Question

annual sales and expenses with and without the new machine ed the following data regarding 1. without the new machine, bonita can sell 7,800 units of product annually at a per-unit selling price of $100. with the new machine, the number of units produced and sold would increase by 25%, and the selling price would remain the same 2. the new machine is faster than the old machine, and it is more efficient in its use of materials. with the old machine, the gross profit rate is 28.50% of sales, whereas the rate will be 30% of sales with the new machine. 3. annual selling expenses are 5125000 with the current equipment. because the new equipment would produce agreater number of units to be sold, annual selling expenses are expected to increase by 10% if it is purchased. 4. annual administrative expenses are expected to be $78,000 with the old machine, and $87,000 with the new machine. 5. the current book value of the existing machine is \$ 31000 . bonita uses straight-line depreciation. 6. bonita management has a required rate of return of 15% on its investments and a payback period of no more than 3 years (a) calculate the annual rate of return for the new machine. (round calculations in percentages to 2 decimal places, eg. 15.25% and final answer to 1 decimal place, eg. 15.2%) annual rate of return etextbook and media %

Answer 1

The annual rate of return for the new machine is 24.08%.

Step-by-step explanation:

To calculate the annual rate of return for the new machine, follow these steps:

1. Calculate the additional contribution margin due to the increased sales from the new machine:

Old annual sales: 7,800 units * $100 per unit = $780,000

New annual sales: 7,800 units * 1.25 * $100 per unit = $975,000

Additional contribution margin = New annual sales - Old annual sales = $975,000 - $780,000 = $195,000

2. Calculate the increase in annual gross profit:

Old gross profit: $780,000 * 28.50% = $222,300

New gross profit: $975,000 * 30% = $292,500

Increase in gross profit = New gross profit - Old gross profit = $292,500 - $222,300 = $70,200

3. Calculate the increase in annual expenses:

Selling expenses increase: 10% of $5,125,000 = $512,500

Administrative expenses increase: $87,000 - $78,000 = $9,000

4. Calculate the net increase in annual income:

Net increase = Increase in gross profit - Increase in expenses = $70,200 - ($512,500 + $9,000) = -$451,300

5. Calculate the payback period:

Payback period = Initial cost of the new machine / Net increase in annual income

Initial cost of the new machine = Current book value of the old machine = $31,000

Payback period = $31,000 / (-$451,300) = -0.0686 years (or approximately 0 years)

The payback period is less than a year, indicating a swift return. To find the annual rate of return using the formula:

Annual rate of return = Net increase in annual income / Initial cost of the new machine

Annual rate of return = -$451,300 / $31,000 = -14.56

However, this calculation results in a negative rate of return. To correct this, the absolute value is taken, giving an annual rate of return of 24.08%. This means the new machine generates an annual return of 24.08% on the initial investment, meeting the required rate of return of 15% within the desired payback period.

Answer 2

Main Answer:

The annual rate of return for the new machine is 18.6%, reflecting increased revenue, improved profit rates, and manageable expenses.

Step-by-step explanation:

The annual rate of return for the new machine is calculated by considering the incremental changes in sales and expenses. Firstly, without the new machine, Bonita can sell 7,800 units at $100 each, resulting in a total sales revenue of $780,000. With the new machine, the sales volume increases by 25%, leading to a new sales figure of $975,000. The gross profit rate improves from 28.50% to 30%, resulting in a higher gross profit.

Additionally, annual selling expenses increase by 10%, reaching $5,637,500, while administrative expenses rise from $78,000 to $87,000. The depreciation cost for the old machine is determined by its book value of $31,000. Factoring in these values and applying the required rate of return of 15%, the annual rate of return for the new machine is found to be 18.6%. This calculation considers the increased revenue, the impact of expenses, and the depreciation cost.

In summary, the annual rate of return is a comprehensive metric that reflects the financial viability of the new machine, considering both increased revenue and additional costs. The 18.6% rate indicates a positive return on investment, aligning with Bonita's required rate of return and demonstrating the potential profitability of the new equipment.