Case Study thinking of opening up an additional ski lift. You run a ski resort a
ID: 383973 • Letter: C
Question
Case Study thinking of opening up an additional ski lift. You run a ski resort and are openin You believe this will attract more skiers andting up an fixed cost for the lift will be $200,000 for nimprove additional you took recently, for every 1000 skiers vth abity Lift tickets $65,000 Food $22,000 on a sample you had the following revenves Drinks$8,000 You estimate that the variable costs for these reve were $6,000 for lift tickets and operation of the lit, $11,000 for food ands ere $5.00 How many additional skiers will have to come to yorus season to breakeven on the new lift? The ski season in your area is effectively 4 months lone March). Your estimate for skiers for the upcongtoecember No New Lift 8 year is through With New Lift December 50% probability 50% probability 1000 800 1750 1550 January 70% 30% 1500 1000 1750 February 90% 10% 1200 1000 1950 1750 March 40% 60% 1000 800 1750 800 Given this forecast, what is your expected additional profitablity (or los) for this season if you add the new lift?Explanation / Answer
Given the Fixed Cost for new additional lift for the season = $200,000
Also given are the revenue and cost components for 1000 skiers.
Revenue for 1000 skiers = Revenue from Lift tickets + revenue from food + revenue from drinks
= 65,000 + 22,000 + 8,000 = $95,000
So revenue per skier = 95000 / 1000 = $95
Similarly, for the above revenue streams, we have the corresponding variable costs
Variable cost(VC) for 1000 skiers = VC of Lift tickets + VC of food + VC of drinks
= 6000 + 11000 + 3000 = $20,000
So Variable cost per skier = 20,000/1000 = $20
We know, at break-even point, Total Revenue = Total cost
Let us assume that the number of skiers needed to break-even would be equal to x
So Total revenue from x skiers = 95x
And Variable cost for x skiers = 20x
Given, fixed cost = 200,000
Total Cost = Total revenue
200,000 + 20x = 95x
or 200,000 = 75x
or x = 200000/75 = 2666.67 = 2667 (Rounding up to higher whole number)
Thus in order to break-even on the new lift, atleast 2667 skiers need to come additionally
The number of skiers for each month during the season, along with the probability in the two scenarios is given.
For the month of December:
With no lift, there is a 50% probability of 1000 skiers and 50% probability of 800 skiers
So the expected skiers in December without lift = 50% x 1000 + 50% x 800 = 500 + 400 = 900
When the lift is installed, there is 50% probability of 1750 skiers and 50% probability of 1550 skiers
So the expected skiers in December with lift = 50% x 1750 + 50% x 1550 = 1650
Similarly, we shall compute the expected number of skiers for each of the remaining months in the season, i.e. January to March. Thus the expected skiers under No New Lift scenario and With New Lift scenario can be computed. The table is as below:
From the above table, we can see that total expected number of skiers in the 'No New Lift' scenario = 4310
However, earlier we had computed the variable cost per skier = $20 and the revenue from each skier = $95
So expected profitability under 'No New Lift' scenario = Total Revenue - Total Cost
= 4310* 95 - 4310 * 20 = $323,250
Thus expected profitability under No New Lift scenario = $323,250
Similarly, if we decide to install new lift, the number of skies expected (from the table above) = 7245
To install a new lift, we would need an additional Fixed cost of $200,000
So total cost = fixed cost + variable cost = 200000 + 7245 * 20 = $344,900
Revenue from the skiers if we install new lift = 7245 x 95 = $688,275
Expected profitability if we install a new lift = Revenue - Cost = $688,275 - $344,900 = $344,375
Thus the expected additional profitability (loss) if we add the new lift = Expected profit with lift - Expected profit without lift = 344,375 - 323,250 = $20,125
No New Lift With New Lift December 900 1650 January 1350 2485 February 1180 1930 March 880 1180 Total 4310 7245