Finance Practice Midterm #1 Solutions

Transcription

1 Finance Practice Midterm #1 Solutions 1) Suppose that you have the opportunity to invest $50,000 in a new restaurant in South Bend. (FYI: Dr. HG Parsa of Ohio State University has done a study that shows that 59% of restaurants fail within the first three years!). a) Given the following data, what is your opportunity cost here? Explain. Asset Annual Return 5 year Government Bond 1.25% DJIA (Stocks) 7% Junk Bonds (CCC or below) 13% Note: CCC bonds have an average default rate of 27% The opportunity cost of the $50,000 investment would be the returns that you could have earned elsewhere. However, the elsewhere has to be an opportunity that is easily risky. In the example, government bonds would not be an equally risky alternative (government bonds are much safer). The Stock market is also probably much safer given the 59% failure rate for restaurants. So we should use the 15% per year junk bond rate. Opportunity Cost =.013 * 50,000 = $650 b) Now, suppose that as a part owner, you are allowed to eat for free as often as you like. How does this change your calculation from (a)? Given that you can eat for free, we would need to deduct your savings in food costs from the above number. 2) Suppose that Amtrak builds a new train line from Chicago to Los Angeles. Unfortunately, the train line passes through thousands of acres of cornfields in Iowa. When the train passes through the cornfields, it throws off sparks that destroy the corn. The corn farmers take Amtrak to court in an attempt to get the train line shut down. a) What would be the right outcome in this case? Explain. The right outcome is a little bit ambiguous. It depends on what we mean by right. Let s assume that the right outcome is the efficient outcome. In that case, we need to figure out the profits of Amtrak and costs to farmers. Let s assume that Amtrak earns $50,000 per year in profits from the train line. If the cost to the farmers is $20,000, then

2 the efficient thing to do would be to rule against the farmers and award the property rights to Amtrak. b) The Coase theorem states that as long as negotiation between the two parties involved is relative costless, the right outcome will result regardless of how the judge might rule. Explain. Suppose that the judge rules for Amtrak. We have the efficient outcome and no side payments are needed. Amtrak Gains: $50,000 Farmer s Loss: $20,000 Suppose that the judge rules for the Farmers. Then Amtrak will be willing to make a payment to the Farmer s (i.e. buy them off) to get the land rights. Suppose that Amtrak pays the farmers $25,000 (we know the payment will be somewhere between $50,000 and $20,000). Amtrak Gain: $25,000 Farmer s Gain: $5,000 3) Consider the following productivities: United States England Services 6 Units/hr. 3 Units/hr. Manufacturing 2 Units/hr. 6 Units/hr. a) Calculate the opportunity cost of services in the and England : Units of manufacturing per unit of services 6 6 England: 2 Units of manufacturing per unit of services 3 b) Calculate the opportunity cost of manufacturing in the and England. Who has the comparative advantage in services? 6 : 3 Units of Services per unit of manufacturing 2 England: 3. 5 Units of Services per unit of manufacturing 6

3 The has a comparative advantage in services while England has a comparative advantage in manufacturing. c) Suppose that the average price of Services is $20 per unit and the average price of manufacturing is $20. What trade pattern will emerge? What will wages be in England and the? With a relative price of $20/$20 = 1 units of services per unit of manufacturing, the will produce and export services while England produces and exports manufacturing. In England, wages will be 6*$20 = $120/hr. In, wages will be 6*$20 = $120/hr. d) Suppose that the inflation rate in England is 3% while the inflation rate in the is 5%. How is your answer in (c) affected In England, wages and prices will rise by 3% per year while in the, wages and prices will rise by 5% per year, but relative prices are unaffected so production and trade patterns do not change. 4) Suppose that you have the following demand and supply curve for sneakers: Q Q d s 400 3P 200 2P a) Solve for the equilibrium price and quantity. So, we need to set supply equal to demand and solve for an equilibrium price P 200 2P 200 5P P 40 Note: as a check, we can plug 40 into both supply and demand to make sure the quantities are equal. Q d 400 3P Q 200 2P s

4 b) Calculate consumer expenditures on sneakers Consumer expenditures would be price times quantity $40*280 = $11,200 Price S 40 11, D Quantity c) Calculate the elasticity of demand at the equilibrium found in (a) % Q Q P % P P Q 280 So, at this price, a 1% rise in price will lower expenditures by.43% d) Would a 5% increase in price cause consumer expenditures to rise or fall? Explain. A 5% rise in price would be from $40 to 40(1.05) = $42. This will cause a 5(.43) = 2.15% drop in quantity to 280( ) = 274. $42*(274) = $11,508. So, spending increases. In general, if the elasticity is smaller than 1 in absolute value, a rise in price cases an increase in expenditures.

5 5) Suppose that you have the following demand curve: Q 120 4P. 001I You know that the current market price is $10 and average income is $40,000. a) Calculate the markets consumer surplus. Price CS 120 D Quantity First, at an income of $40,000, solve for the price where quantity equals zero. Q120 4 P , 000 Q160 4P P P 40 Now, solve for the quantity at a price of $10 Q120 4 P , 000 Q160 4P Q So, Consumer surplus is (1/2)(40-10)(120) = $1,800 b) Calculate the market s total willingness to pay. Actual consumer expenditures are $10*120 = $1200, so total willingness to pay is $ $1800 = $3000

6 6) Suppose that you have the following demand curve. Q 400 6P. 005I Q Represents quantity demanded, P represents price and I represents average income. You know that the current market price is $20 and average income is $20,000 a) Calculate current demand. At a price of $20, we have Q = 400 6($20) +.005($20,000) = 380 b) Calculate the price elasticity of demand. QP PQ 380 c) Calculate the income elasticity of demand QI 20, I Q 380 7) Suppose that you are concerned about drug use in the. You are interested in what the impact would be if authorities could be more effective at getting drugs off the streets. The DEA has estimated the following data: Elasticity of Demand for Cocaine: -.55 Elasticity of Supply: 1 Current Market Price Cocaine: $80 per gram Current Cocaine Sales (annual): 950M grams a) We are using a simply supply/demand framework: Q a bp d Qs c dp Use the data above to find the parameters a,b,c, and d. Q a bp d Q c dp s

7 Use the data above to find the parameters a,b,c, and d. Q 950 b d P 80 a Q bp Q 950 d s P 80 c Q dp b) As a check of the estimated model, solve for the equilibrium price and quantity. Q Q d s P 11.88P P11.88P P $80 Q 11.88* c) Suppose that the DEA is able to seize 100M grams of cocaine and take it off the market. What will happen to the equilibrium price and quantity? So, we need to subtract 100 from the market supply and resolve for price and quantity. Intuitively, what should happen is that the seizure will force the price up, which creates incentives for more supply. Q Q d s P 11.88P P11.88P100 P $85.4 Q 11.88*

8 d) How will cocaine revenues for drug dealers be affected? Revenues prior to the DEA seizure were $80*(950M) = $76,000M = $76B. After the seizure we have $85.40(914M) = $78,055M = $78.055B Looks like the drug dealers win! e) What happens to consumer surplus? First, find the price where demand drops to zero. Qd P P P So, prior to the seizure, CS = (1/2)( )(950) = $69,103M = $69.103B After the seizure, CS = (1/2)( )(914) = $64,016M = $64.016B The drug user lose! 8) Suppose that you observed the following set of data: Average Business School tuition: $30,000 Average Salary for non-mba s: $50,000 per year Average MBA salary: $90,000 per year. The length of an MBA program is 2 years and is assumed that and MBA will have a working career of 20 years after graduation. Further, suppose that, instead of going to get an MBA, you could keep your current non-mba job and invest what you could have used to pay for tuition, risk free, at 4% per year. a) Is this set of data consistent with market equilibrium? Explain. We need to figure out the present value of $40,000 per year, starting two years from now, at an interest rate of 4%.

9 (Note: I did this calculation in excel I wouldn t expect you to calculate it!) 40, , , 000 PV... $539, The opportunity cost of the MBA is the tuition plus the lost salary for two years which is 2(50, ,000) = $160,000. So, the benefits outweigh the costs at an interest rate of 4% (this says that the return to an MBA is higher than 4%). With these numbers, the interest rate would need to be over 20% for the costs to outweigh the benefits! b) If your answer to (a) is no, how will markets adjust? If an MBA was strictly preferred to working without an MBA, demand for MBA degrees should rise, pushing up tuition. Further, as the number of MBAs increases, their salaries should drop. 9) Suppose that a busy restaurant charges $9 for its octopus appetizer. At this price, an average of 48 people order the dish each night. When it raises the price to $12, the number ordered per night falls to 42. a) Assuming that demand is linear, find the demand curve the restaurant faces. So, I know that the coefficient in from of price is 2 (a $3 increase in price lowers sales by 6) Q A 2P I also know that at a price of $9, sales are A 2 9 A 66 Q66 2P b) What price should the restaurant charge to maximize revenues? So, revenues are price times quantity R PQ P P P P

10 So, to maximize revenues, take the derivative with respect to price and set it equal to zero. 66 4P 0 P Q R $ ) Suppose that you are a cattle rancher. You are deciding when to take your cattle to market to sell. You currently have a herd of 100 cattle. Each cow currently weighs 650 pounds and is gaining 50 pounds per month. Your feed costs are $40 per month per cow. Cattle prices are currently $8 per pound, but have been falling at the rate of $0.10 per month. If you are maximizing profits, how many month from now should you sell your cows? So, we have profits equal total revenues minus total costs where (t is time in months) P 8.1t Q t TC t Profits 8.1t 65, t 4000t 2 Profits 520, , 000t 6500t 500t 4, 000t Profits 520, ,500t 500t So, take the derivative with respect to t and solve 29,500 1, 000t 0 t 29.5 P 8.1* 29.5 $5.05 Q * ,500 TC 4, $118, 000 Profits $ ,500 $118, 000 $955,125 2

11 11) Suppose that you are a pizza shop. Your profits depend on your sales of pizza and beer. Specifically, your profits as a function of Pizza sales (P) and beer sales (B) is given by: 2 2 Profits P 140B 8P 12B 4PB Solve for the profit maximizing choices for gasoline and heating oil. We need to take the derivatives with respect to P and B P 4B B 4P 0 Now, we need to solve the above system for P and B. First, solve the first equation for B. 120P 16P 4B 0 B30 4P Now, plug into the second to get P P 4P P 4P P 0 P 6.3 B ) Suppose that your sales are a function of both price (P) and advertising expenses (A) given by Q 3,000 8p 25A 2 pa.5p 3A 2 2 Solve for the combination of price and advertising that maximizes sales. We need to take the derivatives with respect to p and A 8 2A p p 6A 0 Now, we need to solve the above system for p and A. First, solve the first equation for p.

12 8 2A p 0 p2a8 Now, plug into the second to get A A8 6A A16 6A 0 9 2A 0 A 4.5 p 2A ) We need to enclose a field with a fence. We have 500 feet of fencing and a building is on one side and so won t need any fencing. Determine the dimensions of the field that will enclose the largest area. Building x Field x y So, the problem we have is: max xy, So, set up the lagrangian xy subject to 2xy l xy x y take the derivatives with respect to x and y and set them equal to zero y 2 0 x 0 From the second equation, we have x. Plug into the first equation to get y x 2

13 Now, use the constraint with x 2x y 500 y 2 y y 500 y 250 x 125 y 2 14) Suppose that Apple is selling IPads in both the and Europe. Sales in each country are a function of the level of advertising and given by S 12 6A 1.2A 2 S 8 2 A.2A 2 E E E Solve Apples maximization problem; maximize total sales across the two districts subject to a total advertising budget of $4M. How would a $1M increase in Apples advertising budget influence sales? So, the problem we have is: xy, max 12 6A 1.2A 8 2 A.2A subject to A A 4 So, set up the lagrangian 2 2 E E E.2 E 4 E l A A A A A A take the derivatives with respect to A() and A(E) and set them equal to zero 6 2.4A 0 2.4A 0 E E Solve each for lambda and set equal to each other

14 6 2.4A 2.4A A.4A 2.4A 4.4A 6A 10 A Now, use the constraint A A 4 E E E 6A A 14 A A E A 2 2 E E 6 2.4A So, a $1M increase in the advertising budget will raise sales by approximately 1.2(1) = $1.2M. 15) In the game blackjack, face cards are worth 10 points, aces are worth 1 or 11, and all other cards are worth their face value. You are dealt two cards with the objective of getting more points than the dealer. A Blackjack is 21. Assuming a fresh deck (i.e. no cards have been dealt), what are the odds of getting blackjack? First, let s figure out the odds of getting an ace and then a 10 point card. (Remember, once the ace has been dealt, there are only 51 cards left) Prob(Ace) = 4/52 Prob (10 point card/an ace has been dealt)) = 16/51 (4 10s, 4 jacks, 4 queens, 4 kings) So, the probability of an ace first blackjack is (4/52)(16/51) = 64/2652 Now, the alternative would be to get a 10 point card first, and then an ace Prob(10 point card) = 16/52 Prob(ace/a 10 point card has been dealt) = 4/51 So, the probability of an ace second blackjack is (16/52)(4/51) = 64/2652 So, the total probability of a blackjack is 128/2652 =.048 (4.8%) about 1 in ) Assuming two decks of cards (again, assume a fresh deck), if the dealer is showing an ace, and you have not drawn any additional cards yet, what are the odds that the dealer has blackjack?

15 If the first card dealt to the dealer is an ace, then there are 103 cards remaining in the two decks, and 32 of those cards are worth 10 points. So, the odds are 32/103 (31.07%). Now, looking at your hand, if you have one 10 point card, there are 101 cards remaining and 31 of those cards are worth 10 points, so the odds of a dealer blackjack are 31/101 (30.69%) If you have 2 ten point cards, there are 101 cards remaining and 30 of those are worth 10 points, so, we have 30/101 (29.70%) If you have no 10 point cards, then the odds are 32/100 (31.68%) 17) Suppose that you are playing craps. If you roll the dice 10 times, what are the odds that 4 of your rolls come up with a total of seven? Recall, that you can roll a seven 6 ways (1+6, 6+1, 2+5, 5+2, 3+4, 4+34), so the odds of a 7 is 6/36. Now, the binomial distribution gives us the probability of k successes in n tries where p is the probability of success. (Here, the probability of success is 6/36) n! k P p 1 p k! n k! nk So, we want 4 successes (k = 4) out of 10 rolls (n=10) where the probability of success is 6/ ! 6 30 P 4! 6! P (5.4%) 18) Consider the following regression analysis of player performance measures and average winnings per tournament in the PGA (Professional Golf). The data looks at 196 players. a) First, let s consider driving distance (Note: The average driving distance is 287 yards with a variance of 68): W D

16 Where W is average winnings and D is driving distance in yards. SUMMARY OUTPUT Regression Statistics Multiple R 0.20 R Square 0.04 Adjusted R Square 0.03 Standard Error Observations ANOVA df SS MS Regression Residual Total Coefficients Standard Error t Stat Intercept Average Drive a) What would be the impact on a player s average winnings of a 20 yard increase in his average driving distance? What would be a 95% confidence interval for the impact of a 20 yard increase in a player s average drive? The coefficient on average drive is $1, for ever yard of driving distance with a standard error of $ Therefore, a 95% confidence interval for the coefficient would be 2 standard deviations in either direction. $1, /- 2*$ = [$2,250.57, $379.77] So, a 20 yard increase in driving distance would add 20* = $26, to the players average salary. A 95% confidence interval would be 20*[$2,250.57, $379.77] = [$45,011.40, $7,595.40]

17 b) Calculate a forecast with a 95% confidence interval for a player with a 300 yard drive. The forecast would be W 331, $63, To calculate a 95% confidence, we need a standard deviation for the forecast D D SDW / D ˆ 1 N N 1Var D SDW / D , $54, *68 So, our 95% confidence interval is $63, /- 2*$54, (Note, we can t have negative earnings!) [$0, $172,473.98] c) How far must a player be able to drive the ball on average to expect to have positive earnings? We have the regression equation W 331, $63, Set winnings equal to zero and solve for D. We get D = yards

18 Now, suppose that I altered the regression by taking the natural log of winnings. lnw D SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA df SS MS Regression Residual Total Coefficients Standard Error t Stat Intercept Average Drive a) Now, what impact would a 20 yard increase in driving distance have on average winnings? The coefficient on average drive is.013 (1.3%) increase in average winnings for ever yard of driving distance with a standard error of $.9%. Therefore, a 95% confidence interval for the coefficient would be 2 standard deviations in either direction. 1.3% +/- 2*.9% = [3.1%, -.5%] So, a 20 yard increase in driving distance would add 20*1.3 = 26% to the players average salary. A 95% confidence interval would be 20*[3.1%, -.5%] = [62%, -10%]

19 b) Calculate forecast for average winnings for a player with an average drive of 300 yards. The forecast would be W e $35, The Standard Deviation would be D D SDW / D ˆ 1 N N 1Var D SDW / D *68 Note, that s a standard error of over 100%! So, if W = /- 2*1.002, we have W = [8.463, ] e e , , W = [$4,736.25, $260,667.30] 19) Consider the following time series regression: P t Where P is total non-farm payrolls in the and t is time in months. The data used is monthly data from Jan 1939 until August 2016 (t = 0 is Jan 1939). We have 931 observations (so, the average for time is 466 and the variance is 72,463)

20 SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA df SS MS Regression Residual Total Coefficients Standard Error t Stat Intercept Time a) On average, how many jobs do we create per year in the? The coefficient on time is 128,864 per month (employment is in thousands, so this is 128,864 jobs per month). So in a year, we create 128,864*12 = 1,546,368 jobs b) Calculate a forecast for Non-farm payrolls for December 2016 ( t = 935) with a 95% confidence interval. P , So, the forecast for payrolls in Dec is 146,997, t t 1 1 SDP / t ˆ 1 N N Var t SDP / t *72463 So, our forecast is 146,997,421 +/- 2*(4,878,172).

21 Now, suppose that I added seasonal dummies for the first three quarters SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 932 ANOVA df SS MS Regression Residual Total Coefficients Standard Error t Stat Intercept Time D D D a) Is there evidence for seasonality in employment in the? By the coefficients, it says that Quarter 1 jobs created are 1,757,508 lower than the 4 th quarter Quarter 2 jobs are 488,961 lower than the 4 th quarter Quarter 3 jobs are 667,040 lower than the 4 th quarter However, only the 1 st quarter dummy is statistically significant. So we have the 1 st quarter is a slow quarter for job creation! b) Calculate a new forecast for Dec (don t worry about the Standard Dev.) P , So, 147,723,088 jobs!

22 20) Suppose that I repeated the above analysis, but I converted payrolls to logs. ln P t D D D Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 932 ANOVA df SS MS Regression Residual Total Coefficients Standard Error t Stat Intercept Time D D D How does this change the analysis above? So, now we have that payrolls increase by.0016 (.16%) per month or 12*.16 = 1.92% per year. Seasonality is still present with payrolls in the first quarter being 2.47 percent lower than the 4 th quarter. The other quarters are not significantly different. If I were to forecast Dec 2016 (t = 935) ln P e , So, 167,879,208 jobs!