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The project has the following cash flow:

| Year | 0 | 1 | 2 | 3 | 4 | 5 |
|------------|--------|--------|--------|--------|--------|--------|
| Total Cost | 100000 | 20000 | 20000 | 25000 | 25000 | 20000 |
| Total Revenue | - | 50000 | 65000 | 70000 | 80000 | 90000 |

Find its NPV at a 10% discount rate.

Answer :

i) The NPV of the project at a 10% discount rate is $79,284, indicating that ii) the project is viable as it is expected to generate more cash than it costs.

To find the NPV at a 10% discount rate, we use the formula:

NPV = ∑ [[tex](R_t - C_t)[/tex] / [tex](1 + r)^t[/tex]] where[tex]R_t[/tex] is the revenue, [tex]C_t[/tex] is the cost, r is the discount rate, and t is the year.

  1. Year 0: Cash Flow = -$100,000, Discount Factor = 1, Present Value = -$100,000
  2. Year 1: Cash Flow = $50,000 - $20,000 = $30,000, Discount Factor = 0.909, Present Value = $27,273
  3. Year 2: Cash Flow = $65,000 - $20,000 = $45,000, Discount Factor = 0.826, Present Value = $37,187
  4. Year 3: Cash Flow = $70,000 - $25,000 = $45,000, Discount Factor = 0.751, Present Value = $33,795
  5. Year 4: Cash Flow = $80,000 - $25,000 = $55,000, Discount Factor = 0.683, Present Value = $37,559
  6. Year 5: Cash Flow = $90,000 - $20,000 = $70,000, Discount Factor = 0.621, Present Value = $43,470

NPV = -$100,000 + $27,273 + $37,187 + $33,795 + $37,559 + $43,470 = $79,284

Based on its NPV, the project is viable because the NPV is positive ($79,284), indicating that the project is expected to generate more cash than the cost, making it a profitable investment.

Complete question

The project has the following cash flow

Year 0 1 2 3 4 5 Total cost

100000 20000 20000 25000 25000 20000

Total revenue 50000 65000 70000 80000 90000

Required;

i. Find its NPV at 10% discount rate

ii. Based on its NPV, is the project viable or not? Give reasons

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Rewritten by : Barada