Question

A project has annual cash flows of $3,500 for the next 10 years and then $6,000 each year for the following 10 years. The IRR of this 20-year project is 12.1%. If the firm's WACC is 8%, what is the project's NPV?

Answer 1

At IRR, Net present value (NPV) = 0

Where Net present value = Present value of cash inflows - Initial Investment

Computation of Initial Investment.

At IRR, Present value of cash inflows - Initial Investment = 0

So, Present value of cash inflows = Initial Investment

Present value of cash inflows at IRR = [$3,500 / (1.121)¹] + [$3,500 / (1.121)²] + [$3,500 / (1.121)³] + [$3,500 / (1.121)⁴] + [$3,500 / (1.121)⁵] + [$3,500 / (1.121)⁶] + [$3,500 / (1.121)⁷] + [$3,500 / (1.121)⁸] + [$3,500 / (1.121)⁹] + [$3,500 / (1.121)¹⁰] + [$6,000 / (1.121)¹¹] + [$6,000 / (1.121)¹²] + [$6,000 / (1.121)¹³] + [$6,000 / (1.121)¹⁴] + [$6,000 / (1.121)¹⁵] + [$6,000 / (1.121)¹⁶] + [$6,000 / (1.121)¹⁷] + [$6,000 / (1.121)¹⁸] + [$6,000 / (1.121)¹⁹] + [$6,000 / (1.121)²⁰]

Present value of cash inflows at IRR = $30,469.29

So, Initial Investment = $30,469.29.

Computation of NPV at WACC (8%)

NPV =  Present value of cash inflows - Initial Investment

NPV = [$3,500 / (1.08)¹] + [$3,500 / (1.08)²] + [$3,500 / (1.08)³] + [$3,500 / (1.08)⁴] + [$3,500 / (1.08)⁵] + [$3,500 / (1.08)⁶] + [$3,500 / (1.08)⁷] + [$3,500 / (1.08)⁸] + [$3,500 / (1.08)⁹] + [$3,500 / (1.08)¹⁰] + [$6,000 / (1.08)¹¹] + [$6,000 / (1.121)¹²] + [$6,000 / (1.08)¹³] + [$6,000 / (1.08)¹⁴] + [$6,000 / (1.08)¹⁵] + [$6,000 / (1.08)¹⁶] + [$6,000 / (1.08)¹⁷] + [$6,000 / (1.08)¹⁸] + [$6,000 / (1.08)¹⁹] + [$6,000 / (1.08)²⁰] - $30,469.29

NPV = $42,133.68 - $30,469.29

NPV = $11,664.39

So, Project's NPV is $11,664.39

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