Final answer:
Snow Valley Ski Resort should use the snow-removal machine for at least 28 days per year to break even when considering the initial purchase cost, the annual operating cost, and the contracting cost per day with a MARR of 12%. This is a simplified analysis and does not account for other factors that could influence the actual break-even number of days.
Step-by-step explanation:
To determine the break-even number of days for Snow Valley Ski Resort to justify purchasing the snow-removal machine versus contracting the service, we will perform a financial analysis considering the initial purchase cost, annual operating costs, and the cost per day of contracting the service with the given Minimum Attractive Rate of Return (MARR).
The machine costs $25,000 and has a useful life of 6 years, which means it will depreciate to a value of $0 at the end of 6 years. The annual operating cost is $5,000, and the current cost of contracting the service is $400/day. With a MARR of 12%, we want to find the break-even point where the cost of purchasing and operating the machine equals the cost of contracting the service.
First, we must calculate the annualized cost of the machine using the MARR to find the equivalent annual cost over 6 years. We use the present worth of annuity factor (P/A) formula at 12% for 6 years to do this. The factor for 12% over 6 years is about 4.1114. Therefore, the annualized cost of the machine is:
Annualized cost = Purchase cost × (P/A factor)
Annualized cost = $25,000 × 4.1114 = $6,093.5
The total annual cost of the machine, including operating costs, is then:
Total annual cost = Annualized cost + Operating cost
Total annual cost = $6,093.5 + $5,000 = $11,093.5
Dividing the total annual cost by the cost of contracting per day gives us the break-even number of days:
Break-even days = Total annual cost ÷ Cost per day of contracting
Break-even days = $11,093.5 ÷ $400/day
Break-even days = 27.73 days/year
Therefore, the ski resort would need to use the snow-removal machine for at least 28 days per year to break even. However, this is simplified and does not consider potential changes in operating costs, contracting costs, or other factors that could affect the actual break-even point.