Question

A company is considering the replacement of its old, fully depreciated welding machine. Two new models are available: Machine X which has a cost of $216,000.00, a 5 -year expected life, and after-tax cash flows (labor savings and depreciation) of $87,000.00 per year; and Machine Y, which has a cost of $432,000.00, a 10-year life, and aftertax cash flows of $88,000.00 per year. Welding machine prices are not expected to rise, because inflation will be offset by cheaper components used in the machines. Assume that the company's cost of capital is 12.0%. What is the equivalent annual annuity for Machine Y ?

a)$30,615
b)$35,227
c)$45,609
d)$11,543
e)($11,174)

Answer 1

The equivalent annual annuity (EAA) is calculated by dividing the present value of Machine Y's after-tax cash flows by the present value interest factor of an annuity. This provides a constant annual cost that enables comparison of assets with different costs and lifespans.

Step-by-step explanation:

The equivalent annual annuity (EAA) is a method for comparing the cost-effectiveness of different assets with varying lifespans by calculating a constant annual cost for each option. To find the EAA for Machine Y, we can use the formula EAA = PV / PVIFA, where PV is the present value of the cash flows and PVIFA is the present value interest factor of an annuity. Given that Machine Y has a cost of $432,000.00, an expected life of 10 years, after-tax cash flows of $88,000.00 per year, and assuming a cost of capital at 12.0%, we calculate the PV of cash flows by discounting the annual cash flows at the cost of capital, and then we find the PVIFA using a financial calculator or actuarial table for an annuity at 12.0% over 10 years. Once we have both PV and PVIFA, we divide PV by PVIFA to obtain the EAA.