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	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%