The owner of a ski resort is considering installing a new ski lift, which will c

ID: 2727927 • Letter: T

Question

The owner of a ski resort is considering installing a new ski lift, which will cost $750,000. Expenses for operating and maintaining the lift are estimated to be $1,500 per day when operating. The U.S. Weather Service estimates that there is a 60% probability of 80 days of skiing weather per year, a 30% probability of 100 days per year, and a 10% probability of 120 days per year. The operators of the resort estimate that during the first 80 days of adequate now in a season, an average of 500 people will use the lift each day, at a fee of $10 each. If 20 additional days are available, the lift will be used by only 400 people per day during the extra period; and if 20 more days of skiing are available, only 300 people per day will use the lift during those days. The owners wish to recover any invested capital within five years and want at least a 18% per year rate of return before taxes. Based on a before-tax analysis, what is the expected PW of installing the ski lift?

Explanation / Answer

Given Data,

Cost of Ski Lift = $750,000

Required Rate of Return = 18%

Operating costs per day = $1,500

Calculation of Present Worth (NPV): (Amount in $)

Year

Particulars

Cash Flow

Discounting Factor@ 18%

Discounted Cash Flow

Cost of Lift

(750,000)

1-5

Operating Cash Flow(WN-1)

303,000

3.1272

947,542

Present Worth (Net present Value)

197,542

Working Note-1:

Probability(p)

60%

30%

10%

No. of working days

100

120

Total Fees (in $)

(Persons*fee per person*no. of days)

400,000

(500*10*80)

480,000

(500*10*80)+(400*10*20)

540,000

(500*10*80)+(400*10*20)+

(300*10*20)

Less: operating cost (in $)

(Cost per day*no. of working days)

120,000

(1,500*80)

150,000

(1,500*100)

180,000

(1,500*120)

Operating Cash Flow

280,000

330,000

360,000

Equivalent Operating Cash Flow

168,000

99,000

36,000

Total Equivalent Cash Flow = $303,000

Note: As no tax rate is given, it is assumed that the Rate of Return is given before tax rate only.