2. Calculating the price elasticity of demand: A step-by-stepguide

Suppose that during the past year, the price of a laptop computer rose from $2,750 to $2,880. During the same time period, consumer sales decreased from 446,000 to 321,000 laptops.

Calculate the elasticity of demand between these two price–quantity combinations by using the following steps. After each step, complete the relevant part of the table with the appropriate answers. (Note: For decreases in price or quantity, enter values in the Change column with a minus sign.)

Step 1: Fill in the appropriate values for original quantity, new quantity, original price, and new price.

Step 2: Calculate the average quantity by adding the original quantity and the new quantity, and then dividing by two. Do the same for the average price.

Step 3: Calculate the change in quantity by subtracting the original quantity from the new quantity. Do the same for the change in price.

Step 4: Calculate the percentage change in quantity demanded by dividing the change in quantity by the average quantity. Do the same to calculate the percentage change in price.

Step 5: Calculate the price elasticity of demand by dividing the percentage change in quantity demanded by the percentage change in price, ignoring the negative sign.

Using the midpoint method, the elasticity of demand for laptops is about   .

January 3rd, 2013. Jonathan Allen is the CFO of Trojan, Inc., a food-catering company based in Miami, Fla. Founded in 2007, and after struggling during the difficult 2008-2009 recession years in the United states, the company found a successful niche, specializing in the delivery of top quality individual meals for the airline industry’s business class segment. The company went public in June 2012 and its stock currently trades at $35. With the success of its airline business in the US, it is looking to expand its catering services to other highend segments in other markets such as railroad and sea cruise travelers, both domestic and international. The Trojan management team believes that, as a result of this expansion plan, the stock should grow at an average rate of 8% per year for at least the next 10 years to come. As a result of this ambitious expansion program, Allen realizes that the company will need a substantial amount of additional funding, far beyond the proceeds received last year from its I.P.O. A new stock issue is obviously out of the question. Bank debt might be available but only for a relatively short-term maturity (1-3 years), and perhaps not in sufficient amounts. Trojan needs to raise about $50,000,000 for 7 years to complete its expansion program. A traditional bond issue might be an option, but the straight bond market is very crowded at the moment and Allen fears that, since Trojan is relatively young and unrated, investors may not have any interest, unless it pays a high annual coupon, 9% (the current market interest rate for 7-year money for a company similar to Trojan) , which it cannot afford at the moment. So, Allen is looking into either issuing 1) a bond with warrants, or 2) a convertible bond. Both would have a maturity of 7 years, and a total amount issued of $50,000,000 (50,000 bonds at a $1,000 par value). The issue is expected to take place at the beginning of 2014. Allen is working with a local investment bank to help the company design the most appropriate terms for each issue before making a final decision on which to choose. Bond with warrants: Each bond will have 25 warrants attached to it, with a strike price of $42. The warrant may only be exercised at the end of Year 4 or thereafter. The estimated value of each warrant should be $5 when the bond is issued (assuming no significant changes in market conditions between now and the end of the year). The investment bank will charge a one-time 3.50% flotation fee on the total amount of the issue for the bond with warrants, to be paid on the day of the issue. Convertible bond: The bond will have a conversion ratio (CR) of 20 shares per bond. The convertible bond has an annual coupon rate of 7% and is callable by the issuer at the end of Year 5 or thereafter (by callable, we mean that Trojan has the right to force the conversion from bond into stock). The investment bank will charge a one-time 4.00% flotation fee on the total amount of the issue for the convertiible bond, to be paid on the day of the issue.

1) What should be the fixed annual coupon, in US$, of the bond with warrants (please round up to the nearest dollar)? As a result, what will be the percentage coupon rate (rounded up to the nearest percentage point – i.e., no decimals)? 2) What will be the effective cost of capital to Trojan of the bond with warrant issue, if the bondholders exercise their warrants at the end of Year 4? Include all types of costs mentioned in the case, and express the cost as an annual percentage rate (to the nearest 2 decimals)? 3) What is the “floor value” of the convertible bond in Year 0? At the end of Year 5? 4) What will be the effective cost of capital to Trojan of the convertible bond, if Trojan calls the bond (i.e., forces conversion) at the end of Year 5? Include all types of costs mentioned in the case, and express the cost as an annual percentage rate (to the nearest 2 decimals)? 5) From a cost standpoint only, which issue should Trojan choose? 6) Aside from the cost factor above, what would be the pros and cons of either issue to Trojan? 7) All things considered, which of the two above issues would you recommend to Trojan, assuming they must choose between one or the other? Explain.

anuary 3rd, 2013. Jonathan Allen is the CFO of Trojan, Inc., a food-catering company based in Miami, Fla. Founded in 2007, and after struggling during the difficult 2008-2009 recession years in the United states, the company found a successful niche, specializing in the delivery of top quality individual meals for the airline industry’s business class segment. The company went public in June 2012 and its stock currently trades at $35. With the success of its airline business in the US, it is looking to expand its catering services to other highend segments in other markets such as railroad and sea cruise travelers, both domestic and international. The Trojan management team believes that, as a result of this expansion plan, the stock should grow at an average rate of 8% per year for at least the next 10 years to come. As a result of this ambitious expansion program, Allen realizes that the company will need a substantial amount of additional funding, far beyond the proceeds received last year from its I.P.O. A new stock issue is obviously out of the question. Bank debt might be available but only for a relatively short-term maturity (1-3 years), and perhaps not in sufficient amounts. Trojan needs to raise about $50,000,000 for 7 years to complete its expansion program. A traditional bond issue might be an option, but the straight bond market is very crowded at the moment and Allen fears that, since Trojan is relatively young and unrated, investors may not have any interest, unless it pays a high annual coupon, 9% (the current market interest rate for 7-year money for a company similar to Trojan) , which it cannot afford at the moment. So, Allen is looking into either issuing 1) a bond with warrants, or 2) a convertible bond. Both would have a maturity of 7 years, and a total amount issued of $50,000,000 (50,000 bonds at a $1,000 par value). The issue is expected to take place at the beginning of 2014. Allen is working with a local investment bank to help the company design the most appropriate terms for each issue before making a final decision on which to choose. Bond with warrants: Each bond will have 25 warrants attached to it, with a strike price of $42. The warrant may only be exercised at the end of Year 4 or thereafter. The estimated value of each warrant should be $5 when the bond is issued (assuming no significant changes in market conditions between now and the end of the year). The investment bank will charge a one-time 3.50% flotation fee on the total amount of the issue for the bond with warrants, to be paid on the day of the issue. Convertible bond: The bond will have a conversion ratio (CR) of 20 shares per bond. The convertible bond has an annual coupon rate of 7% and is callable by the issuer at the end of Year 5 or thereafter (by callable, we mean that Trojan has the right to force the conversion from bond into stock). The investment bank will charge a one-time 4.00% flotation fee on the total amount of the issue for the convertiible bond, to be paid on the day of the issue.

1) What should be the fixed annual coupon, in US$, of the bond with warrants (please round up to the nearest dollar)? As a result, what will be the percentage coupon rate (rounded up to the nearest percentage point – i.e., no decimals)? 2) What will be the effective cost of capital to Trojan of the bond with warrant issue, if the bondholders exercise their warrants at the end of Year 4? Include all types of costs mentioned in the case, and express the cost as an annual percentage rate (to the nearest 2 decimals)? 3) What is the “floor value” of the convertible bond in Year 0? At the end of Year 5? 4) What will be the effective cost of capital to Trojan of the convertible bond, if Trojan calls the bond (i.e., forces conversion) at the end of Year 5? Include all types of costs mentioned in the case, and express the cost as an annual percentage rate (to the nearest 2 decimals)? 5) From a cost standpoint only, which issue should Trojan choose? 6) Aside from the cost factor above, what would be the pros and cons of either issue to Trojan? 7) All things considered, which of the two above issues would you recommend to Trojan, assuming they must choose between one or the other? Explain.

5. A car insurance company would like to determine the proportion of accident claims covered by the company. According to a preliminary estimate 65% of the claims are covered. How large a sample should be taken to estimate the proportion of accident claims covered by the company if we want to be 95% confident that the sample percentage is within 2% of the actual percentage of the accidents covered by the insurance company?

A car insurance company would like to determine the proportion of accident claims covered by the company. According to a preliminary estimate 40% of the claims are covered. How large a sample should be taken to estimate the proportion of accident claims covered by the company if we want to be 90% confident that the sample percentage is within  2% of the actual percentage of the accidents covered by the insurance company?

A researcher plans to conduct a marketing experiment to decide which shampoo has the better floral scent considering only two brands, "red" shampoo or "pink" shampoo. A sample of 190 people were chosen assuming that they can distinguish between the different scents. What are the symmetrical limits of the population percentage within which the sample percentage is contained with a probability of 90%?

In a study of the accuracy of fast food​ drive-through orders, Restaurant A had 286 accurate orders and 70 that were not accurate. a. Construct a 90​% confidence interval estimate of the percentage of orders that are not accurate. b. Compare the results from part​ (a) to this 90​% confidence interval for the percentage of orders that are not accurate at Restaurant​ B: 0.176less thanpless than0.248. What do you​ conclude?