NPV

Case 1: If the discount rate changes each year (your question)

Use the cumulative discount factor because each year's rate applies sequentially.

Year	Cash Flow (₹)	Discount Factor	Present Value (₹)
0	-12,000	1	-12,000.00
1	4,000
2	5,000
3	7,000
4	6,000
5	5,000

Total Present Value of Inflows

3508.77 + 3813.88 + 4603.22 + 3345.76 + 2321.89 = 17,593.52

Net Present Value (NPV)

\text{NPV} = 17,593.52 - 12,000 = \boxed{₹5,593.52}

Decision

Since NPV is positive (₹5,593.52), the project should be accepted.

Note: This is the mathematically correct method only if the discount rate changes every year. If your teacher intended a constant discount rate, then a single rate (e.g., 14% every year) should be used instead.

For a minimum page occupancy (suitable for a lab record or exam), write it like this:

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Net Present Value (NPV) Calculation

Given Data

Year	Cash Flow (₹)	Discount Rate
0	-12,000	0%
1	4,000	14%
2	5,000	15%
3	7,000	16%
4	6,000	18%
5	5,000	20%

Formula

\text{NPV}=\text{Total PV of Cash Inflows}-\text{Initial Investment}

Calculations

PV_1=\frac{4000}{1.14}=3508.77

PV_2=\frac{5000}{1.14\times1.15}
=\frac{5000}{1.3110}
=3813.88

PV_3=\frac{7000}{1.14\times1.15\times1.16}
=\frac{7000}{1.52076}
=4603.22

PV_4=\frac{6000}{1.14\times1.15\times1.16\times1.18}
=\frac{6000}{1.79450}
=3345.76

PV_5=\frac{5000}{1.14\times1.15\times1.16\times1.18\times1.20}
=\frac{5000}{2.15340}
=2321.89

Total Present Value

3508.77+3813.88+4603.22+3345.76+2321.89
=17,593.52

Net Present Value

\boxed{\text{NPV}=17,593.52-12,000=₹5,593.52}

Decision

NPV = +₹5,593.52 (Positive)

Therefore, the project is financially feasible and should be accepted.

This version fits comfortably on one notebook page while showing all essential calculation steps.