Your company,which is financed entirely with common equity,plans to manufacture a new product,a cell phone that can be worn like a wristwatch.Two robotic machines are available to make the phone,Machine A and Machine B.The price per phone will be $250.00 regardless of which machine is used to make it.The fixed and variable costs associated with the two machines are shown below,along with the capital (all equity) that must be invested to purchase each machine.The expected sales level is 25,000 units.Your company has tax loss carry-forwards that will cause its tax rate to be zero for the life of the project,so T = 0.How much higher or lower will the project's ROE be if you select the machine that produces the higher ROE,i.e.,what is ROE_B − ROE_A? (Hint: Since the firm uses no debt and its tax rate is zero,ROE = EBIT/Required investment.)

Question

Quizplus · Accepted Answer

To calculate the project's ROE, we need to find the EBIT (earnings before interest and taxes) and required investment for each machine.

Machine A:

EBIT = (25,000 units * $250.00 price) - $480,000 fixed costs - (25,000 units * $35.00 variable cost) 
EBIT = $1,875,000 - $480,000 - $875,000 
EBIT = $520,000

Required investment = $1,200,000

ROE = EBIT/Required investment = $520,000/$1,200,000 = 0.4333 or 43.33%

Machine B:

EBIT = (25,000 units * $250.00 price) - $800,000 fixed costs - (25,000 units * $25.00 variable cost) 
EBIT = $1,875,000 - $800,000 - $625,000 
EBIT = $450,000

Required investment = $1,600,000

ROE = EBIT/Required investment = $450,000/$1,600,000 = 0.2813 or 28.13%

The difference in ROE between the two machines is:

ROE (Machine B) - ROE (Machine A) = 0.2813 - 0.4333 = -0.152 or -15.2%

Therefore, if we select Machine A, the project's ROE will be higher by 15.2% compared to if we select Machine B.

Therefore, the best choice is to select Machine A.

Your Company,which Is Financed Entirely with Common Equity,plans to Manufacture