Question

LG Company is considering the purchase of a new machine. Its invoice price is $98,000, freight charges are estimated to be $2400, and installation costs are expected to be $4,000. Salvage value of the new machine is expected to be zero after a useful life of 4 years. Existing equipment could be retained and used for an additional 4 years if the new machine is not purchased. At that time, the salvage value of the equipment would be zero. If the new machine is purchased now, the existing machine would be sold. Company's accountant, Ethan Ng, has accumulated the following data regarding annual sales and expenses with and without the new machine.

Without the new machine, company can sell 8,500 units of product annually at a per unit selling price of $90. If the new unit is purchased, the number of units produced and sold would increase by 25%, and the selling price would remain the same.
The new machine is faster than the old machine, and it is more efficient in its usage of materials. With the old machine the gross profit rate will be 29% of sales, whereas the rate will be 30% of sales with the new machine. (Note: These gross profit rates do not include depreciation on the machines. For purposes of determining net income, treat depreciation expense as a separate line item.).
Annual selling expenses are $128,000 with the current equipment. Because the new equipment would produce a greater number of units to be sold, annual selling expenses are expected to increase by 10% if it is purchased.
Annual administrative expenses are expected to be $80,000 with the old machine, and $90,000 with the new machine.
The current book value of the existing machine is $32,000. LG uses straight-line depreciation.
LG’s management has a required rate of return of 15% on its investment and a cash payback period of no more than 3 years. Calculate the annual rate of return of the new machine.

Answer 1

To calculate the annual rate of return for the new machine, the increased net income from the machine is divided by the initial investment cost, resulting in an approximate annual rate of return of 41.4%.

Step-by-step explanation:

The question asks us to calculate the annual rate of return of the new machine that LG Company is considering purchasing. To do this, we first need to determine the additional annual net income that the new machine would generate and then compare it to the initial investment of the machine.

First, we'll calculate the increased number of units sold due to the new machine, which is 8,500 units plus an additional 25%, totaling 10,625 units. At a selling price of $90 per unit, total sales with the new machine would be $956,250. With a gross profit rate of 30%, the gross profit will be $286,875.

Deduct the increased selling expenses (10% higher than $128,000, thus $140,800) and higher administrative expenses ($90,000), without including depreciation. Then, subtract the annual depreciation expense, which is the cost of the new machine including freight and installation ($104,400) divided by its useful life (4 years), resulting in $26,100 per year. The annual net income increase is the gross profit minus the incremental operating expenses and depreciation, which is $286,875 - $140,800 - $90,000 - $26,100 = $29,975.

To find the annual rate of return, we divide the annual net income increase by the initial investment of the machine and express it as a percentage. The initial investment is the cost of the machine including freight and installation ($104,400) minus the book value of the old machine that could be sold ($32,000), resulting in a net investment of $72,400. The annual rate of return is then $29,975 / $72,400 * 100% ≈ 41.4%. Therefore, the annual rate of return of the new machine is approximately 41.4%.