Question

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The management of an amusement park is considering purchasing a new ride for $80,000 that would have a useful life of 10 years and a salvage value of $10,000. The ride would require annual operating costs of $32,000 throughout its useful life. The company's discount rate is 9%. Management is unsure about how much additional ticket revenue the new ride would generate-particularly since customers pay a flat fee when they enter the park that entitles them to unlimited rides. Hopefully, the presence of the ride would attract new customers. (Ignore income taxes.)

Required: How much additional revenue would the ride have to generate per year to make it an attractive investment?

Answer 1

To determine how much additional revenue the new ride would have to generate per year to make it an attractive investment, we need to calculate the net present value (NPV) of the project.

Step-by-step explanation:

To determine how much additional revenue the new ride would have to generate per year to make it an attractive investment, we need to calculate the net present value (NPV) of the project. NPV is a financial metric that takes into account the time value of money, considering the initial investment, annual operating costs, salvage value, and the company's discount rate.

Using the formula for Discounted Cash Flow (DCF), we can calculate the annual cash flows as follows:

• Initial Investment: -$80,000
• Annual Operating Costs: -$32,000
• Salvage Value: +$10,000

Discounting these cash flows using the discount rate of 9% and summing them up for the 10-year period, we can find the NPV. The annual additional revenue should be large enough to make the NPV positive and attractive.

Answer 2

In this case, the ride would have to generate additional revenue of at least $62,276 per year to make it an attractive investment and achieve a positive NPV. However, since the exact additional revenue is uncertain, management would need to conduct further analysis and consider other factors to make an informed decision.

Step-by-step explanation:

To determine how much additional revenue the new ride would have to generate per year to make it an attractive investment, we need to calculate the net present value (NPV) of the investment. The NPV represents the difference between the present value of the cash inflows (revenues) and the present value of the cash outflows (costs).

Here are the steps to calculate the NPV:

1. Calculate the annual cash inflow from ticket revenue that the ride would need to generate to cover the annual operating costs:

Annual cash inflow = Annual operating costs + Salvage value

Annual cash inflow = $32,000 + $10,000 = $42,000

2. Determine the present value factor for the cash inflows. This factor accounts for the time value of money and the discount rate. The formula for the present value factor is:

Present value factor = 1 / (1 + Discount rate)^Number of years

Present value factor = 1 / (1 + 0.09)^10 = 0.422

3. Calculate the present value of the cash inflows by multiplying the annual cash inflow by the present value factor:

Present value of cash inflows = Annual cash inflow * Present value factor

Present value of cash inflows = $42,000 * 0.422 = $17,724

4. Calculate the initial investment as the purchase cost of the ride:

Initial investment = $80,000

5. Calculate the NPV by subtracting the initial investment from the present value of the cash inflows:

NPV = Present value of cash inflows - Initial investment

NPV = $17,724 - $80,000 = -$62,276

If the NPV is negative, it means that the investment is not attractive because the present value of the cash inflows is lower than the initial investment.