Suppose one chairlift costs $2 million and the slopes along with the lift have to be install for $1.3 million, this lift allows 300 skiers on the slopes, for 40 days out of a year. Running the lift will cost $500 a day for 200 days that the ski resort will be opened, now suppost the lift tickets cost $55 a day and the cash expenses for each skier-a-day are $5. now the chairlift has an economic life span of 20 years.
1. Assume before-tax required of return for the resort is 14%. Compute the before-tax NPV of the new lift and advise the manager whether to add the lift as a profitable investment.
2. Assume after-tax required of return is 8% the income tax rate is 40% and the MACRS recovery period is 10 years. Compute after-tax NPV of the new lift and tell managers whether to add as a profitable investment.
3. What subjective factors would affect the investment decision?
see my post to your earlier post
1. To calculate the before-tax NPV of the new lift, we need to determine the cash flows associated with the investment over its economic life span of 20 years.
Initial Investment:
The cost of the chairlift and installation is $2 million + $1.3 million = $3.3 million.
Annual Cash Flows:
Revenue:
Revenue per skier-a-day: $55
Number of skiers per day: 300
Number of days ski resort is open in a year: 200
Total annual revenue: $55 * 300 * 200 = $3,300,000
Operating Expenses:
Cost per skier-a-day: $5
Number of skiers per day: 300
Number of days ski resort is open in a year: 200
Total annual expenses: $5 * 300 * 200 = $3,000,000
Additional Operating Expenses:
Cost of running the lift per day: $500
Number of days ski resort is open in a year: 200
Total additional annual expenses: $500 * 200 = $100,000
Net Annual Cash Flow:
Net Annual Cash Flow = Total annual revenue - Total annual expenses - Total additional annual expenses
= $3,300,000 - $3,000,000 - $100,000
= $200,000
Now we can calculate the before-tax NPV using the formula:
NPV = (Cash Flow Year 1 / (1 + Required Rate of Return)^1) + (Cash Flow Year 2 / (1 + Required Rate of Return)^2) + ... + (Cash Flow Year n / (1 + Required Rate of Return)^n) - Initial Investment
Where n is the number of years (20 in this case) and the Required Rate of Return is 14%.
NPV = ($200,000 / (1 + 0.14)^1) + ($200,000 / (1 + 0.14)^2) + ... + ($200,000 / (1 + 0.14)^20) - $3,300,000
By calculating this equation, we can determine the before-tax NPV of the new lift. If the NPV is positive, it means the investment is profitable.
2. To calculate the after-tax NPV of the new lift, we need to consider the after-tax cash flows. The after-tax NPV is calculated using the same formula as before-tax NPV, but with the after-tax cash flows and the after-tax required rate of return.
To calculate the after-tax cash flows, we need to account for the income tax rate and the MACRS recovery period. The MACRS recovery period in this case is 10 years.
Since the chairlift has an economic life span of 20 years, we need to calculate the annual depreciation expense for the first 10 years using the MACRS recovery period.
Annual Depreciation Expense per Year = (Initial Investment - Salvage Value) / MACRS Recovery Period
Salvage value is the expected value of the chairlift at the end of its 20-year economic life. We'll assume it is $0.
Annual Depreciation Expense per Year = ($3,300,000 - $0) / 10 = $330,000
Now, we can calculate the taxable income for each year by subtracting the annual depreciation expense from the net annual cash flow.
Taxable Income = Net Annual Cash Flow - Annual Depreciation Expense per Year
Taxable Income = $200,000 - $330,000 = -$130,000
Since the taxable income is negative, there will be no tax payments. Therefore, the after-tax cash flow for each year will be the same as the net annual cash flow.
Using the same formula as before-tax NPV, but with the after-tax cash flows and the after-tax required rate of return of 8%, we can calculate the after-tax NPV of the new lift. If the NPV is positive, it means the investment is profitable.
3. Subjective factors that could affect the investment decision include market demand for skiing, competition from other ski resorts, potential future changes in ski resort regulations, overall economic conditions, and the strategic goals of the ski resort. Additionally, the manager should consider any potential environmental impacts, customer preferences, and the long-term sustainability of the investment. Ultimately, these subjective factors would help assess the overall viability and profitability of the investment beyond just the quantitative analysis.
To calculate the before-tax NPV of the new lift, we need to calculate the net cash flows for each year and discount them using the required rate of return. The formula for NPV is:
NPV = Σ [CFt / (1 + r)^t]
Where NPV is the Net Present Value, CFt is the cash flow in year t, r is the required rate of return, and t is the time period.
1. Before-tax NPV calculation:
The initial cost of the chairlift is $2 million and the installation costs $1.3 million. So, the initial outflow is $3.3 million (-$3.3M).
Now, let's calculate the net cash flows for each year:
- The lift allows 300 skiers per day for 40 days, so the total number of skiers per year is 300 * 40 = 12,000 skiers.
- The lift operates for 200 days, so the total number of skiers per year is 12,000 * 200 = 2,400,000 skier-days.
- The lift tickets cost $55 per day, so the revenue per year is 2,400,000 * $55 = $132 million (+$132M).
- The cash expenses per skier per day are $5, so the cash expenses per year is 2,400,000 * $5 = $12 million (-$12M).
The net cash flow per year is then calculated as revenue - cash expenses - running cost:
Net Cash Flow = $132M - $12M - ($500 * 200) = $132M - $12M - $100,000 = $119.9 million (+$119.9M).
Since the lift has an economic life span of 20 years, we need to calculate the NPV for 20 years, discounting each year's net cash flow using the required rate of return of 14%.
Now, plug the values into the formula and calculate the NPV:
NPV = (-$3.3M) + ($119.9M / (1 + 0.14)^1) + ($119.9M / (1 + 0.14)^2) + ... + ($119.9M / (1 + 0.14)^20)
Calculate the NPV by discounting each year's net cash flow and summing them up. If the NPV is positive, it means the investment is profitable. If it is negative, the investment is not profitable.
2. After-tax NPV calculation:
To calculate the after-tax NPV, we need to consider the income tax rate of 40%. We also need to factor in the MACRS recovery period of 10 years.
To calculate the depreciation expense per year, we divide the initial cost by the recovery period:
Depreciation Expense = $3.3M / 10 = $330,000 per year (-$330,000).
The taxable income per year is calculated as: Revenue - Cash Expenses - Depreciation Expense:
Taxable Income = $132M - $12M - $330,000 = $119.67 million.
The income tax per year is calculated as: Taxable Income * Tax Rate:
Income Tax = $119.67M * 0.4 = $47.868M (-$47.868M).
The net cash flow after taxes per year is: Net Cash Flow + Depreciation Expense - Income Tax:
Net Cash Flow after taxes = $119.9M - $330,000 - $47.868M = $71.702M (+$71.702M).
Now, we calculate the after-tax NPV using the same formula as before but with the after-tax net cash flows and the required rate of return of 8%.
Similarly, plug the values into the formula and calculate the NPV:
NPV = (-$3.3M) + ($71.702M / (1 + 0.08)^1) + ($71.702M / (1 + 0.08)^2) + ... + ($71.702M / (1 + 0.08)^20)
3. Subjective factors affecting the investment decision:
Some subjective factors that may affect the investment decision include:
- Market demand for skiing and popularity of the ski resort.
- Competition from other ski resorts.
- Potential for growth in the number of skiers and revenue.
- Overall economic conditions and trends in the industry.
- Long-term goals and strategies of the ski resort company.
- Environmental impact and sustainability considerations.
- Regulatory and legal factors.
- Risks, such as weather-related factors impacting ski seasons.
- Potential synergies with existing resort facilities.
- Stakeholder interests and expectations.
Considering these subjective factors alongside the NPV calculations will help the manager make a well-informed investment decision.