OPIM 5641 - Business Decision Modeling Spring 2016, University of Connecticut Practice Problems Module 1 Solution:
(This example comes from page 483 in the course textbook.) The Big Rig Rental Rental Company Company, which owns and rents out 50 trucks, trucks, is for sale for $350,000. Tom Grossman, the company’s owner, wants you to develop a five-year economic analysis to assist buyers in evaluating the company. The current annual rental rate for trucks is $12,000 per year per truck. At this base rate, an average of 62 percen percentt of the trucks trucks will be rented rented each year. year. Tom beli b eliev eves es that if the rent rent were were lowe lowered red by $1,200 per truck in a given year, utilization would increase by seven percentage points. He also believes that this relationship would apply to additional reductions in the base rate. For example, at a $7,200 rental rate, 90 percent of the trucks would be rented, until the rental rate drops to the point where 100 percent percent of the fleet will be rented. This relationshi relationship p would apply to increases increases in the base rate as well. well. Over Over the next five years, years, the base rental rental rate should remain constant constant each year. At the end of five years, it is assumed that the buyer will resell the business for cash. Tom estimates that the selling price will be three times the gross revenue in the final year. The cost of maintaining the fleet ran about $4,800 per truck per year (independent of utilization) this past year, which includes inspection fees, licenses, and normal maintenance. Big Rig has fixed officee costs offic costs of $60, $60,000 000 per year year and paid propert property y taxes taxes of $35, $35,000 000 per year. year. Propert Property y taxes taxes are expected to grow at a rate of 3 percent per year, and maintenance costs are expected to grow 9 percen percentt per year year due to the age of the fleet. fleet. Ho Howe weve ver, r, offic officee costs costs are predic predicted ted to remain remain level. level. Profits are subject to a 30 percent income tax. The tax is zero if profit is negative. Cash Cash flow flow in the final final year year would would include include cash from the sale sale of the busines business. s. Becaus Becausee the trucks trucks have all been fully depreciated, there are no complicated tax effects: Revenue from the sale of the business will effectively be taxed at the 30 percent rate. Investment profit for the buyer is defined to be the Net Present Value (NPV) of the annual cash flows, computed at a discount rate of 10 percen percent. t. All operating operating reven revenues ues and expenses expenses are in cash. The calcula calculation tion of NPV include includess the purchase price, incurred at the beginning of year 1, and net income from operations (including the sale price in year 5) over five years (incurred at the end of the year). There would be no purchases or sales of trucks during the five years. The NPV can be calculated via Excel’s NPV function, or by ‘hand’. The calculation is: NPV =
N
Cash Flow in Year t . t (1 + Discount Rate) t=0
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Problem 1
In order to begin analyzing the problem, please create an influence chart, using the conventions described in class, using only and all of the following elements: •
Net Present Value: the total value of the investment
•
Discount Rate : annual discount rate for NPV calculation
•
Purchase Price: the amount that the company is being purchased for
•
Selling Price Factor : the amount that the last year revenue will be multiplied by to
calculate the selling price •
Selling Price: the amount the company will sell for in five years
•
Total Income : the annual income amount, before tax
•
Cash Flow: the final amount of money earned each year after paying taxes
•
Income Tax: the amount of income tax paid each year
•
Income Tax Rate: the percentage of total income that is paid in taxes each year
•
Net Operating Income : the operating revenue minus operating expenses
•
Operating Expenses: the cost per year to maintain the fleet, pay office expenses, and pay
property taxes •
Revenue: the amount of money the company receives from renting out trucks
•
Rental Rate : the amount that trucks are rented for
•
Number of Rented Trucks: the number of trucks that are rented per year
•
Utilization Rate : the fraction of the fleet size that are rented each year
•
Rental Discount Factor : the amount that the fraction of the fleet size decreases per dollar
increase in rental rate •
Incremental Rent Change: the assumed amount of increase/decrease in annual rental
amount that will cause a 7% increase/decrease in truck utilization rate •
Incremental Utilization Change : the assumed percent increase/reduction in truck rentals
if annual rental amount changes by $1,200.00 •
Base Utilization Rate: the assumed percent of truck rentals if the annual rental cost is
$1,200.00 •
Fleet Size: the number of trucks the company owns
•
Maintenance Expenses: the annual maintenance cost
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•
Maintenance Cost Base : the current maintenance cost per truck per year
•
Maintenance Cost Growth Rate : the rate at which the maintenance cost is assumed to
increase each year •
Office Expenses: the annual office expense incurred
•
Office Expenses Base: the current office costs
•
Office Expenses Growth Rate: the rate at which the office expenses are assumed to
increase each year •
Property Taxes: the annual property tax paid
•
Office Expenses Base: the current annual property tax
•
Office Expenses Growth Rate: the rate at which the property tax rate is assumed to
increase each year Please be sure to identify the type of each of the elements through the objects that you use to depict them, by using hexagons for the outcome, rectangles for decisions, upside-down triangles for inputs, and ovals for auxiliary variables, preferably colored blue, green, purple, and black, respectively. The outcome should be on the right of the diagram, so that one can read it left to right. The direction of the arrows should follow the precedence relations required to calculate the elements from one another. Solution: See influence chart.pptx
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Problem 2
Use your influence chart from the previous problem to create a spreadsheet model, analyzing the investment decision of buying the company for $350,000.00. What is the base case NPV of the investment? Solution: The base case NPV is $20,141.20 as can be seen from the Excel file Module 1 Practice Problem - Solution.xlsx
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Problem 3
There are many parameters that have been estimated, to assist in making a base case model. Perhaps the two most important parameters that are estimated are the selling price factor (currently estimated at 3) and the annual maintenance growth rate (current estimated at 9%). In reality, the selling price factor can range anywhere from 2 to 4, and the annual maintenance growth rate can range anywhere from 7% to 11%. 1. Use Excel’s scenario manager to input base case, pessimistic, and optimistic scenarios for the NPV, where in the base case everything is set as in the original problem description, in the pessimistic case the selling price factor is 2 and the annual maintenance growth rate is 11%, and finally, in the optimistic case the selling price factor is 4 and the annual maintenance growth rate is 7%. How much do these parameters affect the NPV? Solution: Refer to sheet 3.1 in Excel file Module 1 - Practice Problem - Solution.xlsx
2. Holding all else equal, what value for the purchase price is the break-even price? Solution: $370,141.20, as determined through using Goal Seek in Excel.
3. Holding all else equal, what value for the purchase price would ensure an NPV of at least $20,000? Solution: $350,141.20, as determined through using Goal Seek in Excel.
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Problem 4
You are now interested in investigating how much the eventual purchasers should charge as the rental rate. 1. Create a table and a chart showing the NPV, setting the minimum rental rate to $10,000 and the maximum rental rate to $14,000. Use 100 points. Solution: Refer to sheets 4.1a and 4.1b in Excel file Module 1 - Practice Problem Solution.xlsx
2. The values used for calculating the rental discount factor is also a best guess value. Suppose, instead, that varying 7% in the rental amount may change the incremental rent change anywhere from $1,000 to $1,400. Create a chart using this range of values together with the range of values from the previous problem to see the effect of both of these values changing concurrently. Use 50 points for each axis, and vary the parameters independently. Solution: Refer to sheets 4.2a and 4.2b in Excel file Module 1 - Practice Problem Solution.xlsx
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