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.

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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