BUS 204 Quantitative Business Analysis
Last Name, First name: USF Email address: Student ID Number: BUS 204 Quantitative Business Analysis "Victory has a thousand fathers, but defeat is an orphan. - John F. Kennedy " Homework 5: Growth Rates Due by noon Saturday, 10/4/14. Email to: huxleyqbata@gmail.com You must put your identification as shown in the syllabus and several emails. You must show your work and all formulas must be present in cells where needed. You should answer all questions on the attached tabs. Note: Gautum Chandiok, TA, is available in MH 310 Mondays 12:30- 2PM, Wednesdays, 3:30-5PM and in room (TBA) on Thursdays, 6:35-7:30 to provide assistance. He can answer specific questions regarding the homework but will not do it for you (one student actually expected him to do her homework in a prior semester - does such a person really belong in college?) You can also get tutorial assistance from the Learning and Writing Center in Cowell Hall with Jeff Wagstaffe or a Peer Tutor assigned to Bus 204: http://www.usfca.edu/lwc/ See the questions on the attached tabs. You should notice that less and less help is provided in terms of how to formulate the inputs, outputs, and calculations. You will need to develop the formats for the later questions on your own - in the real world, you will rarely receive templates. Extra Credit: The problems on tab Q9 and Q10 are eligible for 5% extra credit each on this homework. Q1 Bob's grandfather dies and leaves him an inheritance that he uses to make the initial investment below. Bob plans to invest it and hopes to earn the constant rate of return per year shown shown below for the next 10 years. If he doesn't add to it or withdraw from it at any time but allows it to be reinvested automatically year after year, what will it be worth in 10 years? Inputs: Initial Investment: $50,000 Return: 8% Output: Value after 10 Years: $0 Calculations: Year Investment 0 $50,000 1 2 3 4 5 6 7 8 9 10 Q2 Assume it is Dec. 31 of the starting year shown below. Bob's grandfather dies and leaves him an inheritance that he uses to make the initial investment below. Bob invested it immediately in the S&P 500. What was it worth on Dec. 31 exactly 10 years later, and what was the compounded rate of return over that span? (See last tab for the annual rate of return for money invested in the S&P 500 Index since 1928.) Parameters: Assumed Starting Year: 1981 Assumed Ending Year: 1991 Inputs: Initial Investment: $50,000 Return: Varies Output: Value after 10 Years: $0 Annualized Compounded Rate of Return? 0.0% Calculations: Year 12/31/XX Date Return Investment 0 1981 1 1982 2 1983 3 1984 4 1985 5 1986 6 1987 7 1988 8 1989 9 1990 10 1991 Compounded Rate: Q3 Assume it is Dec. 31 of the starting year shown below. Bob's grandfather dies and leaves him an inheritance that he uses to make the initial investment below. Bob invested it immediately in the S&P 500. a) What was it worth on Dec. 31 exactly 10 years later, and what was the compounded rate of return over that span? b) What do you notice about the difference between this 10 year span and the one in the last question? (See last tab for the annual rate of return for money invested in the S&P 500 Index since 1928.) Parameters: Assumed Starting Year: 2000 Assumed Ending Year: 2010 Inputs: Initial Investment: $50,000 Return: Varies Output: a. Value after 10 Years: Annualized Compounded Rate of Return? Calculations: Year 12/31/XX Date Return Investment 0 1 2 3 4 5 6 7 8 9 10 Compounded Rate: b. Q4a. What would have been the internal rate of return for a single lump sum investment of $1,000 in the S&P 500 over the 40 year span beginning Dec. 31, 1973 ? Q4b. If return rates in the future match the above rate, how much would you have to save each month to reach $1 million in 40 years? Q4c. If return rates in the future match the aveage return rate for the decade beginning Dec. 31, 1981, solved earlier, how much would you have to save each month to reach $1 million in 40 years? Q4d. If return rates in the future match the average return rate for the decade from 2001-10 solved earlier, how much would you have to save each month to reach $1 million in 40 years? Q4e. What do you conclude about how much must be saved when comparing the differences in the above results? Q5. You work for the "My Pride and Toy" yacht company and are involved with setting the prices for a new model. The cost of each unit is $20,000. Company policy is to earn a gross profit (before fixed and other costs) of 100%, meaning you need to sell them for at least $40,000. Some customers might prefer to pay over time, however, so your boss has asked you to devise a purchase contract to allow the customers to buy the product over 5 years. You have developed the idea that, as an incentive for customers to buy, they will pay nothing until the end of the first year, then make 5 equal payments at the end of each year thereafter - six years overall. You have connected with a bank that will buy any purchase contract - that is, will pay you $40,000 immediately - so long as it can earn 10% on the deal and the buyer is credit-worthy. How much should you quote for each annual payment? Q6 Bob's grandfather dies and leaves him the same inheritance as before. Bob plans to invest it with a friend to help with a start-up. The friend says the earnings from the investment will likely be nothing in the first year but will be $10,000 in the second year, $20,000 in the third year, and $30,000 in the fourth year (nothing thereafter). If these forecasts are accurate, what would be Bob's internal rate of return? Q7 Bob's grandfather dies and leaves him the inheritance shown below. Bob plans to invest it with a friend to help with a start-up. The friend says he redid the calculations and the return will still be nothing in the first year but likely be the reverse of before in years 2, 3, and 4. A. If these forecasts are accurate, what would be Bob's internal rate of return? B. Why is the IRR higher for this problem? Q8. It is 12/31/1991.  Tom wants to save $50,000 for the down payment on a house. He feels he can comfortably save only the amount shown below as monthly savings but will increase it each to equal inflation which he assumes will be 3%.   He saves it the first year in his bank account then, on 12/31/1992, he is ready to invest his money.   He invests it 100% in the S&P 500 and continues to invest all of his saving each year in the same way. A. How long would it have taken him to reach his goal? B. In hind sight, how much should he have save to reach his goal by the end of 1997? Inputs: Monthly Savings: $150 Inflation: 3% Q9 A. Fred plans to start saving $100 into a retirement account as soon as he gets his first job and will continue to do so for the next 40 years. How much will he have at the end of 40 years if he earns 8% per year? Q9 B. Susan and Bob are friends at USF. They plan different saving strategies once they get their first job. Susan plans to suck it up and live a bit on the frugal side for the first 20 years of her work life, then stop saving and allow whatever money she has accumulated by then to grow for the last 20 years of her accumulation phase. Bob figures you are only young once and plans to spend what he has for the first 10 years of his work life, then save for the next 30 years. For each $100 saved, who will be better off if they follow their plans and earn 8% percent per year on their savings? Q10 Do your own research on Macs vs. PC in terms of installed base now and projected growth rates. Then make a prediction as to how long it will take Macs to catch up. You must give the source of your information and provide a link to the website. Get your estimates from at least two sources. S&P 500 Returns per year Annual Inflation based on US Consumer Price Index 1928 38.0% -1.0% 1929 -10.5% 0.2% 1930 -27.9% -6.0% 1931 -43.4% -9.5% 1932 -8.1% -10.3% 1933 51.5% 0.5% 1934 3.4% 2.0% 1935 43.6% 3.0% 1936 30.5% 1.2% 1937 -33.1% 3.1% 1938 26.8% -2.8% 1939 3.3% -0.5% 1940 -7.3% 1.0% 1941 -10.1% 9.7% 1942 15.3% 9.3% 1943 25.9% 3.2% 1944 19.2% 2.1% 1945 35.3% 2.2% 1946 -5.3% 18.2% 1947 4.1% 9.0% 1948 2.8% 2.7% 1949 20.2% -1.8% 1950 28.7% 5.8% 1951 21.3% 5.9% 1952 13.9% 0.9% 1953 1.1% 0.6% 1954 49.3% -0.5% 1955 25.9% 0.4% 1956 8.3% 2.9% 1957 -9.6% 3.0% 1958 43.3% 1.8% 1959 12.1% 1.5% 1960 1.4% 1.5% 1961 26.8% 0.7% 1962 -9.2% 1.2% 1963 21.5% 1.7% 1964 16.0% 1.2% 1965 12.3% 1.9% 1966 -9.0% 3.3% 1967 23.9% 3.0% 1968 11.5% 4.7% 1969 -9.1% 6.1% 1970 4.0% 5.5% 1971 14.3% 3.4% 1972 19.0% 3.4% 1973 -14.7% 8.8% 1974 -26.5% 12.2% 1975 37.2% 7.0% 1976 23.8% 4.8% 1977 -7.2% 6.8% 1978 6.6% 9.0% 1979 18.4% 13.3% 1980 32.5% 12.4% 1981 -4.9% 8.9% 1982 21.6% 3.9% 1983 22.6% 3.8% 1984 6.3% 4.0% 1985 31.7% 3.8% 1986 18.7% 1.1% 1987 5.3% 4.4% 1988 16.6% 4.4% 1989 31.7% 4.6% 1990 -3.1% 6.1% 1991 30.5% 3.1% 1992 7.6% 3.0% 1993 10.1% 2.8% 1994 1.3% 2.7% 1995 37.6% 2.7% 1996 23.0% 3.3% 1997 33.4% 1.7% 1998 28.6% 1.6% 1999 21.0% 2.7% 2000 -9.1% 3.4% 2001 -11.9% 1.6% 2002 -22.1% 2.4% 2003 28.7% 1.9% 2004 10.9% 3.3% 2005 4.9% 3.4% 2006 15.8% 2.5% 2007 5.5% 4.1% 2008 -37.0% 0.1% 2009 26.5% 2.7% 2010 15.1% 1.5% 2011 2.1% 3.0% 2012 16.0% 1.7% 2013 32.4% 1.5%