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Unformatted text preview: Homework 6: Net Worth Evaluations key 1. (15 Points) A businessman is considering purchasing a delivery truck. He does not now provide delivery service. He feels that the service will bring in additional revenue of $7000 per year. The truck costs $11,000 and will last for 5 years. Its resale value at that time will be zero. A parttime driver for the truck will be hired for $2000 a year. Gas, oil and repairs for the truck will be $1000 in the first year, $1500 the second year, and continue to increase by $500 per year thereafter. If the minimum acceptable rate of return for the businessman is 10%, advise him whether or not he should buy the truck. a. Using equivalency factors, write the formula for the NPW of the investment. NPW = 11000 500(P/G, 0.1, 5) + (3000 + 7000)(P/A, 0.1, 5) b. Using equivalency factors, write the formula for the NAW of the investment. Find the NAW for each term directly using the A/P and A/G factors. NAW = 11000(A/P, 0.1, 5) 500(A/G, 0.1, 5) 3000 + 7000 c. Evaluate the NPW and NAW and determine whether the businessman should buy the truck. NPW =732, NAW = 193. Both are positive. Accept the investment. It returns more than 10%, d. To what level would the annual income have to decrease before the project would become unacceptable? By trial and error, the solution is about $6545. For that income, the NPW is 7. Project Definition Name Truck Life (yrs) Repetitions Study Period Periods 5 1 5 MARR(/yr) Rates (%) 10.% Present (Life) Uniform (Life) Present (SP) IRR Worth($) 7 2 7 0.% Cash Flow Data Amounts Negative for Expenditures and Positive for Revenues Index Description 1 Purchase 2 Revenue 3 Driver 4 Maintenance 5 Maint. Grad Amount($) Type Start 0 *** 1 1 1 2 5 5 5 5 End Parameter *** 1 1 1 1 Factor 1.0000 3.7908 3.7908 3.7908 6.8618 CF. NPW($) (10000) 24811 (7582) (3791) (3431) (10000) Single 6545 Uniform (2000) Uniform (1000) Uniform (500) Grad 1 2. (15 Points) An entrepreneur is considering purchasing a small business for $30,000. The net revenue for the business is seasonal as shown in the figure. In the spring and winter the business loses $1000, while in the summer the business makes $4000 and in the fall it makes $8000. Assume the minimum acceptable rate of return is nominally 16% per year however, we use a quarterly compounding period. We assume the business will last five years with no salvage value. The quarterly cash flows have the same pattern in each of the five years. Is this an acceptable business opportunity? The periodic nature of the cash flow is easily represented with the addin using the cycle parameter. Use the Multiple Compounds option for this problem. Project Definition Name Business Life (yrs) Repetitions Comp./yr Study Period Periods Rates (%) 5 MARR(/yr) 16.% 1MARR(/per) 4.% 4 20 Worth($) Present (Life) 3673 Uniform (Life) 270 Present (SP) 3673 Nom. IRR 21.21% Eff. IRR 22.96% Net Investment Cash Flow Data Amounts Negative for Expenditures and Positive for Revenues Index Description Amount($) Type Start End Parameter 1 Purchase (30000) single 0 *** *** 2 Spring (1000) Uniform 1 20 4 3 Summer 4000 Uniform 2 20 4 4 Fall 8000 Uniform 3 20 4 5 Winter (1000) Uniform 4 20 4 Factor CF. NPW($) 1.0000 (30000) 3.6000 (3600) 3.4615 13846 3.3284 26627 3.2004 (3200) Because the NPW is positive, this is a good investment. 2 3. (15 Points) A new car has a purchase price of $30,000. You are deciding whether to buy (with a loan) or lease the car. The two options are shown below. Assume endof month payments. A. To purchase the car, you will pay $6000 down payment. You can arrange a 3year loan (36 months) with a nominal annual interest rate of 6%. This results in monthly payments of $730. After the 3 years, you will sell the car. B. The lease arrangement requires a $3000 down payment and 36 monthly payments of $400. At the end of the 36month period the car will be returned to the dealer with no final cash payment. Your MARR is nominally 12% a year or 1% per month. If you purchase the car using plan (a), you can sell the car after 36 months. What resale value will make the two plans equivalent? Use S for the resale value. The NPW of costs for plan A is NPW(A) = 6000 + 730(P/A, 0.01, 36) S(P/F, 0.01, 36) NPW(B) = 3000 + 400(P/A, 0.01, 36) NPW(AB) = 3000 + 330(P/A, 0.01, 36) S(P/F, 0.01, 36) = 0 S = [3000 + 330(P/A, .01, 36)] / (P/F, 0.01, 36) = 12,935 / 0.698925 S = $18,507 The problem can be solved using the addin and trial and error. 4. (15 Points) A company must buy a heavyduty earthmoving machine. It has three alternatives. A. The first involves a $50,000 initial investment with no maintenance costs and a fouryear life. The resale value of this machine after four years is $20,000. B. The second alternative involves a $30,000 initial investment, a $20,000 overhaul expense after four years, and $2000 per year operating expense. The alternative is discarded with no salvage value after six years. C. The third alternative involves renting the machine at $8000 per year, payable at the beginning of the year. The operating cost is $2500 per year. The machine can be rented for any number of years. Use the addin and construct models for all three cases. Compare the alternatives with using the company's MARR of 8%. Make the end of the year assumption regarding operating costs. Rental or investment costs occur at the beginning of the year. The company has a need for the machine for an indefinite period. Rank the alternatives economically using the net annual cost criterion. Compute the NAW with costs as positive. 3 NAW(A) = 30(A/P, 0.08, 4) + 20*0.08 = 10.66 NAW(B) = (30 + 20(P/F, 0.08, 4))(A/P, .08, 6) + 2 = 44.701(A/P, .08, 6) + 2 = 11.67 NAW(C) = 8(A/P, 0.08, 1) + 2.5 = 11.14 The ranking is A, C, B, with A best. 4 5. (20 Points) This problem is the same as Pedro's problem considered in Event 6 except that demand is increasing with time. The problem is repeated here. Pedro is thinking of starting a treetrimming service. He plans to run the business for 5 years and then close it down. Truck Costs He will buy three new Ford F150 trucks for the business, which can be purchased for $24,000 each. This cost includes taxes and fees at purchase. The resale value for a truck after 5 years is estimated at $8000. The following describes the annual operating costs for a single truck. Annual insurance cost is $1200 and annual license and inspection fees are $100. Maintenance cost is $400 in the first year and increase by $200 in each subsequent year. The cost of repairs is zero for the first two years and will be $200 in the third year. In subsequent years the cost will grow by $200 per year. Fuel Costs Fuel costs are $0.15/mile. In addition to job mileage, each truck will drive 2,000 miles a year. The round trip to each job averages 20 miles. Shredders In addition to trucks he must purchase wood shredders. He needs one shredder that costs $5000. The shredder must be replaced at the beginning of the third year for a cost of $5000. Shredders have no resale value. Labor Each job requires two trimmers for an 8hour day and $50 in supplies. Tree trimmers earn $15 an hour. The workers are hired hourly. Overhead (office, phone, secretary, etc.) for running the business is 40% of the trimmer labor cost. Pedro will be the manager with an annual salary $30,000. Demand The demand in the first year is 150 jobs. The number of jobs increases by 50 in each subsequent year (i.e., 200 for year 2, 250 for year 3, and so on). The revenue is $650 for each job. Note that the demand increases as a gradient. The model for the revised problem will require gradients for each variable cost. Problem If Pedro's MARR is 15%, is this an acceptable business plan? Find the NPW and NAW. Show the cash flow in each year. For what MARR is the plan just acceptable? 5 Solution to Problem 5. The variable costs are proportional to the demand. The resulting costs and revenue for the 5 years are shown in the table below. Because demand is increasing linearly, the costs and revenue can be modeled as uniform series plus a gradient series. Variable Costs and Revenue Production Per job Trimmers Overhead Supplies Variable Fuel Revenue 240 96 50 3 650 Total 36000 14400 7500 450 97500 1 150 2 200 Total 48000 19200 10000 600 130000 3 250 Total 60000 24000 12500 750 162500 4 300 Total 72000 28800 15000 900 195000 350 Total 84000 33600 17500 1050 227500 Uniform 36000 14400 7500 450 97500 Gradient 12000 4800 2500 150 32500 The gradient components are added to Pedro's economic model as shown below. From the form we see that NPW = $11,635, NAW = $3471 and IRR = 19.2%. All indicate that the investment returns more than the MARR. Project Definition Name Pedro_5 Periods Life (yrs) Repetitions Study Period 5 1 5 MARR(/yr) Rates (%) 15.% Worth($) Present (Life) 11635 Uniform (Life) 3471 Present (SP) 11635 IRR 19.2% Net Investment Salvage 33.33% Factor Fin. NPW($) 0.8343 (60069) Investment Data Amounts Negative for Investments Index Description Amount($) Type 1 Truck (72000) Investment Start 0 End 5 Cash Flow Data Amounts Negative for Expenditures and Positive for Revenues Index Description Amount($) Type Start End Parameter 1 Insurance (3600) Uniform 1 5 *** 2 License (300) Uniform 1 5 *** 3 Maintence (1200) Uniform 1 5 *** 4 Maint. Grad (600) Grad 2 5 *** 5 Rep. Grad (600) Grad 3 5 *** 6 Fuel Fixed (900) Uniform 1 5 *** 7 Fuel Variable (450) Uniform 1 5 *** 8 Shredder 1 (5000) Single 0 *** *** 9 Shredder 2 (5000) Single 2 *** *** 10 Trimmers (36000) Uniform 1 5 *** 11 Overhead (14400) Uniform 1 5 *** 12 Supplies (7500) Uniform 1 5 *** 13 Pedro (30000) Uniform 1 5 *** 14 Revenue 97500 Uniform 1 5 *** 15 Trimmers_G (12000) Gradient 2 5 1 16 Overhead_G (4800) Gradient 2 5 1 17 Supplies_G (2500) Gradient 2 5 1 18 Fuel_G (150) Gradient 2 5 1 19 Rev_G 32500 Gradient 2 5 1 Factor CF. NPW($) 3.3522 (12068) 3.3522 (1006) 3.3522 (4023) 5.7751 (3465) 3.2926 (1976) 3.3522 (3017) 3.3522 (1508) 1.0000 (5000) 0.7561 (3781) 3.3522 (120678) 3.3522 (48271) 3.3522 (25141) 3.3522 (100565) 3.3522 326835 5.7751 (69302) 5.7751 (27721) 5.7751 (14438) 5.7751 (866) 5.7751 187692 6 The cash flow for the 5 years is in the figure below. Cash flow Pedro_5 Pedro_5 Simple Investment Payback(yr): 3.9 MARR(/Yr) 15.% Min. Per. 0 NPW 11634.61 IRR Guess 15.% IRR(/Yr) 19.2% Cash Flow Period Cash Flow Cum. Val. 0 (77000.00) (77000.00) 1 3150.00 (73850.00) 2 10600.00 (63250.00) 3 27450.00 (35800.00) 4 39300.00 3500.00 5 75147.60 78647.60 7 6. (20 Points) Your company is considering an investment in equipment to manufacture a new product. The projected costs and revenues are described below. You are to do an economic analysis to justify the investment. The company's MARR is 18%. Time 0 is defined as the time when the first expenditure occurs. Times are measured in years from the beginning of the project. The project ends at year 15. Revenue from sales will begin in year 3. Other financial aspects of the project are also listed below. All cash flows occur at the end of the appropriate year. Component a. b. c. d. Purchase the rights for the product design Purchase equipment Initial engineering and installation Income from sales Costs and revenues @200 at time 0. $250 at year 1. $50 per year for years 1 and 2. Revenue from sales starts in year 3 at $200. Revenue remains at $200 for years 4 and 5. Starting at year 6 revenues grow by $50 per year until year 11. ($250 in year 6, $300 in year 7..., $500 in year 11). Revenue stays constant at $500 for years 12 through 15. $75 for each year starting in year 3 and continuing through year 15 $300 in years 8 and 12 $400 at year 15. e. f. g. Maintenance costs Overhaul costs Sell design and equipment at end of the project Analyze this investment with the Economics addin. Use no more than 12 cash flow amounts in your model. Answer the numerical questions below. Include the Excel model and turn it in as part of your homework submission. a. What is the NPW and do you accept or reject the project? NPW = $225. Because it is positive accept the investment. b. What is the IRR of the project? IRR = 23.99% 8 c. What is the payback period? From the cash flow we find the payback period is 6 years. Project Definition Name P_6 Life (yrs) Repetitions Study Period Periods 15 1 15 MARR(/yr) Rates (%) 18.% Present (Life) Uniform (Life) Present (SP) IRR Worth($) 225 44 225 23.99% Net Investment Investment Data Amounts Negative for Investments Index Description 1 Inv. 1 Amount($) Type Start 0 End 15 Salvage 0.% Factor 1.0000 Fin. NPW($) 0 0 Investment Cash Flow Data Amounts Negative for Expenditures and Positive for Revenues Index Description Amount($) Type Start 0 *** 1 *** 1 3 6 12 3 8 *** 12 *** 15 *** 2 11 11 15 15 *** *** *** End Parameter *** *** 1 1 1 1 1 Factor 1.0000 0.8475 1.5656 3.0904 4.6251 0.4356 3.5259 0.2660 0.1372 0.0835 CF. NPW($) (200) (212) (78) 618 231 218 (264) (80) (41) 33 1 Purchase Design 2 Equipment 3 Eng./Instaloation 4 Sales 311 5 Grad. 611 6 Sales 1215 7 Maintenance 8 Overhaul 9 Overhaul 10 Resale (200) sing (250) sing (50) Uniform 200 Uniform 50 Gra 500 Uniform (75) Uniform (300) Sing (300) Sing 400 Sing 9 ...
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 Spring '10
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