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26 December, 09:59

Mimi Company is considering a capital investment of $275,000 in new equipment. The equipment is expected to have a 5-year useful life with no salvage value. Depreciation is computed by the straight-line method. During the life of the investment, annual net income and cash inflows are expected to be $25,000 and $80,000, respectively. Mimi's minimum required rate of return is 10%. The present value of 1 for 5 periods at 10% is. 621 and the present value of an annuity of 1 for 5 periods at 10% is 3.791.

Required:

Compute each of the following:

a. The cash payback period.

b. The net present value of the total investment.

c. The profitability index.

d. The Internal rate of return.

e. The annual rate of return.

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Answers (1)
  1. 26 December, 10:26
    0
    Payback Period: 11 Years

    Net Present Value: $123,055

    Profitability Index: 0.45

    Internal rate of return: 53.48%

    Annual rate of return: 38.18%

    Explanation:

    Payback Period:

    The Cash Payback Period can be calculated from the following formula, when the cash inflows are even Cash flows:

    Payback Period = Investment / Even Cash flow

    Here total annual even cash flow = $25,000 + $80,000 = $105,000

    By putting values, we have:

    Payback Period = $275,000 / $25,000 = 11 Years

    Net Present Value:

    As we know:

    Net present Value = Present Value of Cash inflow - Present Value of Cash Outflow

    Here

    Present Value of Cash Inflow = Even Cash flow * Annuity Factor

    By putting values:

    Present Value of Cash Inflow = $105,000 * 3.791 = $398,055

    Now Present value of cash outflow which is investment will the same because the money is invested in the year zero.

    Which means:

    Net present Value = $398,055 - 275,000 = $123,055

    Profitability Index:

    The profitability Index can be calculated using the following formula:

    PI = NPV / Investment

    So by putting values, we have:

    PI = $123,055 / $275,000 = 0.45

    Internal rate of return:

    At 10%, NPV is $123,055 so all we have to do is to use a higher cost of capital to find using the formula at the end, the breakeven rate of return at which NPV is zero.

    So I choose 20%.

    At 20%, annuity factor is 2.990 which is approximately 3.

    So

    NPV = $125,000 * 3 - $275,000 = $100,000

    By putting values in the following formula:

    IRR = Lower Percentage + (Higher percentage - Lower percentage) * (NPV at Higher Percentage) / (NPV at lower - NPV at higher)

    By putting values, we have:

    IRR = 10% + (20% - 10%) * ($100,000) / ($123000 - $100,000)

    IRR = 10% + 10% * 4.348 = 53.48%

    Annual rate of return:

    Annual rate of return can be calculated using the following formula:

    Annual rate of return = Earnings Before Interest and tax / Investment

    Here

    Earnings before interest and tax is $105,000

    So by putting formula, we have:

    Annual rate of return = $105,000 / $275,000 = 38.18%
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