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11 January, 06:12

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%.

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  1. 11 January, 06:39
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    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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