Question

1A.The equivalent annual cost for a machine that requires a $100,000 investment at time-period zero, and a $10,000 annual expense each of the next 5 years, if the opportunity cost of capital is 10%, is $ …………..………………. 1B.The EAC for a machine that requires a $100,000 investment at time zero, a $10,000 annual expense each of the next 5 years, but has a $10,000 net cost recovery in 5 years, if the opportunity cost of capital is 10%, is $ …………..……………….

Answer 1

1A.

Equivalent annual cost of machine is $ 36,379.75

1B.

Equivalent annual cost of machine is $ 34,741.77

Explanation:

EAC = Asset price x r / [1-(1+r)^-n] + Annual maintenance cost

r = Discount rate = 10 % or 0.1

n = Number of periods = 5

1A.

EAC = $ 100,000 x 0.1/ [1 – (1+0.1)^-5] + $ 10,000

       = $ 100,000 x 0.1/ [1 – (1.1)^-5] + $ 10,000

       = $ 10,000/ (1 – 0.620921323059155) + $ 10,000

       = $ 10,000/0.379078676940845 + $ 10,000

       = $ 26,379.7480794745 + $ 10,000

       = $ 36,379.7480794745 or $ 36,379.75

1B.

Asset price = Initial cost - PV of cost recovery in year 5

                    = $ 100,000 - $ 10,000/ (1+0.1)⁵

                    = $ 100,000 - $ 10,000/ (1.1)⁵

                    = $ 100,000 - $ 10,000/1.61051

                    = $ 100,000 - $ 6,209.21323059155

                    = $ 93,790.78676940845

EAC = $ 93,790.78676940845 x 0.1/ [1 – (1+0.1)^-5] + $ 10,000

       = $ 93,790.78676940845 x 0.1/ [1 – (1.1)^-5] + $ 10,000

       = $ 9,379.078676940845/ (1 – 0.620921323059155) + $ 10,000

       = $ 9,379.078676940845/0.379078676940845 + $ 10,000

       = $ 24,741.7732715271 + $ 10,000

       = $ 34,741.7732715271 or $ 34,741.77