Thereafter, I earn 10% on my money.
Column D – I earn money on my $1,000 until I pay it out, then get my refund three months after I file my 2005 return.
Columns F and H just show the cash out because IRR is supposed to take the time value of money into consideration.
You can download CharityIRR.zip to see how it works. And if you know where I have erred, please educate me.