Question

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.

Answer 1

Answer:

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%

Answer 2

The value of the computations will be:

• 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%

The Payback Period will be calculated as:

Payback Period = Investment / Even Cash flow

Cash flow = $25,000 + $80,000 = $105,000

Payback Period will now be:

= $275,000 / $25,000

= 11 Years

The net present value will be:

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

where,

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

= $105,000 × 3.791

= $398,055

Therefore, the net present value will be:

= $398,055 - 275,000

= $123,055

The profitability index will be:

PI = NPV / Investment

PI = $123,055 / $275,000

= 0.45

The internal rate of return will be:

NPV = ($125,000 × 3) - $275,000

NPV = $375000 - $275000

= $100,000

Therefore, IRR will be:

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

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

= 10% + (10%  × 4.348)

= 53.48%

Lastly, the annual rate of return will be:

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

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

Therefore, the annual rate of return is 38.18%.

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