i) The first is to compare the marginal benefit versus the marginal cost of going to school

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1 Economics MBA814 Spring 2016 Mike Conlin Fundamentals of Managerial Economics SOLUTIONS 1. Suppose you own a food distributorship that is located in East Lansing and you serve the southern Michigan area. The revenue you earn as a food distributor is five percent of the merchandise you sell. (For example, suppose you sell a truckload of shrimp to a grocery chain for $200,000, then the revenue generated for your company from this sale is $10,000 so $190,000 goes to the shrimp company that provided and delivered the shrimp to the grocery store.) The offices in East Lansing are able to serve southern Michigan but you are thinking of expanding into the Chicagoland area. In order to do this, you would have to establish a satellite office in Chicago and hire five salespeople, along with an office administrator. The office administrator will be paid $70,000 annually and office supplies would cost $30,000 annually in the Chicago office. Each salesperson would be compensated strictly on a commission basis. For each dollar of product they sell, they would earn three cents (i.e., have a three percent commission rate). You would purchase a small office building in Chicago which will cost $400,000 and can be sold after two years for $500,000. You plan to liquidate the food distributorship in two years and retire. What is the minimum amount of annual sales the Chicago office must generate in order for you to expand in the Chicagoland area? Assume that the Chicago office obtains the same amount of annual sales each year. For simplicity, also assume all revenue is received at the beginning of each year, salaries are paid at the beginning of each year and supplies are purchase at the beginning of each year. Let the interest rate be 10%. Show calculations. Marginal Benefit of Chicago Office.02*Sales+.02*Sales/ /1.1 2 Marginal Cost of Chicago Office 400+(70+30)+((70+30)/1.1) MB>MC if.02*sales+.02*sales/ /1.1 2 > 400+(70+30)+((70+30)/1.1) or when Sales > 4,654, Sue currently works as a salesperson but is considering becoming a manager. To become a manager, she needs to go full-time to business school. Tuition and fees are $20,000 per year and her salary as a salesperson is $18,000 per year. The salary of a manager is $42,000 per year. The annual interest rate is 10%. Salaries are paid at the beginning of the year, as is tuition and fees. Suppose business school takes 2 years and she does not have time to work while going to school. What is the minimum number of years Sue must plan to work in order for her to quit her current job and attend school? (Assume that Sue is indifferent between going to school, working as a salesperson and working as a manager. Therefore, she strictly makes the decision of whether to attend school based solely on monetary issues.) Show your calculations. The easiest way to determine the minimum number of years Sue must plan to work in order for her to quit her current job and attend school is by trail and error. To make it not as tedious, you can just use excel to do the present value calculations. You can determine the minimum number of years in one of two ways. i) The first is to compare the marginal benefit versus the marginal cost of going to school Comparing marginal benefit with marginal cost if Sue plans to work for 4 years after attending school for two. Marginal benefit of attending school is ( )/ ( )/ (42000-

2 18000)/ ( )/1.1 5 =69,161 Marginal cost of attending school is /1.1=72,545. Since marginal benefit is less than marginal cost, Sue should not go to school if she only plans to work for 4 years after attending school. Comparing marginal benefit with marginal cost if Sue plans to work for 5years after attending school for two. Marginal benefit of attending school is ( )/ ( )/ ( )/ ( )/ ( )/1.1 6 =82,708 Marginal cost of attending school is /1.1=72,545. Since marginal benefit is greater than marginal cost, Sue should go to school if she only plans to work for at least 5 years after attending school. ii) The second way is to calculate the present values of payoffs associated with going to school and not going to school. Payoffs if Sue plans to work for 4 years after attending school for two. Payoff from attending school is / / / / /1.1 5 =82,849 Payoff from not attending school is / / / / /1.1 5 =86,234 Payoffs if Sue plans to work for 5 years after attending school for two. Payoff from attending school is / / / / / /1.1 6 =106,557 Payoff from not attending school is / / / / / /1.1 6 =96,395 Either way you do it, Sue should go to school only if she plans to work for at least 5 years after completing school.. 3. Mike and Stacy just bought a house for $50,000. They plan to live in the house for three years and then sell it. They are deciding whether install new hardwood floors before moving into the house. The cost of the hardwood floors is $15,000. Suppose Mike and Stacy will sell the house in three years for $70,000 if they do not install hardwood floors and for $80,000 if they do install the hardwood floors. If Mike and Stacy decide to install the hardwood floors, what is the minimum amount Stacy and Mike would have to benefit in present value terms from living in a house with hardwood floors for three years? (Let the annual interest rate be 15%.) The present discounted value of the $10,000 difference between the selling price with and without hardwood floors is 10,000/(1+.15) 3 =6575. If Mike and Stacy decide to install the hardwood floors, the minimum amount Stacy and Mike would have to benefit in present value terms from living in a house with hardwood floors for three years is = Mike use to manage an asphalt plant for Barrett Paving. While employed at Barrett Paving, Mike did a cost-benefit analysis on whether to replace the burner that heated the asphalt liquid. Mike discovered that a new burner would cost $800,000 and calculated that it would burn more efficiently than the current burner. Mike expected the burner to last 5 years. This increased efficiency would result in fuel savings of $200,000 per year. For simplicity, assume that the cost savings were obtained at the start of each year. Let the annual interest rate be 15%. Should Mike advise Barrett Paving to purchase the burner? Show calculations. What simplifying assumptions are required to determine whether Mike should purchase the burner? The marginal benefit of replacing the burner (compared to not replacing the burner for the next 5 years) is 200, ,000/ ,000/ ,000/ ,000/ =770,996.

3 The marginal cost is 800,000. Since the marginal benefit is less than the marginal cost, Mike should not replace the burner. There are a lot of simplifying assumptions being made in this word problem. For example, I am assuming that if Mike does not replace the burner this year, than Mike does not replace the burner for the next 5 years. I am also assuming that Mike could perfectly predict future fuel costs. 5. You own a factory that manufactures bicycles. The machine that paints the bicycles is somewhat dated which causes the paint to lack luster. You purchased this machine ten years ago for a price of $700,000 and you could sell it today for $100,000. If the machine is sold two years from today, you expect to be able to sell it for $50,000. You are now deciding whether to purchase a new paint machine today for $500,000 and believe it could be sold for $350,000 in two years. Assume you are currently selling 2,000 bicycles per year at a price of $500 and, if you are purchase the new paint machine, you would sell 2,000 bicycles per year at a price of $550. For simplicity, also assume the revenue is received at the beginning of each year and the interest rate is 10%. If you plan to sell the factory in two years and retire, should you purchase the new paint machine? Show Calculations. Payoff if Buy New Machine: / /1.1+C=1989+C where the C is some constant incorporating other revenues and costs. Payoff if Don t Buy New Machine: 50/ /1.1+C =1950+C Because 1989+C >1950+C, buy machine. Could also show that MB>MC by =39 as I do below. Marginal Benefit of Buying New Machine 100+( )+( )/ /1.1 2 =580 Marginal Cost of Buying New Machine /1.1 2 = Farmer Brown owns 200 acres in Western Pennsylvania where he grows corn. Farmer Brown purchased this acreage ten years ago for $500,000. Every year, Farmer Brown must decide whether and how much corn to grow based on his expectation of corn prices. Recently, geologists informed him that there was a pool of natural gas under his land that could be extracting using a process called fracking. In order to extract the natural gas by fracking, an energy company would have to drill wells on his land and this would prohibit him from growing any corn. How does the discovery of the natural gas influence Farmer Brown s decision of whether to grow corn and, conditional on growing corn, how much to grow? Using the cost discussions in class, provide a detailed explanation. The discovery of natural gas would not influence Farmer Brown s decision how much to grow, conditional on not drilling, because it does not affect his marginal costs. However, it does affect his decision of whether or not to grow because it affects the opportunity cost of using the land for growing corn. You can think of this change in opportunity cost a number of different ways. Perhaps the simplest way is that you can think of Farmer Brown having fixed costs and a smaller portion of that fixed costs being sunk because now he can sell/lease his land to the energy company. He would obviously do a NPV calculation to determine whether or not to do the fracking and also consider the risks/uncertainty involved. This NPV calculation would take into many factors which numerous

4 people listed. To obtain full credit, you need to specifically answer how the discovery of natural gas influences how much corn to grow, conditional on growing corn. 7. Suppose you own a store that produces unique lawn furniture and you are currently selling this furniture from your retail store located in East Lansing. You produce only one type of lawn furniture and currently price this lawn furniture at $200. At a price of $200, each month you sell a quantity of 300 lawn furniture at your store. The marginal cost associated with producing lawn furniture is constant at $50 and fixed costs are $4,000 per month. You are deciding whether to start a website so that you can sell your lawn furniture over the internet for $175. Selling over the internet will cause some customers who would have purchased the lawn furniture in your store to purchase it from your website so that if you do start a website you would only sell 200 per month at your store. For simplicity, assume the price charged at your store would remain $200. Finally, suppose the cost of hiring a company to develop your website is $10,000 which must be paid immediately. A benefit of the website is that it will enable you to attract new customers. For simplicity, assume that you plan to remain in the lawn furniture business for only two more months at which time you will close shop and retire. Assuming a monthly interest rate of 10%, what is the minimum number of lawn furniture you would need to sell through your website in order for it to be worthwhile to start a website immediately? Assume that all sales and production occur at the start of the month. Show calculations. Profits without website Monthly profits are 200*300-50* = 41,000 The PDV of two months of profits are 41, /1.1 = 78,273 Profits with website Let X be the number of sales over the internet per month. Monthly profits are 200*200-50* = 26,000 The PDV of two months of profits are 26,000-10,000+(175-50)X+ [26,000+(175-50)X]/1.1 Minimum number of sales over the internet for you to start website is where 26,000-10,000+(175-50)X+[26,000+(175-50)X]/1.1 > 78,273 Solving for X, X> You can obtain the same answer if you consider marginal benefit and marginal cost instead of payoffs. There are other ways to do this calculation as well. Also, those who inferred that two more months meant a total of three months, no points were deducted for this inference. 8. In Britain, taxes pay for public health care. However, taxes do not cover the full cost of medical care. To contain costs, providers ration health care, in part by having patients wait for treatment. Suppose Prince William requires a knee replacement. Prince William can obtain a knee replacement in Britain for $2,500 (U.S dollars) but would have to wait 2 years to obtain the surgery. If Prince William decides to have the surgery in Britain, he would pay the $2,500 at the time he receives the surgery - in two years. Another option is for Prince William to travel to the United States and have the knee replacement performed immediately. If he had the operation in the United States, he would have to pay $500 for a plane ticket and $2,500 for the surgery. Suppose the maximum Prince Williams is willing to pay for a knee replacement is $3,500 and that his annual interest rate is 15%. For simplicity, assume that besides the cost of the operation, Prince William incurs no cost associated with delaying the knee replacement (i.e., the knee does not bother him before or after the surgery). Will Prince Williams have the knee surgery in Britain or travel to the United States for the knee

5 surgery? Show Calculations. Benefit Prince William derives from having the surgery in Britain /(1.15) 2 = 1,610 Or if you assume that Prince Williams willingness to pay is two years from now, ( )/(1.15) 2 = 756 (I actually meant it the second way but was not clear in the problem.) Benefit Prince William derives from having the surgery in US = 500 Either way, Prince William should have the surgery in Britain. 9. Kalin Lucas is the point guard on the MSU basketball team. He is a very good basketball player with an NBA career in his future. Kalin is deciding whether to enter the 2010 NBA draft or play another year at MSU and then enter the 2011 NBA draft. The NBA draft occurs every year at the end of June. Suppose Kalin believes that if he enters the 2010 NBA draft, he will agree to a 5 year contract that pays him a guaranteed $4M ($4,000,000) a year starting in (For simplicity, assume that Kalin would receive the first $4M payment in June of 2010 and the last in June of 2014.) If Kalin plays next year at MSU and then enters the 2011 NBA draft, he believes he will sign a 5 year contract for a guaranteed $4.7M per year. (For simplicity, assume that Kalin would receive the first $4.7M payment in June of 2011 and the last in June of 2015.) If Kalin decides to play for MSU next year, he will purchase an insurance policy in June of 2010 because of the risk of a career ending injury. Suppose the insurance policy stipulates that if Kalin has a career ending injury while playing for MSU, he will receive insurance payments equivalent to those associated with the NBA contract he would have signed in 2011 (basically 5 annual payments of $4.7M starting in June of 2011 with the last being in June of 2015). Suppose this insurance policy will cost Kalin $1M to be paid in June of Assume that Kalin s annual interest rate is 10%. a. If Kalin expects not to work after his NBA career or if he collects the insurance payments, should Kalin enter the 2010 NBA draft or stay at MSU next year and then enter the 2011 NBA draft? Assume that this decision is strictly based on monetary considerations. Show your calculations. PDV of payoff if enter 2010 NBA Draft: 4+4/1.1+4/(1.1) 2 +4/(1.1) 3 +4/(1.1) 4 = M PDV of payoff if stay at MSU next year and enter 2011 NBA Draft: / /(1.1) /(1.1) /(1.1) /(1.1) 5 = M Therefore, Kalin should stay at MSU for the year and enter 2011 NBA Draft. b. Now suppose that after his 5-year NBA career, Kalin expects to take over for Tom Izzo as MSU men s basketball head coach. If he plays for MSU next year, is injured, and collects his insurance payments, Kalin expects to become the head coach at MSU starting in June of For simplicity, assume that this probability of Kalin getting injured is.10. Suppose Kalin expects his compensation as head coach to be $1M per year and this payment is collected in June of each year. He also expects to retire at age 65 no matter what. If this is the case, should Kalin enter the 2010 NBA draft or stay at MSU next year and enter the 2011 NBA draft? As in part a), assume that this decision is strictly based on monetary considerations. Show your calculations. PDV of payoff if enter 2010 NBA Draft: 4+4/1.1+4/(1.1) 2 +4/(1.1) 3 +4/(1.1) 4 +1/(1.1) 5 = M PDV of payoff if stay at MSU next year and enter 2011 NBA Draft: / /(1.1) /(1.1) /(1.1) /(1.1) 5 +.1[1/1.1+1/(1.1) 2 +1/(1.1) 3 +1/(1.1) 4 +1/(1.1) 5 ]= M

6 Therefore, Kalin should enter the 2010 NBA draft. I only consider the PDV of payments until 2015 because the PDV of payments after 2015 is the same no matter what Kalin decides. 10. On weekends, Professor/Coach Conlin moonlights at a rate of $20/hour giving basketball lessons. He is such a good teacher that he has more students than he can possible see in a day. Coach Tom Izzo also knows a thing or two about basketball and charges $40/hour giving basketball lessons on weekends. Like Conlin, Izzo has more students than he can possible see in a day. Both Coach Conlin and Coach Izzo are interested in buying the NBA09 video game. Conlin values the video game at $170 and Izzo values the video game at $190. The game can be purchased in East Lansing for $170 or for $115 at a store in the Howell outlet mall. The Howell outlet mall is an hour and a half drive from East Lansing. Assume that Coach Conlin and Coach Izzo only have time to purchase the game on a weekend and it takes $20 in gas to drive from East Lansing to Howell, Michigan. For simplicity, assume the only costs associated with traveling to the Howell outlet mall are gas and time. Assume that the round trip from East Lansing to Howell takes 1.5 hours and that the cost of gas is based on a round trip as well. Also assume purchasing the video game in East Lansing takes no time and no gas. a. Will Conlin purchase the NBA09 video game and, if so, will he purchase it in East Lansing or Howell? Explain. The net benefit Conlin derives from buying the game in East Lansing is =0. The net benefit Conlin derives from buying the game in Howell is (1.5)-20=5. Therefore, Conlin will purchase the game in Howell. Another way to do this is to compare the marginal benefit with the marginal cost of making the trip to Howell. The marginal benefit is =55 and the marginal cost is 20(1.5)+20=50. b. Will Coach Izzo purchase the NBA09 video game and, if so, will he purchase it in East Lansing or Howell? Explain. The net benefit Izzo derives from buying the game in East Lansing is =20. The net benefit Izzo derives from buying the game in Howell is (1.5)-20= -5. Therefore, Izzo will purchase the game in East Lansing.

Final Exam SOLUTIONS. 1. (10 points) (This question is based on the Comcast article on the class website.)

Final Exam SOLUTIONS. 1. (10 points) (This question is based on the Comcast article on the class website.) MBA814 Spring 214 Mike Conlin EXAM A Final Exam SOLUTIONS 1. (1 points) (This question is based on the Comcast article on the class website.) Comcast has instituted a new pricing scheme which raises the