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manny2012 · Aug 23, 2009, 12:02 PM

How do I calculate the NPV of cash inflow and out flows
Sales are at 225,000 in the first year and incremental @ 6% per year for 10 years.
Expenses at 190,000 in the firs year and incremental @ 5% per year for 10 years.
Tax rate @ 34%.

Thanks

ArcSine · Aug 23, 2009, 02:36 PM

If you need to show the NPV of each of those three items separately, you can hit Sales and Expenses with a handy formula...

$\left( \frac{C_1}{r-g} \right) \ \times\ \left( 1-\left( \frac{1+g}{1+r} \right)^n \right)$

... where C1 is the first cash flow; r is the discount rate (unspecified in your question); g is the constant growth rate of the cash flow sequence; and n denotes the total number of cash flows.

Tax Expense is a bit of a fly in the ointment, though. With Sales and Expenses growing at different rates, taxable income (and thus tax expense) will not be growing at a constant rate each period, making the previous shortcut formula inapplicable.

You'll need to compute the tax expense for each period, then hit each one with the basic comp for the PV of a single amount: $PV\ =\ \frac{C}{(1+r)^n}$ where n is the period in which the cash flow C occurs.

The PV of the tax expense stream will be the sum of the individual PVs. A basic spreadsheet app (Excel, e.g.) is a great time-saver for this kind of exercise, but you'll do yourself a disservice if you don't develop an understanding of the underlying principles first.

Enjoy!