Deer Valley Lodge, a ski resort in the Wasatch Mountains of Utah, has plans to eventually add five new chair lifts. 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 in the slopes, but there are only 40 days a year when the extra capacity will be needed. (Assume that Deer park will sell at 300 lift tickets on those 40 days) Running that 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 and the added cosh expenses for each skier-day are $5. The new lift has an economic life of 20 year.
1. What if 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 adding the lift to be profitable investment.
2. What if 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 adding the lift will be profitable investment.
3. What subjective factors would afect the investment decision?
An Excel spreadsheet is very helpful for these kinds of questions. Plug in what you know. The capital cost is $3.3 million. The net increase revenue stream is 40*300*(55-5) = $0.6 million for 20 years. Discount the first year by 1.14, the second year by 1.14^2, and so on. Add discounted revenues to get the NPV of all future revenues. Compare this to $3.3 million to see if the lift is a profitable investment.
2) Taxes complicate the problem, but do not change the basic nature of the problem. Instead of a 14% discount rate, use an 8% rate. Second, convert the revenue stream to and after-tax stream. Using straight line depreciation, the Lodge would get a $0.33 deduction for the first 10 years. So year 1 after tax revenue is (1-.4)*(0.6-.33)=$.162 million. Deflate this by 1.08. Repeat for 9 more years, at which time the depreciation deduction goes away. But keep going for another 10 years.
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
To calculate the before-tax NPV of the new lift, we need to discount the net increase in revenue stream over the 20-year period using the before-tax required rate of return.
The capital cost of the lift is $3.3 million, and the net increase revenue stream is $0.6 million for each of the 20 years.
Using the formula for calculating the present value of future cash flows, we discount each year's revenue by the appropriate rate:
Year 1: $0.6 million / (1 + 0.14)^1 = $0.5263 million
Year 2: $0.6 million / (1 + 0.14)^2 = $0.4605 million
...
Year 20: $0.6 million / (1 + 0.14)^20 = $0.0706 million
Summing up all the discounted revenues, we get:
NPV = $0.5263 + $0.4605 + ... + $0.0706
Using Excel or calculator, the NPV is approximately $5.44 million.
Since the NPV is positive ($5.44 million > $3.3 million), the lift is a profitable investment.
For the after-tax NPV calculation, we need to consider the income tax rate and MACRS recovery period.
Using straight-line depreciation, the deductible amount per year is $3.3 million / 10 = $0.33 million.
The after-tax revenue for each year is calculated as follows:
Year 1: (1 - 0.4) * ($0.6 million - $0.33 million) = $0.162 million
...
Year 10: (1 - 0.4) * ($0.6 million - $0.33 million) = $0.162 million
Year 11 and onwards: $0.6 million - $0.33 million = $0.27 million
Applying the after-tax required rate of return of 8%, we discount each year's after-tax revenue:
Year 1: $0.162 million / (1 + 0.08)^1 = $0.1500 million
...
Year 10: $0.162 million / (1 + 0.08)^10 = $0.0800 million
Year 11 and onwards: $0.27 million / (1 + 0.08)^11 = $0.1196 million
Summing up all the discounted after-tax revenues, we get:
NPV = $0.1500 + $0.1500 + ... + $0.0800 + $0.1196 + $0.1196 + ...
Using Excel or calculator, the NPV is approximately $2.34 million.
Since the NPV is positive ($2.34 million > $3.3 million), the lift is still a profitable investment.
3) Subjective factors that could affect the investment decision may include:
- Seasonal and weather variations: If there are significant fluctuations in weather conditions from year to year, it could impact the number of skiers visiting the resort and the revenue generated.
- Competitor analysis: If other ski resorts in the area are planning similar expansions or offering attractive deals, it could impact Deer Valley Lodge's ability to attract additional skiers.
- Customer demand and preferences: Understanding the target market's preferences, demographics, and willingness to pay for additional lifts is crucial in determining the potential success of the investment.
- Environmental regulations and sustainability: Compliance with environmental regulations, sustainability practices, and potential impact on the local ecosystem may also play a role in the decision-making process.
- Overall market conditions: Economic conditions, changes in disposable income, and market trends can affect the demand for ski resorts and the likelihood of a successful investment.
To compute the after-tax NPV of the new lift and advise the managers of Deer Valley, we need to follow these steps:
Step 1: Calculate the after-tax cash flows for each year
- Determine the net increase in revenue stream, which is calculated as 40 * 300 * (55 - 5) = $0.6 million per year for 20 years.
- For the first 10 years, apply straight-line depreciation to the capital cost of $3.3 million. This means that the depreciation deduction is $3.3 million / 10 = $0.33 million per year.
- Apply the income tax rate to calculate the after-tax cash flows. For example, in year 1, the after-tax revenue would be: (1 - 0.4) * (0.6 - 0.33) = $0.162 million.
- Repeat this calculation for each year, adjusting the depreciation deduction and applying the income tax rate.
Step 2: Calculate the present value of each cash flow
- Use the required rate of return of 8% to discount the cash flows. For example, the present value of the after-tax cash flow in year 1 would be: $0.162 million / (1 + 0.08) = $0.15 million.
- Repeat this calculation for each year, discounting the cash flows based on the required rate of return.
Step 3: Sum up the present values of all cash flows
- Add up all the discounted cash flows to find the total present value of the cash flows.
Step 4: Compare the total present value of cash flows with the initial capital cost
- If the total present value of cash flows is higher than the capital cost ($3.3 million), then the lift is considered a profitable investment. If it is lower, then it may not be profitable.
Using this approach, you can calculate the after-tax NPV of the new lift and provide advice to the managers of Deer Valley regarding the profitability of adding the lift.