A small manufacturer is considering two alternative machines.Machine A costs $1.0 million,has an expected life of 5 years,and generates after-tax cash flows of $350,000 per year.At the end of 5 years,the salvage value of the machine is zero,but the company will be able to purchase another Machine A at a cost of $1.2 million.The second Machine A will generate after-tax cash flows of $375,000 a year for another 5 years,at which time its salvage value will again be zero.Alternatively,the company can buy Machine B at a cost of $1.5 million today.Machine B will produce after-tax cash flows of $400,000 a year for 10 years,after which it will have an after-tax salvage value of $100,000.Assume that the cost of capital is 12%.Based on the equivalent annual annuity,if the company chooses the machine that adds the most value to the firm,by how much will the company's value increase per year?
A)$792,286.54
B)$347,802.00
C)$140,227.71
D)$61,557.88

Question

Quizplus · Accepted Answer

To determine which machine adds the most value to the firm per year, we calculate the Equivalent Annual Annuity (EAA) for each machine. The EAA converts the net present value (NPV) of each machine's cash flows into an annual amount over the machine's life, making it easier to compare machines with different costs and lifespans.For Machine A, we first calculate the NPV of the first 5 years and then the NPV of the second 5 years, considering the purchase cost at the end of the first 5 years. We then find the EAA for the total NPV over the 10-year period.For Machine B, we calculate the NPV of its cash flows over 10 years, including the salvage value, and then find the EAA over the 10-year period.The machine with the higher EAA adds more value to the firm per year. The correct answer reflects the difference in EAA between the two machines, indicating by how much the chosen machine's EAA exceeds the other's, thus showing the annual increase in the company's value by choosing the more valuable machine.

A Small Manufacturer Is Considering Two Alternative Machines