EGCP 401 Spring 2015 Homework 4 Due February 9

Egcp 401 Spring 2015homework 4 Due February 9, 2-8, 2-9, 2-52 and 3-5

Compare two amusement park rides based on their annual operating costs, assuming both generate the same revenue. The Tummy Tugger has fixed costs of $10,000 and variable costs of $2.50 per visitor, while the Head Buzzer has fixed costs of $4,000 and variable costs of $4 per visitor. Address the following questions to aid in decision-making:

1. Determine the breakeven number of visitors per year at which both rides have equal annual costs.
2. Create a breakeven graph illustrating:
   • The total cost lines for both rides, including their equations and slopes.
   • The breakeven point in terms of the number of visitors.
   • The ranges of visitors per year where each ride is more cost-effective.

Next, analyze a breakeven graph for an investment, focusing on the following:

1. The equation for total revenue when selling x units annually.
2. The equation for total costs for x units annually.
3. The breakeven quantity of x units.
4. Profit or loss when selling 1500 units, and by how much.
5. The marginal and average costs at 1500 units.

Additionally, consider Al Smith’s car purchase scenario:

• Al purchased a car for $18,500 with an immediate payment of $5,000 and three subsequent payments of $6,000 each at the end of 1, 2, and 3 years, which include principal and interest.
• Annual maintenance costs are projected at $1,000 at the end of the first year and $2,000 at the end of each subsequent year.
• Al plans to sell the car at the end of four years for $7,000, after all maintenance expenses.
• Construct a table of cash flows for this investment.

Finally, analyze a situation where a company invested $450,000 ten years ago in a new technology now worth $1,000,000. Calculate the simple interest rate earned over this period.

Paper For Above instruction

In this essay, we will analyze various economic and financial scenarios related to amusement park ride costs, investment breakeven analysis, vehicle financing, and investment return calculations. Each problem will be addressed through mathematical modeling, graphical representation, and financial formulas to elucidate decision-making processes and cash flow evaluations.

Comparison of Amusement Park Rides Based on Operating Costs

The primary goal is to determine the point at which two rides, the Tummy Tugger and the Head Buzzer, incur equal annual costs. Let x represent the number of visitors per year.

The total cost for the Tummy Tugger (C_TT) can be expressed as:

CTT = 10,000 + 2.50x

Similarly, the total cost for the Head Buzzer (C_HB) is:

CHB = 4,000 + 4.00x

To find the breakeven point, we set C_TT equal to C_HB:

10,000 + 2.50x = 4,000 + 4.00x

Solving for x:

6,000 = 1.50x
x = 4,000 visitors

At 4,000 visitors annually, both rides have identical costs.

The breakeven graph plots these linear cost functions, with lines crossing at 4,000 visitors. The slope of the Tummy Tugger’s cost line is 2.5, and that of the Head Buzzer is 4.0. For visitor counts below 4,000, the Head Buzzer is less costly; above 4,000, the Tummy Tugger becomes more economical. Such graphical analysis assists park management in selecting the optimal ride based on expected attendance.

Analysis of Revenue, Costs, and Profitability

Assuming a selling price per unit (or visitor) is p, the total revenue is:

TR = p x

Total costs (TC) encompass fixed and variable costs:

TC = Fixed Costs + Variable Cost per Unit × x

If the fixed costs are F and variable cost per unit is v, then:

TC = F + v x

The breakeven level is:

TR = TC
p x = F + v x
x = F / (p - v)

When selling 1500 units, profit or loss is:

Profit = TR - TC = p(1500) - [F + v(1500)]

If this value is positive, there is a profit; if negative, a loss. Marginal cost (MC) equals the variable cost per unit, v, and average cost (AC) is:

AC = TC / x = (F + v x) / x = F / x + v

At 1500 units, AC reflects fixed costs spread over the quantity plus the variable cost per unit.

Al Smith’s Car Purchase and Cash Flow Analysis

The purchase involves an initial payment of $5,000, followed by three payments of $6,000 each at the end of years 1, 2, and 3, including interest components. Maintenance costs are $1,000 at the end of year 1 and $2,000 annually thereafter, totaling four years. The resale value after four years is estimated at $7,000.

The cash flow table considers the initial expense, subsequent payments, maintenance costs, and final sale proceeds. It appears as:

This cash flow analysis facilitates calculation of net present value and return on investment based on discount rates, which are essential in evaluating the investment's profitability.

Simple Interest Rate Calculation on a Past Investment

The initial investment was \$450,000, and after ten years, it has grown to \$1,000,000. Using the simple interest formula:

Future Value = Principal + (Principal × rate × time)

or equivalently:

FV = P (1 + r t)

solving for r:

r = (FV / P - 1) / t

substituting the given values:

r = (\$1,000,000 / \$450,000 - 1) / 10 ≈ (2.2222 - 1) / 10 = 1.2222 / 10 ≈ 0.1222 or 12.22%

Thus, the company earned approximately 12.22% annually in simple interest over the ten-year period.

Conclusion

This comprehensive analysis illustrates how mathematical and financial principles underpin operational and investment decisions. The breakeven calculations guide managerial choices regarding ride selection, while cash flow and interest rate computations enable investors to evaluate profitability and returns. Employing graphical tools and formulas enhances clarity and strategic planning in various economic contexts.

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