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29 December, 11:08

Shannon Co. is considering a project that has the following cash flow and cost of capital (r) data. What is the project's discounted payback? r = 10.00%Year 0 1 2 3 4Cash flows - $950 $525 $485 $445 $405a. 1.61 yearsb. 1.79 yearsc. 1.99 yearsd. 2.22 yearse. 2.44 years

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  1. 29 December, 14:50
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    d. 2.22 years

    Explanation:

    The formula to compute the payback period is shown below:

    = Initial investment : Net cash flow

    In this question, the discount rate is given i. e 10%

    The discount factor should be computed by

    = 1 : (1 + rate) ^ years

    where,

    rate is 10%

    Year = 0,1,2,3,4

    Discount Factor:

    For Year 1 = 1 : 1.10^1 = 0.9091

    For Year 2 = 1 : 1.10^2 = 0.8264

    For Year 3 = 1 : 1.10^3 = 0.7513

    For Year 4 = 1 : 1.10^4 = 0.6830

    Yearly cash inflows:

    Year 1 = Year 1 cash inflow * Present Factor of Year 1

    = $525 * 0.9091

    = $477.27

    Year 2 = Year 2 cash inflow * Present Factor of Year 2

    = $485 * 0.8264

    = $400.80

    Year 3 = Year 3 cash inflow * Present Factor of Year 3

    = $445 * 0.7513

    = $334.33

    Year 4 = Year 4 cash inflow * Present Factor of Year 4

    = $405 * 0.6830

    = $276.62

    If we sum the first 2 year cash inflows than it would be $878.03

    Now we deduct the $878.03 from the $950, so the amount would be $71.97 as if we added the fourth year cash inflow so the total amount exceed to the initial investment. So, we deduct it

    And, the next year cash inflow is $334.33

    So, the payback period equal to

    = (2 years + $71.97) : ($334.33)

    = 2.22 yeas

    In 2.22 yeas, the invested amount is recovered.
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