Question

A B C Market Summary > Dow Jones Industrial Average INDEXIX DJI + Follow 9) Suppose someone you know from home heard you are taking Engineering Economy and wants some financial advice. Their neighbor is a small business owner who is investing $125,000 into a T-shirt printing company (year 0). He believes that this should lead to annual sales of $22,500 per year (starting in year 1). There will be an increase yearly of $2,250 starting in year 2 in sales. There are expenses associated with this business of $2,500 in raw t-shirts and labor for the business. Your family friend has been ask to invest in this business, but only a small amount money for 6 years. To figure out if you should do it you analyze multiple return on investments and analyze the risk of all options. 27,625.63 -49.17 (0.18%) + Nov 8, 2:07 PM EST Disclaimer 1 day Juays 1 month 6 months YTD 1 year 5 years Max 30,000 10,539.01 Nov 12, 2004 To get a benchmark, you are going to evalute 2 data points: 1) What has been the historical rate of return of Adidas stock from 2014 to 2019 (Q8)? 2) What is the Rate of return of the Dow Jones Industrial Average for the last 15 years (2004 - 2019) 3) What is the rate of return for the T-shirt busines? 4) Considering the risk, do you think it is wise to invest in the t-shirt buisness. 20.000 10,000 1985 1995 2005 2015 Low 27,578.97 Open High 27,686.20 27,694.95 A What is the rate of return of DJIA over last 15 years? B What is the rate of return for Adidas over last 5 years? C What is the expected rate of return for T-shirt Business? DlShould you invest in the T-Shirt Business (Yes/No) → Financial news, comparisons and more

Answer 1

To answer such type of questions where time lengths are different, we should try to get annualised rate of return for various options and compare

A) For DJIA, Index P_0 (Y= 2004 )= 10539.01, Index P_15 ( Y = 2019) = 27625.63
Using CAGR formula, annualised rate of return = (P_15/P_0)^(1/15) -1 = (27625.63/10539.01)^(1/15)-1=6.63%

B) For Adidas, using finance.yahoo.com, we get P_0 (date 23Nov14) =Eur 64.5, P_5 (23Nov19) =178.05
Similar to part A, annualised rate of return = (178.05/64.5)^(1/5) -1 =22.5% (Note than we need to take 5th route here ag 15th in part A since time period length is 5 yrs from 2014 to 2019)

C) For T Shirt business, since obviously market index kind of data is not available, we need to calculate IRR which would enable comparison with other two options above. Ignoring taxes (since not given in question), it's quite easy to make cashflows as below and use excel solver function to get IRR as below:

Year	Cashflow				Remarks	IRR	Discount Factor (df = (1/1+IRR)^Y)	Present Value (PV = CF*df)
Y	Initial Investment (i)	Annual Sales (ii)	Expenses (iii)	Net Cashflow (CF=i+ii+iii)		5.8%
0	-125000			-125000		5.8%	1.0	-125000.0
1		22500	-2500	20000		5.8%	0.9	18904.7
2		24750	-2500	22250	Increase in annual sales from year 2 onwards as given in qn	5.8%	0.9	19879.6
3		27000	-2500	24500		5.8%	0.8	20691.0
4		29250	-2500	26750		5.8%	0.8	21354.0
5		31500	-2500	29000		5.8%	0.8	21882.2
6		33750	-2500	31250		5.8%	0.7	22288.6
Total								0.0

In solver we need to keep value of highlighted cell to zero by changing green cell and we shall get 5.8 % as answer

D)Since expected annualised rate of return of T-Shirt business is both less than peer (Adidas) and market Index (Dow Jones), we should not invest in the business