NPV?
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By table, I'm guessing you're referring to the discount rates?
As you know, NPV = (Sum of (cashflows year t) * (discount rate year t) from year t = 1 to N ) + Initial investment
The discount rates are 1 / (1 + discount rate )^t
The table is just a look-up table for those discount rates. On one axis you have years/time periods, on the other discount rate.
Let's say you have the following data:
Initial investment = -20
CF(t=1) = 10
CF(t=2) = 20
CF(t=3) = 30
And with different discount rates
r(t=1,2,3) = 5%
Your NPV is then
NPV = CF(t=1) x r(t=1)+CF(t=2) x r(t=2)+CF(t=3) x r(t=3)-Investment
From the lookup table (https://image.slidesharecdn.com/npvtable-140826205336-phpapp02/95/npv-t…</a">for example this link) you find the following:
Period 1, Discount Rate 5% : 0.9524
Period 2, DR 5% : 0.9070
Period 3, DR 5%: 0.8638
Ok, now you can insert all the data into your NPV equation
NPV = CF(t=1) x r(t=1)+CF(t=2) x r(t=2)+CF(t=3) x r(t=3)-Investment NPV = (10)x(0.9524)+(20)x(0.9070)+(30)x(0.8638)-20 = 33.575
If the yearly rates are different (year 1, i = 5%, year 2, i =3%, etc.), you simply multiply the discount rates, instead of using the table.
i.e
CF(1) * 1/(1+r1) + CF(2) * 1/((1+r1)(1+r2)) + ... + CF(N) * 1/((1+r1)(1+r2)...(1+rN))
.
Could you provide visual examples of your problem? Having a real hard time figuring out what you're trying to say.
NPV is a sum of PV future cash flows, so that NPV = PV(CF1) + PV(CF2) + PV(CF3), nothing more to it than that.
To find PV of any future CF, you simply divide/multiply by the appropriate discount rates. If the rate is fixed, you the formula is PV = FV/(1+r)^n, if the rate is not fixed, you need to divide by every previous rate (1+r_1)(1+r_2)...(1+r_n), up to your future year / period n.
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