Problem 1:
Two new rides are being compared by a local amusement park in terms of their annual operating costs. The two rides are assumed to be able to generate the same level of revenue (thus the focus on costs). The Tummy Tugger has fixed costs of $10,000 per year and a variable costs of $2.50 per visitor. The Head Buzzer has fixed costs of $4,000 per year and a variable costs of $4 per visitor. Provide answers to the following questions so the amusement park can make the needed comparison.
(a) Mathematically determine the breakeven number of visitors per year for the two rides to have equal annual costs.
(b) Develop a breakeven grap that illustrates the following:
- Accurate total cost lines for the two alternative (show line, slopes, and equations).
- The breakeven point for the two rides in terms of number of visitors.
- The ranges of visitors per year where each alternative is preferred.
Problem 2:
Consider the accompanying breakeven graph for an investment, and answer the following questions.
(a) Give the equation for total revenue for x units per year.
(b) Give the equation for total costs for x units per year.
(c) What is the "breakeven" level of x?
(d) If you sell 1500 units this year, will you have a profit or loss? How much?
(e) At 1500 units, what are your marginal and average costs?
Problem 3:
On December 1, Al Smith Purchased a car for $18,500. He paid $5,000 immediately and agreed to pay three additional payments of $6,000 each (which includes principal and interest) at the end of 1, 2, and 3 years. Maintenance for the car is projected at $1,000 at the end of the first year and $2000 at the end of each subsequent year. Al expects to sell the car at the end of the fourth year (after paying the maintenance work) for $7,000. Using these facts, prepare a table of cash flows.
Problem 4:
A company invested $450,000 ten years ago in a new technology that is now worth $1,000,000. What rate of interest did the company earn on a simple interest basis?