Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17The best monthly income you can earn if you work for somebody else is $5,000. You decide to open and manage a gift shop instead.You lease a retail space in the local shopping mall, agreeing to pay rent of $10,000 per month for 12 months. The lease cannot be broken. In addition to your monthly rent you have other monthly operating costs (payroll, inventory, electricity, etc.) of $22,000. Any profit the business makes is your income.Your monthly revenues are $28,000. Should you stay in business? Or close the shop?Total Variable Costs = $22,000 + 5,000 = 27,000 < $28,000 = Total RevenueApplication: Suppose you can earn 9 percent interest. What is a promised payment of $1,000 five (5) years from now worth to you today?Application: You put $100,000 into an account with a mutual fund, and expect to earn 9.5 percent per year. What will your balance in this account be 12 years from today?APPLICATION: Suppose you purchase a Treasury Bond which promises to pay you $10,000 when it matures 10 years from today. You pay $5,854.31 for this bond. What is the bond’s annual interest yield, or return on your investment?Application: You deposit $1,000 into an account with offers an annual interest rate of 5.9 percent. Complete the table below, showing how you would calculate the balance you will have in this account in 20 years under different rates of compounding, and what this balance will be.CompoundingFuture Value in 20 YearsFormula BalanceAnnualSemi-AnnualQuarterlyMonthlyContinuousDate 1 mo 3 mo 6 mo 1 yr 2 yr 3 yr 5 yr 7 yr 10 yr 20 yr 30 yr02/11/11 0.08 0.12 0.16 0.30 0.85 1.40 2.38 3.05 3.64 4.49 4.71Annual percentage yields offered on U.S. Treasury Bills, Notes, and Bonds on Friday, February 11, 2011 were:A one month (30 day) T-Bill offering par or face value of $100,000 sold on this date cost ____________ dollars. Each dollar invested in 20 year Bonds will grow to _________ dollars when the bond matures.Date 1 mo 3 mo 6 mo 1 yr 2 yr 3 yr 5 yr 7 yr 10 yr 20 yr 30 yr02/11/11 0.08 0.12 0.16 0.30 0.85 1.40 2.38 3.05 3.64 4.49 4.71Annual percentage yields offered on U.S. Treasury Bills, Notes, and Bonds on Friday, February 11, 2011 were:Assuming that bond traders are risk neutral, and that the transactions costs of buying/selling bonds are negligible, we can determine from these yields that bond traders expect the annual percentage yield offered on 3 mo T – Bills 3 months from this date equals approximately ______.Date 1 mo 3 mo 6 mo 1 yr 2 yr 3 yr 5 yr 7 yr 10 yr 20 yr 30 yr02/11/11 0.08 0.12 0.16 0.30 0.85 1.40 2.38 3.05 3.64 4.49 4.71Annual percentage yields offered on U.S. Treasury Bills, Notes, and Bonds on Friday, February 11, 2011 were:Assuming that bond traders are risk neutral, and that the transactions costs of buying/selling bonds are negligible, we can determine from these yields that bond traders expect the annual percentage yield offered on 10 year T – Bills 20 years from this date equals approximately ______.I.O.U$1,000on 8/26/16. I will also pay 6 percent of Par on each of the dates below.-Bob Holland 8/26/14 8/26/15 8/26/16Consider the following Coupon Bond:Suppose this bond sells for $948.46. What is the formula you would use to calculate this bond’s annual interest yield?APPLICATION: It is usually the annuity value of lottery jackpots that is advertised in efforts to attract ticket buyers. Suppose you win a $26 million dollar lottery. The prize money is paid in 26 equal installments: one today and one at the end of each of the next 25 years. Long term government bonds currently offer annual interest yields of 6 percent.What is the Present Value of your prize?You are shopping for a new car, and fall in love with a shiny new convertible on the show room floor. A salesman approaches you and says: “I can get you into that car for $2,000 down and $659.00 per month through our special financing offer. You pay 5.9 APR over 5 years.”What is this salesman (and his dealership) charging you for this car?Suppose a Consol Bond promises to pay $50 at the end of each year forever. If bonds of comparable risk are offering an annual yield of 6 percent, what will the selling price of this bond be?Suppose your firm earns $50 million this year, and profits are expected to grow by 6 percent per year in the future. The current rate of interest is 9 percent. What is the market value of your firm?If you have already paid dividends this year, equal to profits earned by the firm, the market value of your firm is:Marginal Analysis: Discrete DecisionsControl VariableTotal BenefitsTotal CostsMarginal BenefitMarginal CostMarginal Net BenefitNet BenefitQ B(Q) C(Q) MB(Q) MC(Q) MNB(Q) N(Q)Given Given Given B(Q)/Q C(Q)/Q MB(Q)-MC(Q) B(Q)-C(Q)0 0 501 120 752 220 1053 310 1404 390 1805 460 2256 520 2757 570 3308 610 3909 635 455What is the optimal level of the control variable Q?Total versus Marginal Benefits – Graphical ApproachB(Q) in the graph below represents the Total Benefit derived from activity level Q:Q$B(Q)At any given level of activity, the slope of B(Q) represents the Marginal Benefit MB(Q) of increasing activity from this level of activity.Diminishing Marginal BenefitsTotal versus Marginal Costs – Graphical ApproachC(Q) in the graph below represents the Total Cost derived from activity level Q:Q$C(Q)At any given level of activity, the slope of C(Q) represents the Marginal Cost MC(Q) of increasing activity from this level of activity.Q3Increasing Marginal CostsYou are a manager in charge of deciding the level of activity Q, the total benefits and costs of which are depicted in the graph below:Q$B(Q)C(Q)As a profit maximizing manager, what will your choice, Q*, be?This exercise is easier when we have constant marginal costs:Q$B(Q)C(Q)If we have constant marginal benefits:Q$B(Q)C(Q)We are given the Benefit and Cost Equations:B(Q) = 50Q – 3Q2 and C(Q) = 50 + 2Q2Our experts also tell us that:MB(Q) = 50 – 6Q and MC(Q) = 4QWhat is the optimal level of activity Q*? What is the level of Net Benefits to the firm from this level of