CAGR is the rate at which the EPS has grown.
Please see the timeline below http://www.daulatguru.com/finance-fo...0&d=1345874193
Easily we can solve this with the financial calculator
So, the number of periods from 2002 to 2008 is equal to 6, therefore N = 6
The parameters of TVM are :
FV = -$14; PV = $5; PMT = 0; N=6; I/Y =?
CPT -> I/Y =>I/Y = 18.72%
So, the EPS has grown at an average rate of 18.72% for the 6 years.

Note that you will get option A as the answer when you mistakenly take n = 7, so ensure that you input correct data.
You will get error in your calculator, when you dont take PV and FV values having opposite sign.

Thanks
Ratan

Quote:

Originally Posted by ratankv

Today's Question (Questions and answers provided by Knowledge Varsity)
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Q2. A Firm's EPS was $5 in 2002, In year 2008 the EPS was $14. Find the compounded annual growth rate (CAGR) of the EPS.
A. 15.85 %
B. 18.7 %
C. Can’t be determined from the given options

25-08-2012, 12:36 PM

ratankv

Question #3

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Today's Question (Questions and answers provided by Knowledge Varsity)

Q3. An investor purchased one share of Goldman Sachs (NYSE:GS) at $100 at T = 0, he again purchased one more share of GS at $120 at T =1. He received total dividend of $2 at T= 1 and a dividend of $3 per share at T =2, the investor sold the shares at T=2 for a total consideration of $260 (or $130 per share). Find money weighted and time weighted return?
A. Money weighted = 14.4% ; Time weighted = 16.41%
B. Money weighted = 16.41% ; Time weighted = 14.4%
C. Money weighted = 14.4% ; Time weighted = 16.28%

@Ratan Sir:- Thanks a lot for explaining the concept. Right, the end pts takes long steps than middle one.

25-08-2012, 11:24 PM

Prabir Bansal

@Sir:- What are the basic applications of CAGR ?? Also, AMR (Arithmetic Mean Return) is the only tool to compare with CAGR or any other is also there..?? Plz explain.

Answer of Q3 shud be C.

26-08-2012, 08:11 PM

ratankv

Hi Prabir,

CAGR can be used to find out the average growth over a period of time, so essentially it gives an idea on the growth rate.
Arithmetic mean return should not be used to compute gorwth rate over multiple periods because it will give wrong answer.
Wait for sometime and I will be posting a question related to that concept also.

@Sir:- What are the basic applications of CAGR ?? Also, AMR (Arithmetic Mean Return) is the only tool to compare with CAGR or any other is also there..?? Plz explain.

Answer of Q3 shud be C.

26-08-2012, 08:14 PM

ratankv

Hi Rohit,

The number of period should be 6 and not 7.
Just think this way, we want to find out the growth in 1 year, you start with ending EPS of 2009 and ending EPS of 2010. So, here you have 2 EPS values, but the time period is 1.
So, in the problem we had 7 years, but the number of period was 6.
I hope it clarifies.

We can use PV = -5, FV = 14 and calculate rate.
According to my calculation, CAGR = 15.8%
So answer is A.

26-08-2012, 08:40 PM

ratankv

Solution for Question # 3

Q3 Answer is C

Check the Video Solution Q#3 below:

Text Solution for Question #3 is below

Important assumption : We assume that the dividend is paid just before the period ends. Money Weighted Return Calculation: Step 1 : We should identify the cash flows that are happening at the various intervals. As per our sign convention, money going out from investor should be treated as negative and money coming to an investor should be treated as positive. At T =0 : Purchase of 1st share was done => Cash outflow of $100 => CF0 = -$100 At T =1 : Purchase of 2nd share was done => Cash outflow of $120
Dividend is received => Cash Inflow of $2
Sum of these two results in cash outflow of $118 => CF1 = -$118 At T =2 : 2 shares are sold => Cash inflow of $260
Dividend is received => Cash Inflow of $3 * 2 = $6
Sum of these two results in cash inflow of $266 => CF1 = $266

Step 2: Plug the cash flow values in the financial calculator to compute the IRR (because MWR is nothing but IRR)
IRR = 14.438% or Money Weighted Return is 14.438%

Time Weighted return Calculation: Step 1: We should first find out the number of periods, here significant cash in-flow is happening at T=1 and cash outflow is happening at T=2. So we have one period from T=0 to T=1 and another period from T=1 to T=2

Step 2: Compute the portfolio value just before the significant cash inflow or outflow. For Period 1: Beginning Value = $100; Ending Value = $120; Dividend Received = $2 For Period 2: Beginning Value = $120 (for the 1st share) + $120 (amount that is invested) = $240
Ending Value = $260; Dividend Received = $6 (for 2 shares) Note: Many candidates have confusion regarding why the beginning value of the portfolio should be $240, why not it should be $220, the point here is that at the beginning of period 2, the first share could be sold for $120 and there is an investment of $120 more, hence the portfolio value is $240. Also we should consider the dividend in this period for both the shares.

Step 3:Find out the holding period return of the periods
For Period 1:HPR = (120 – 100 + 2)/100 = 22%
For Period 2: HPR = (260 – 240 + 6)/240 = 10.83%

Step 4: Find out the geometric mean return or TWR from the holding period returns
(1 + TWR)^2 = (1+ HPR1)*(1+ HPR2)
=>(1 + TWR)^2 = (1.22) * (1.1083) = 1.3522
=>(1 + TWR) = 1.1628 => TWR = 0.1628
Or Time Weighted return is 16.28%
Is it always the case that Time Weighted return is less than money weighted return? Please note that this is not the case and we got into this situation for this problem only.

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Today's Question (Questions and answers provided by Knowledge Varsity)

Q3. An investor purchased one share of Goldman Sachs (NYSE:GS) at $100 at T = 0, he again purchased one more share of GS at $120 at T =1. He received total dividend of $2 at T= 1 and a dividend of $3 per share at T =2, the investor sold the shares at T=2 for a total consideration of $260 (or $130 per share). Find money weighted and time weighted return?
A. Money weighted = 14.4% ; Time weighted = 16.41%
B. Money weighted = 16.41% ; Time weighted = 14.4%
C. Money weighted = 14.4% ; Time weighted = 16.28%

Q4. A T bill having 120 days to maturity is yielding 3.5% on bank discount basis, how much will be its money market yield?
A. 3.5%
B. 3.54%
C. 3.4%

27-08-2012, 12:53 AM

Shubhojit

@Sir:- It's thumb rule to assume that the dividend is paid just before the period ends or we can hv some other assumptions as well ?? Also, why Time wt return is always less than Money wt return ?? Kindly explain the concept.

Regards,
Shubhojit.

27-08-2012, 12:59 AM

mahesh

Answer of Q-4 should be A.

@Prabir:-

Some of the common CAGR applications are :
a) Calculating and communicating the average returns of investment funds
b) Demonstrating and comparing the performance of investment advisors
c) Comparing the historical returns of stocks with bonds or with a savings account
d) Forecasting future values based on the CAGR of a data series (you find future values by multiplying the last datum of the series by (1 + CAGR) as many times as years required). As every forecasting method, this method has a calculation error associated.
e) Analyzing and communicating the behavior, over a series of years, of different business measures such as sales, market share, costs, customer satisfaction, and performance.