GETTING READY FOR THE MBA. A common question we get asked is Is there anything I can do to get myself ready for what lies ahead?

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1 GETTING READY FOR THE MBA A common question we get asked is Is there anything I can do to get myself ready for what lies ahead? Your professors for Finance and Modelling Business Decisions, Mary Kelly and Kevin Hendricks, have found that a better understanding of basic math skills and familiarity with Excel spreadsheets would improve many students chances for success in their courses. On the following pages you will find a Math quiz and some suggested sources for more information on Excel. The quiz won t be marked we have even provided the answers so go ahead and see how much math you remember. While some of you have experience and high levels of comfort in these areas, many of you will want to spend some time exploring the recommended resources and plan to join us on August 20 for a basic math and excel refresher camp. MATH & EXCEL REFRESHER CAMP (Optional, but highly recommended) When: Monday August 20, :00 A.M. 4:00 P.M. Where: School of Business & Economics building Room SBE1220 On Monday August 20, the day before the 2012 MBA Program officially kicks off, we are holding a one day refresher course for those of you who would like to brush up on your math and excel skills. Everyone is encouraged to attend but attendance is optional. Not sure if you need to be there? Try the questions on the following pages and see how much math you remember. You can also check out the excel resources and see if any of it looks familiar. Please let Marita know if you will be attending. [email protected]

2 Module BASIC MATH SKILLS YOU WILL NEED FOR YOUR FINANCE COURSE Math skills required / highlighted 1 Introduction Data management reading pie charts and line charts, interpreting percentages Basic arithmetic and order of operations Word problems Using formulas and solving for unknowns 2 Time Value of Basic arithmetic, exponents and logarithms, and order of operations Money Word problems and using formulas and solving for unknowns Using goal seek in excel 3 How to Value Basic arithmetic, exponents and logarithms, and order of operations Stocks and Bonds Word problems and using formulas and solving for unknowns Interpreting and building graphs, Using goal seek in excel 4 Stock Valuation: Risk and Return and the CAPM Introductory statistics: mean, variance, covariance and correlation Data management and basic linear regression in excel Interpreting and building graphs Basic arithmetic, exponents and logarithms, and order of operations Word problems and using formulas and solving for unknowns 5 Cost of Capital Basic arithmetic, exponents and logarithms, and order of operations Word problems and using formulas and solving for unknowns Using goal seek in excel Interpreting graphs 6 Project Basic arithmetic, exponents and logarithms, and order of operations Evaluation Word problems and using formulas and solving for unknowns Building and interpreting graphs 7 and 8 Project Cashflows, Capital Budgeting and Risk Analysis 9 Corporate Financing Debt and Equity 10 Capital Structure Basic arithmetic, exponents, and order of operations Word problems Word problems and using formulas and solving for unknowns, including sensitivity analysis Decision trees and probability Using goal seek in excel Basic arithmetic and order of operations Interpreting graphs Basic arithmetic and order of operations Word problems and using formulas and solving for unknowns Interpreting graphs Introductory game theory

3 Math Quiz (Solutions are at the end) 1. Desmond earns commission income of 5% on the first $100,000 of sales, 10% on the next $100,000 and 7% on amounts greater than $200,000. If he has annual sales of $230,000, what commission does he earn? 2. The age of an account receivable is the length of time it has been outstanding. A firm has $78,000 in receivables that are 30 days old, $135,540 in receivables that are 60 days old and $23,459 in receivables that are 90 days old. What is the average age of the firm s account receivables 3. What is the minimum value of x such that 2 x x 5 4. Great Waves Surf Resort charges $72 for a day pass including surf lessons. a) If it collects $1080 between 9 and 10 am, how many passes did it sell in one hour? b) Suppose there is a second pass for $30 that does not include surf lessons. Great Waves Surf Resort sells 190 passes in total and collects $10,320. How many passes sold did not include surf lessons? 5. A mortgage broker is developing a business plan for a residential building inspection service. The cost to hire an inspector is $2500 a month. The fixed costs for a vehicle for the inspector would be $500 a month. He estimates that the additional variable office costs (word processing and supplies) would be $50 per inspection. He also anticipates a monthly advertising budget of $200, and a cost of $200 for utilities (phone and internet for the inspector). a) If the price per inspection is $300, how many inspections per month are required so that the inspection service does not operate at a loss? b) How many inspections a month are required so the mortgage brokers nets $1000 per month in income from the inspection service? 6. ABC Stock decreased in value by 50% last month. It then increased in value 25% this month. What is its current value as percentage of its starting value? Solve A butcher buys 240 kg of beef for $380. If 20% of the beef is unusable, what is the average price per kilogram that the usable beef must be sold so the butcher can make a profit of 25% on the original purchase price? 9. Find the missing numbers that make the following 3 fractions equivalent 16 x y From January 1 st 2008 to December 31 st 2008, Betty s pension savings decreased by 33% to $37,000. How much was her pension savings worth on January 1 st, 2008? 11. Graph the following 2 equations over the range x = 0 to x = +15

4 12. If Equation 1: y = 2.5x Equation 2: y+4x = 38 Use the graph to answer the following questions: a) Over which range of x is equation 1 greater than equation 2? b) Over which range of x is equation 2 greater than equation 1? c) Over which range of x are equations 1 and 2 both negative? 4 27 n 9, what is n? 13. A Canadian visitor to Britain wants to exchange $350 into pounds and the exchange rate is $1.58 to get one pound. The bank also charges a fee of 5 to do the conversion. How many pounds does the visitor get? 14. T.D. Hughes Ltd. are builders and retailers of high quality furniture. In particular they have a dining room set that sells for $3200. Last summer they had difficulty procuring the wood required for the table, and raised the price of the dining room set by 20%. When the wood was easier to obtain, they reduced their higher price by 20% and advertised this as part of a sale. Customers complained saying that this was not really a sale: the dining room set was just reduced back to its original price. What do you think? Support your answer. 15. University Stadium can sell 2200 tickets for a concert. University Stadium offers a 20% discount to alumni and a 40% discount to students. It expects that alumni will purchase one quarter of the tickets, and students will purchase 10% of the tickets. The remaining tickets will be sold at full price to members of the community. If the stadium needs to generate at least $40,000 in ticket sales to cover its costs, what is the minimum full price it can charge for a ticket? The unit cost to produce x units of a good is given by cost=1.5 x 120x 4000.Draw a graph to find the lowest unit cost. What production level does this correspond to? 17. If ln(a)=0.310, ln(b)= and ln(c)=0.6021, what is the value of ln(ab/c). 18. With simple interest, the interest is computed on the original principal during the duration of the loan at the stated annual rate of interest. Interest never accrues on previously earned interest. The formula for simple interest, where r is the annual interest rate, t is the time in years. P is the principal or original amount and S is the accumulated value is S=P(1+rt) a. How long will it take $1000 to accumulate to $1800 if the rate of simple interest is 6%? b. A manufacturing company receives an invoice for $4000 of inventory. The inventory is sold with terms 4/30 n/100. This means that if the bill is paid within 30 days, the purchaser will receive a 4% cash discount on the purchase price. Otherwise the full amount must be paid no later than 100 days from the date of the invoice. What is the highest rate of simple interest at which it can afford to borrow money in order to take advantage of the discount?

5 19. Rewrite the equation 2 a 7 3 b 5 in terms of y (i.e. y is on the left side of the equal sign, and all 6y 2c other variables are on the right hand side of the equal sign. a. Solve for y if a=2, b =3 and c =4. b. If b=3, and c=4, what is the minimum level of a such that y is greater than zero? 20. Fine Leather Enterprises sells its single product for $129 a unit. The firm s fixed operating costs are $473,000 annually and its variables operating costs (cost to produce each unit of its product) are $86 a unit. a. How many units must the firm sell to break even (have zero profits)? Graph the firm s total operating (fixed plus variable costs), the firm s fixed costs and the firm s revenues on the same graph. The x axis should be number of units sold and the y axis is costs/revenues measured in dollars

6 MATH QUIZ SOLUTIONS x 100, x 100, x 30,000 = $17,100. Commission earned is $17, The solution is a weighted average of the number of days 78, , , ,583,710 Average Number Days = , ,540 23, ,999 Check that your answer makes sense. In this case, the bulk of the receivables are due at 60 days, but more are due at 30 days than at 90 days, so something less than 60 is right. 3. Rearrange terms to get x on one side of the inequality 2x x 5 2x 6x x 30x x 30x x 32 x The minimum value of x is a) Let y be the number of day passes sold. 72 y = 1080 Y = 1080/72 Y = 15 Great Waves Surf Resort sold 15 passes. b) Let y be the number of day passes with surf lessons and x be the number of day passes without surf lessons. Equation 1 refers to the revenue collected: 72 y + 30 x = 10,320 Equation 2 refers to the number of passes sold y + x = 190. We are not interested in solving for y, only x. So we can rewrite equation 2 as y = 190 x, and substitute into equation 1: 72 y + 30 x = 10,320 72(190 x) + 30x = 10,320

7 13,680 72x + 30x = 10,320 ( 72+30) x = 10,320 13,680 X = ( 3360)/( 42) X = day passes without surf lessons were sold. 5. First detail the costs and revenues of the project: Fixed costs Inspector Salary = 2500; Vehicle costs = 500; Advertising = 200; Utilities= 200 Variable costs Office costs = 50 per inspection; Revenue = 300 per inspection a) Let n be the number of inspections required so that the project breaks even Profit revenue per inspection number of inspections inspector salary+vehicle costs advertising utilities office cost per inspection number of inspection Profit 300 n n n n 250 n 13.6 Obviously a firm cannot complete a fraction of an inspection, so n should be rounded up to the next whole integer (even if the fraction component were less than 0.5, the number should be rounded up). Therefore the number of inspections required so that the firm does not operate at a loss is 14. b) Let n be the number of inspections required so that the project earns at least $1000 profit.

8 Profit revenue per inspection number of inspections inspector salary vehicle costs advertising utilities office cost per inspection number of inspections Profit 300 n n n n 250 n 17.6 At least 18 inspections per month are necessary to net an additional $1000 per month in income. 6. Let x be the starting stock price. Ending stock price = x x 0.625x Total proceeds required from retail sale = 380 x 1.25 = $475 Number of kilograms that can be sold = 240 x (1.2) = 192 Average price per kilogram = 475/192 = $ Equate the first and second fraction and solve for x. 16 x x 96 3x x 32 and then equate the first and third fraction and solve for y. 16 y y First note that negative. Therefore %change = final value - initial value, where in this case, the percentage change is initial value

9 37, 000- initial value 0.33 initial value 0.33 initial value 37, 000- initial value 37, , 000 initial value = $55, The graph is as below: equation 1 equation 2 Now solve for the intersection of the 2 graphs by substituting equation 1 into equation 2 y 4x x x x x a) Equation 1 is greater than equation 2 for all values of x>5. b) Equation 2 is greater than equation 1 for all values of x<5 c) From the graph, both equations will produce negative values when equation 1 crosses the x axis. To find this point, solve for the value of x such that y = 0 in equation 1 y 2.5x x 30.5 Both equations are negative when x> x

10 12. The easiest way to solve this is to take natural logarithms of each side. n n ln27 4ln9 n ln9 2 4 ln n $350 is equivalent to 350/1.58 = The bank then takes its fee of 5, and so the visitor would receive = The new price is actually lower than the original price, but not by a huge amount. The original price was $3200; the increased price was 3200(1.20)=$3840 and the new sale price was $3840(1 0.20) = $3072. $3072 is 4% lower than the original selling price of $3200, not a huge discount, but a sale nonetheless. 15. Let p be the full price of a ticket. # tickets sold to alumni = 0.25 x 2200 = 550 # tickets sold to students = 0.1 x 2200 = 220 # tickets sold to community = = 1430 Therefore p must solve: revenue from alumni revenue from students revenue from community 40, p p 1430 p 40, ,000 p p p 40, The price of the ticket must be at least $19.98, or more realistically $20.

11 16. The lowest production costs occurs at 40 units. # units (x) cost # units (x) cost Production Cost Number of Units ab ln lna ln b ln c c Substitute for the values into S=P(1+rt): a) r =.06; P=1000; S=1800 S P 1rt t t t years It would take years b) Note that it would never make sense to pay before the 30 days are up, nor would it make sense to pay the full amount before the 100 days are up. If the company pays at day 30, it will pay 4000(1 0.04)=$3840. Otherwise, it would pay $ days later, at day 100. If the company borrows the money, the interest that it will

12 have to pay cannot exceed the $160 cash discount that it receives. Let r be the maximum interest rate it would pay; P =3840; S=4000; t=70/365 S P 1rt r r r r 21.73% Therefore if it can borrow at less than 21.73%, the firm should do so. 19. First rewrite the equation in terms of y: 2a 7 3b 5 6y 2c 2c 2a 7 3b 5 6y. c 2a 7 y 33 b 5 a) Substitute for a=2, b =3 and c =4 in the above equation. c 2a y 1 33b b) b=3, and c = 4, find a such that y>0: c 2a 7 y 0 33b 5 42a a a 2

13 20. Let x be the number of units sold. a) Total cost =473,000+86x; Total revenues = 129x Breakeven occurs when total cost = total revenues 473,000 86x 129x 473,000 43x 0 473,000 x 11, ,000 units must be sold for the firm to break even b) From a) it makes sense that we graph the number of units in thousands, and graph the revenues in $100,000 increments total revenues Costs / Revenues $ operating costs fixed operating costs breakeven number of units number of units Fixed costs operating total cost total revenues 0 473, , , , ,000 2, , , ,000 3, , , ,000 4, , , ,000 5, , , ,000 6, , , ,000 7, ,000 1,075, ,000 8, ,000 1,161,000 1,032,000 9, ,000 1,247,000 1,161,000 10, ,000 1,333,000 1,290,000

14 11, ,000 1,419,000 1,419,000 12, ,000 1,505,000 1,548,000 13, ,000 1,591,000 1,677,000 14, ,000 1,677,000 1,806,000 15, ,000 1,763,000 1,935,000 16, ,000 1,849,000 2,064,000 17, ,000 1,935,000 2,193,000 18, ,000 2,021,000 2,322,000 19, ,000 2,107,000 2,451,000 20, ,000 2,193,000 2,580,000

15 SOME EXCEL 2010 RESOURCES Excel 2010 is the spreadsheet program that will be most useful in your Modelling Business Decisions course. If you have never used Excel before, or want to brush on the basics, the following training course from Microsoft.com is a good place to start. RZ aspx If you are familiar with Excel 2003, or an earlier version, and want to understand what s new in Excel 2010, the following training course will be for you: More information on getting started with Excel is available at the following location: An Excel 2010 tutorial from a non-microsoft source is also available at: This tutorial is provided for free by GCFLearnFree.org