Calculate the net present value for a project with an investment cost of $104,000 and would develop cash flows of $20,000 the first year, $22,000 the second year, $23,000 the third year, $24,000 the fourth year, $25,000 the fifth year, and $30,000 the sixth year. the discount rate is 12.00%.

The net present value for a project is -$7,596.61

Explanation:

The computation of the Net present value is shown below

= Present value of all yearly cash inflows after applying discount factor - initial investment

The discount factor should be computed by

= 1 ÷ (1 + rate) ^ years

where,  

rate is 9%  

Year = 0,1,2,3,4 and so on

Discount Factor:

For Year 1 = 1 ÷ 1.12^1 = 0.8928

For Year 2 = 1 ÷ 1.12^2 = 0.7971

For Year 3 = 1 ÷ 1.12^3 = 0.7117

For Year 4 = 1 ÷ 1.12^4 = 0.6355

For Year 5 = 1 ÷ 1.12^5 = 0.5674

For Year 6 = 1 ÷ 1.12^6 = 0.5066

So, the calculation of a Present value of all yearly cash inflows are shown below

= Year 1 cash inflow × Present Factor of Year 1 + Year 2 cash inflow × Present Factor of Year 2 + Year 3 cash inflow × Present Factor of Year 3 + Year 4 cash inflow × Present Factor of Year 4 + Year 5 cash inflow × Present Factor of Year 5 + Year 6 cash inflow × Present Factor of Year 6  

= $20,000 × 0.8928 + $22,000  × 0.7971 + $23,000 × 0.7117 + $24,000  × 0.6355 + $25,000  × 0.5674 + $26,000  × 0.5066

= $17,857.14  + $17,538.27  + $16,370.95  + $15,252.43  + $14,185.67  + $15,198.93  

= $96,403.39

And, the initial investment is $104,000

So, the NPV =   $96,403.39 - $104,000 = -$7,596.61

Since the NPV is negative so the project would not be accepted.

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