You are considering building a shopping mall. The initial investment is $1.33 million. The cash flows...

You are considering building a shopping mall. The initial investment is $1.33 million. The cash flows are $480,000 for year 1, $250,000 for year 2. $160,000 for year 3, and $170,000 for year 4. What are the net present value (NPV), and profitability index (PI) of the project if the cost of capital is 7%? Compute the internal rate of return (IRR) for the project. What is the NPV of the shopping mall?

Solutions

Expert Solution

Net present value = Present value of cash inflows - present value of cash outflows

Net present value = -1,330,000 + 480,000 / (1 + 0.07)¹ + 250,000 / (1 + 0.07)² + 160,000 / (1 + 0.07)³ + 170,000 / (1 + 0.07)⁴

Net present value = -1,330,000 + 927,257.6953

Net present value = -402,742.34

Profitability index = Present value / initial investment

Present value = 480,000 / (1 + 0.07)¹ + 250,000 / (1 + 0.07)² + 160,000 / (1 + 0.07)³ + 170,000 / (1 + 0.07)⁴

Present value = 927,257.6953

Profitability index = 927,257.6953 / 1,330,000

Profitability index = 0.697

IRR is the rate of return that makes NPV equal to 0

Net present value = -1,330,000 + 480,000 / (1 + R)¹ + 250,000 / (1 + R)² + 160,000 / (1 + R)³ + 170,000 / (1 + R)⁴

Using trial and error method, i.e., after trying various values for R, lets try R as -10.30

Net present value = -1,330,000 + 480,000 / (1 + -0.1030)¹ + 250,000 / (1 + -0.1030)² + 160,000 / (1 + -0.1030)³ + 170,000 / (1 + -0.1030)⁴

Net present value = 0

Therefore, IRR is -10.30%

Note: Calculating IRR using trial and error method can be time consuming. It is always best to use a financial calculator to calculate IRR

jeff jeffy answered 11 months ago

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