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.

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.
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 after-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.
What subjective factors would affect the investment decision?

What the answer

To compute the before-tax NPV of the new lift, we need to calculate the net cash flows for each year and then discount them to the present value using the before-tax required rate of return. Here's how you can calculate it:

1. Calculate the initial investment:
Initial investment = Cost of lift + Cost of preparing slope and installing lift = $2 million + $1.3 million = $3.3 million

2. Calculate the annual cash flows:
- Additional revenue from lift tickets = 300 skiers x $55 per day x 40 days = $660,000
- Operating cost per year = $500 per day x 200 days = $100,000

Net cash flow per year = Additional revenue - Operating cost = $660,000 - $100,000 = $560,000

3. Calculate the before-tax NPV using the formula:
NPV = (Net Cash Flow / (1 + Required Rate of Return)^Year) - Initial Investment

Here's the NPV calculation for each year:

Year 1: NPV1 = ($560,000 / (1 + 0.14)^1) - $3.3 million
Year 2: NPV2 = ($560,000 / (1 + 0.14)^2) - $3.3 million
...
Year 20: NPV20 = ($560,000 / (1 + 0.14)^20) - $3.3 million

Sum up all the NPV values for each year to find the before-tax NPV.

To compute the after-tax NPV of the new lift, we need to consider the income tax rate and the after-tax required rate of return. Here's how you can calculate it:

1. Calculate the tax depreciation using the MACRS recovery period:
The MACRS recovery period for the lift is 10 years, so you can use the MACRS depreciation table provided by the IRS to determine the annual depreciation expense.

2. Calculate the annual tax shield from the depreciation:
Annual tax shield = Depreciation expense x Tax rate

Since the income tax rate is 40% and the lift has an economic life of 20 years, you can use the same depreciation expense for the first 10 years.

3. Calculate the after-tax annual cash flows:
After-tax net cash flow per year = Net cash flow per year - Annual tax shield

4. Calculate the after-tax NPV using the formula:
After-tax NPV = (After-tax Net Cash Flow / (1 + After-tax Required Rate of Return)^Year) - Initial Investment

Here's the NPV calculation for each year:

Year 1: After-tax NPV1 = (After-tax Net Cash Flow1 / (1 + 0.08)^1) - Initial Investment
Year 2: After-tax NPV2 = (After-tax Net Cash Flow2 / (1 + 0.08)^2) - Initial Investment
...
Year 20: After-tax NPV20 = (After-tax Net Cash Flow20 / (1 + 0.08)^20) - Initial Investment

Sum up all the after-tax NPV values for each year to find the after-tax NPV.

Subjective factors that could affect the investment decision may include:
- Market demand for skiing and the growth potential in the ski industry.
- Competitors' actions and the potential for increased competition in the region.
- The overall financial health and stability of Deer Valley Lodge.
- The long-term strategic goals and objectives of Deer Valley Lodge.
- The potential impact on customer satisfaction and experience.
- Environmental and community considerations.
- Political and regulatory factors that may affect the ski resort industry.
- Any potential risks or uncertainties associated with the investment.
- Feedback from customers or stakeholders regarding the need for additional lift capacity.
- Potential future developments or expansions that may impact the profitability of the investment.

Consideration of these subjective factors, in addition to the financial analysis, can help the managers of Deer Valley make a more informed decision about whether adding the lift will be a profitable investment.