Deer Valley Lodge, a ski resort in the Wasatch Mountains of Utah, has plans to eventually add five new chairlifts. Suppose that one lift costs $2 million, and preparing the slope and installing the lift costs another $1.3 million. The lift will allow 300 additional skiers on the slopes, but there are only 40 days a year when the extra capacity will be needed. (Assume that Deer park will sell all 300 lift tickets on those 40 days.) Running the new lift will cost $500 a day for the entire 200 days the lodge is open. Assume that the lift tickets at Deer Valley cost $55 a day. The new lift has an economic life of 20 years.
1. Assume that the before-tax required rate of return for Deer Valley is 14%. Compute the before-tax NPV of the new lift and advise the managers of Deer Valley about whether adding the lift will be a profitable investment. Show calculations to support your answer.
As I understand the lodge is considering adding one lift only.
Initial outlay=cost of lift + preparing and installing cost
=2,000,000+1,300,000=3,300,000
Let’s compute the incremental revenue and incremental cost.
Incremental revenue=$55 per day per ticketx300 ticketsx40 days=660,000
Incremental cost=$500 per day x 200 days=100,000
Incremental profit=660,000-100,000=560,000
The before-tax cash flow is then
Year 0: -3,300,000
Year 1-20: 560,000
Before-tax NPV is then
-3,300,000+560,000(1/1.14+1/1.142+…+1/1.1420)
=-3,300,000+560,000x6.62313055
=-3,300,000+3,708,953.11
=408,953.11
Since the NPV is positive, it is profitable to add a new lift.
2. Assume that the after-tax required rate of return for Deer Valley is 8%, the income tax rate is 40%, and the MACRS recovery period is 10 years. Compute the ...