Question

The owner of a ski resort is considering installing a new ski lift that will cost $850,000. Expenses for operating and maintaining the lift are estimated to be $2,000 per day when operating. The U.S.Weather Service estimates that there is a 55% probability of 70 days of skiing weather per year, a 35% probability of 100 days per year, and a 10% probability of 130 days per year. The operators of the resort estimate that during the first 70 days of adequate snow in a season, an average of 500 people will use the lift each day, at a fee of $9 each. If 30 additional days are available, the lift will be used by only 350 people per day during the extra period; and if 30 more days of sking are available, only 300 people per day will use the lift during those days. The owners wish to recover any invested capital within six years and want at least a 18% per year rate of return before taxes. Based on a before-tax analysis, should the lift be installed? Click the icon to view the interest and annuity table for discrete compounding when the MARR is 18% per year. (a) Calculate the net annual revenue (i.e., total revenue-total cost) for each scenario. The net anual revenue based on 70 days of skiing weather is S(Round to the nearest whole number.) The net anual revenue based on 100 days of skiing weather is Roud to the nearest whole number.) The net anual revenue based on 130 days of skiing weather is $(Round to the nearest whole number.) (b) The expected net annual revenue is $(Round to the nearest whole number.) (c) The expected PW of installing a new ski lift is $L. (Round to the nearest whole number) (d) Based on the E(PW), the lift V be installed.

Answer 1

Net Annual Revenue based on days' of skiing weather = total revenue - total costs

Total Revenue = No. of days of skiing weather x No. of people expected to use the lift x lift fee per person

Total Cost = Expenses for operating and maintaining the lift per day x No. of days' of skiing weather

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Skiing weather = 70 days

Total revenue = 70 days x 500 people x $ 9 per person = $315,000

Total Cost = 70 days x $2000 per day = $140,000

Net Annual Revenue based on 70 days' skiing weather = $315,000 - $140,000 = $ 175,000

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Skiing weather = 100 days

Total revenue = (70 days x 500 people x $ 9 per person ) + ( 30 days x 350 people x $ 9 per person) = $315,000 + $94,500 = $409,500

Total Cost = 100 days x $2000 per day = $200,000

Net Annual Revenue based on 100 days' skiing weather = $409,500 - $200,000 = $ 209,500

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Skiing weather = 130 days

Total revenue = (70 days x 500 people x $ 9 per person ) + ( 30 days x 350 people x $ 9 per person) + (30 days x 300 people x $9 per person )= $315,000 + $94,500 + $81,000 = $490,500

Total Cost = 130 days x $2000 per day = $260,000

Net Annual Revenue based on 130 days' skiing weather = $490,500 - $260,000 = $ 230,500

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b. Expected Net Annual Revenue = Σ (Net Annual Revenue in each scenario x Corresponding Probability)

No. of days' weather	Net Annual Revenue(A)	Probability(B)	A x B
70	175,000	55%	96,250
100	209,500	35%	73,325
130	230,500	10%	23,050
		Expected Net Annual Revenue	192,625

So, Expected Net Annual revenue = $192,625

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c. Expected Present Worth of installing a ski lift = Present Value of Expected Net annual revenue for 6 years - Present value of costs of installing the ski lift

Present Value of Expected Net annual revenue for 6 years:

Discounting rate for calculating Present Value = Required rate of return = 18%

Expected Net Annual Revenue = $192,625

PV of Expected Net Annual Revenue = $192,625 x PVIFA (18%, 6 years) = $192,625 x 3.4976 = $673,725.2

(The learner should search in the annuity table for 18% rate (0.18) for 6 years)

PV of costs of installing the ski lift = $850,000 ( as the cost is to be incurred at the beginning of the project, the present value is same as the actual cost incurred)

Expected Present Worth of the project = $673,725.20 - $850,000 = $ -176,274.80

Thus, the Expected Present Worth is in minus, that is PV of inflows is less than PV of outflows. This means that the business would not be able to recover the invested capital alongwith annual return of 18%

d. Based on the E(PW), the lift should not be installed.

Answer 2

The owner of a ski resort estimates that a new 4-person ski lift will cost $5,000,000. The owner begins making payments on March 1 and every three months thereafter for 5 years into an account that earns 4% annual interest compounded quarterly. What payment amount must the owner make to have the cost of the ski lift in 5 years? (Round your answer to the nearest cent.)