Question

Snow Valley Ski Resort has been contracting snow removal from its parking lots at a cost of $350/day. A snow-removal machine can be purchased for $27,000. The machine is estimated to have a useful life of 6 years with a zero salvage value at that time. Annual costs for operating and maintaining the equipment are estimated to be $7,000. Determine the break-even value for the number of days per year that snow removal is required in order to justify purchasing the snow-removal machine. MARR is 12%/year.

Answer 1

Answer:

The number of days needs to be found is 39 days

Explanation:

The number of days per year the machine is used that brings the Snow Valley Ski Resort to break-even for the two alternative ways given in the question is the number of days that equalized the net present value of the two alternatives being discounted at MARR 12%.

Net Present value of alternative 1 : Buying the machine ; calculated as below

Cost of buying the machine + annual cost of operating and maintaining = -27,000 - (7,000/12%) x (1-1.12^-6) = $-55,779.85

Net Present value of alternative 2: Renting the machine; which is the present value of annual renting cost for 6 years period. Annual renting cost is denoted as $(350 x n) with n is the number of days in use. Thus, net present value is calculated as: (-350n/ 0.12) / ( 1 - 1.12^-6)

As explained above, the number of days to bring to break-even point is:

(350n/ 0.12) x ( 1 - 1.12^-6) = 55,779.85  <=> 350n = 13,567.1 <=> n = 39 days.