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The tax amortization benefit factor (or TAB factor) is the result of a mathematical function of a corporate tax rate, a discount rate and a tax amortization period: T A B f a c t o r = 1 [ 1 − t n ∗ ( 1 k − 1 ( k ∗ ( 1 + k ) n ) ) ] {\displaystyle TAB_{factor}\,=\,{1 \over [1-{t \over n}*({1 \over k}-{1 \over (k*(1+k)^{n})})]}}
In discount cash flow analysis, all future cash flows are estimated and discounted by using cost of capital to give their present values (PVs). The sum of all future cash flows, both incoming and outgoing, is the net present value (NPV), which is taken as the value of the cash flows in question; [ 2 ] see aside.
With an interest rate of i = 10%, and n = 10 years, the CRF = 0.163. This means that a loan of $1,000 at 10% interest will be paid back with 10 annual payments of $163. [2] Another reading that can be obtained is that the net present value of 10 annual payments of $163 at 10% discount rate is $1,000. [2]
Equivalently C is the periodic loan repayment for a loan of PV extending over n periods at interest rate, i. The formula is valid (for positive n, i) for ni≤3. For completeness, for ni≥3 the approximation is . The formula can, under some circumstances, reduce the calculation to one of mental arithmetic alone.
The NPV formula accounts for cash flow timing patterns and size differences for each project, and provides an easy, unambiguous dollar value comparison of different investment options. [10] [11] The NPV can be easily calculated using modern spreadsheets, under the assumption that the discount rate and future cash flows are known.
The present value formula is the core formula for the time value of money; each of the other formulas is derived from this formula. For example, the annuity formula is the sum of a series of present value calculations. The present value (PV) formula has four variables, each of which can be solved for by numerical methods: