Question

You have to buy a new copier. The cost of the copier is $ 2 comma 000​, plus $ 400 per year in maintenance costs. The copier will last for five years. Alternatively a local company offers to lease the copier to you and do the maintenance as well. If your discount rate is 6 %​, what is the most you would be willing to pay per year to lease the copier​ (your first lease payment is due in one​ year)?

Answer 1

Answer:

The annual maximum cost to be paid =$874.79

Explanation:

To determine the maximum to paid for the lease perv year, we  will work out the an annual cost which is the same as the total present value of cost over the  five years investment period. This annual cost that is comparable to the total present value cost is called the equivalent annual cash flow (EAC)

EAC =Present Value of cost over the copier life/Number of years

Present value of cost

PV of maintenance cost = A × (1- (1+r)^(-n)/r

= 400× (1- 1.06^(-5))/0.06= 1,684.94

Total present value of cost = 2000+ 1684.94 = 3,684.94

Annuity factor for the five year life span = A × (1- (1+r)^(-n)/r

=  (1- 1.06^(-5))/0.06=4.2123

The annual maximum cost to be paid = 3,684.94/4.2123=874.79

The annual maximum cost to be paid =$874.79

=

Answer 2

The most you would be willing to pay per year to lease the copier should be $874.79.

Here, we need work out the the annual cost (total present value of cost) over the five years investment period.

This annual cost that is comparable to the total present value cost is called the equivalent annual cash flow (EAC).

• PVIFA of (6%,5) = (1 - (1/(1 + r%)^n) ) / r%

PVIFA of (6%,5) = (1 - (1/(1 + 6%)^5) ) /6%

PVIFA of (6%,5) = 4.21236379

PVIFA of (6%,5) =4.21236379

• Equivalent annual cost of new copier = (Cost / (PVIFA discount rate%,life)) + Annual maintenance cost

Equivalent annual cost of new copier = (2000/(PVIFA 6%,5)) + $400

Equivalent annual cost of new copier = (2000/4.21236379) + $400

Equivalent annual cost of new copier = 474.7928004 + $400

Equivalent annual cost of new copier = 874.7928004

Equivalent annual cost of new copier = $874.79

Therefore, the most you would be willing to pay per year to lease the copier should be $874.79.

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