Understanding Types of Returns &
Time Value of Money Using Excel
July 2012
Annualized Returns
Annualized Return – It is a method of arriving at a comparable one-year return (annual return) for investments made for a
period of time other than a year
Computing Annualized Return
Sachin has invested in mutual funds over a period of time. He decides to sell off his investment on 31-Dec-2010; on that day the
value of his investment is as shown below:
Date
Purchase Cost
Market Value as on 31-Dec 2010
10-Dec-07
6000
8000
10-Apr-08
10000
12000
18-Jun-09
20000
19000
What is the annualized rate of return on his investment?
All figures mentioned in this presentation are for illustrative purpose, these figures does not indicates performance of scheme of DSP BlackRock Mutual Fund
2
Computing Annualized Return
Date
Purchase cost
Market Value
Return
Absolute Return
Date of sale
Holding period in days
Annualized Return
A
B
C
D
E
F
G
H
C-B
D/B*100
F-A
E*(365/G)
10-Dec-07
6000
8000
2000
33.33%
31-Dec-10
1117
10.89%
10-Apr-08
10000
12000
2000
20.00%
31-Dec-10
995
7.34%
18-Jun-09
20000
19000
-1000
-5.00%
31-Dec-10
561
-3.25%
To annualize, we multiply the absolute rate of return by a factor such as:
• 365/number of days the investment was held
• 12/number of months the investment was held
• 1/number of years the investment was held
All figures mentioned in this presentation are for illustrative purpose, these figures does not indicates performance of scheme of DSP BlackRock Mutual Fund
3
Yield or Return on Investment
It refers to the interest or dividends received from a security and is usually expressed annually as a percentage based on its market
value/purchase price.
Computing Dividend Yield
An equity share was bought for Rs 150. A dividend of 20% was declared on the face value of Rs 10 per share. What is the
return to the investor?
Face Value
10
Dividend on the equity Share
20%
Dividend on the equity Share (10*20%)
Purchase Price of equity share
2
150
Dividend Earned
2
Dividend yield or return on investment (2/150)*100
1.33%
All figures mentioned in this presentation are for illustrative purpose, these figures does not indicates performance of scheme of DSP BlackRock Mutual Fund
4
Total Return
Return can be earned both in the form of dividends and gain/loss on sale of investment. Total return captures the return
generated by an asset both from capital appreciation/loss and interest/dividend earned, if any.
Computing Total Return
Sunil bought an equity share whose face value is Rs 10 for Rs 200 and earned 30% dividend in year 1, 40% dividend in
year 2, and sold it off after three years for Rs 250. what is his return on investment?
Face Value
10
Year 1 dividend
30%
i.e. 30% of Rs 10
3
Year 2 dividend
40%
i.e. 40%*10
4
Purchase Price
200
Sold at
250
Profit from selling
50
Total return ( 3+4+50)
57
The rate of return percent per annum(57/200)*1/3*100
9.50%
Annualized return :1/number of years the investment was held
All figures mentioned in this presentation are for illustrative purpose, these figures does not indicates performance of scheme of DSP BlackRock Mutual Fund
5
Compounded Annual Growth Rate
Compound Annual Growth Rate (CAGR) - The year-over-year growth rate of an investment over a specified period of time.
Compounded return takes time value into account. It is an accepted standard for calculating returns for any period greater than a
year.
Assume that Rs 10,000 was invested in a mutual fund on 1st Jan 2010 and redeemed at Rs 13,000 on 1st Jan 2012 i.e. at the end of
2 years. What is the compounded rate of return?
We could say that Rs 10,000 grew at some compounded rate to become Rs 13,000 at the end of 2 years.
10000*(1+R)2 = 13000
R = (13000/10000)(1/2) - 1 = 14.02%
The above calculation may look very complicated, but we can use Microsoft Excel to do this in a very simple manner using XIRR
function
All figures mentioned in this presentation are for illustrative purpose, these figures does not indicates performance of scheme of DSP BlackRock Mutual Fund
6
XIRR
XIRR is used for computing CAGR for multiple cash flows. It calculates the internal rate of return of an investment where cash
flows may or may not be periodic in nature.
Let’s consider the previous example
Table 1
• Open MS excel and key in the data as shown in table 1. On
1st Jan 2010 there is an outflow of Rs 10,000 hence it is shown as
–ve and on 1st Jan 2012 the investment was redeemed, hence
there is an inflow of Rs 13,000.
• Go to Insert and select function option and select category
as Financial
Ignore the guess field. You don’t have to key in anything there
Note: The date field is mandatory for XIRR calculations
All figures mentioned in this presentation are for illustrative purpose, these figures does not indicates performance of scheme of DSP BlackRock Mutual Fund
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Computing XIRR
Computing XIRR
Anil buys an equity share on 18th Jan 2007 for Rs 200. He received a dividend of Rs 10 on 31st March 2008; Rs 8 on 2nd April
2009; Rs 12 on 31st March 2010; Rs 10 on 5th April 2011. He sells the share on 5th Jan 2012 at Rs 275.What is the CAGR of his
investment?
Date
Cash Flow
18-Jan-07
-200
31-Mar-08
10
02-Apr-09
8
31-Mar-10
12
05-Apr-11
10
05-Jan-12
275
XIRR
10.26%
All figures mentioned in this presentation are for illustrative purpose, these figures does not indicates performance of scheme of DSP BlackRock Mutual Fund
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Internal Rate of Return (IRR)
IRR calculates the internal rate of return where cash flows are periodic in nature.
Computing IRR
An investor has book an under construction property worth 50 lacs with an initial payment of Rs 10 lacs. The remaining 40 Lacs
has to be paid in 4 installments of Rs 10 lacs each for the next 4 years. At the end of the 5th year the investor sold it at Rs 75 lacs.
The cash flows are mentioned below. Calculate the return on investment.
Dates
Investment
01-Jan-2007
(1,000,000)
01-Jan-2008
(1,000,000)
01-Jan-2009
(1,000,000)
01-Jan-2010
(1,000,000)
01-Jan-2011
(1,000,000)
01-Jan-2012
7,500,000
IRR
13.83%
IRR is used when there is a periodic cash flow. Hence in the formula only the “values” are
considered as the cash flows are periodic.
All figures mentioned in this presentation are for illustrative purpose, these figures does not indicates performance of scheme of DSP BlackRock Mutual Fund
9
Weighted Average Portfolio Return
The expected return on a portfolio is the sum of weighted average of the expected return on individual securities in the
portfolio.
Computing expected return on portfolio
Asset Class
Expected Rate
Investment Amount
Weight
Expected Return of Portfolio
A
B
C
E= (A*C)
Equity MF
15%
270,000
0.23
3.49%
ELSS
15%
100,000
0.09
1.29%
Stocks
15%
200,000
0.17
2.59%
Liquid Funds
5%
300,000
0.26
1.29%
Bonds
7%
180,000
0.16
1.09%
Bank FD
7%
50,000
0.04
0.30%
Gold
10%
60,000
0.05
0.52%
1.00
10.57%
Total
1,160,000
Expected return of the portfolio is 10.57%
All figures mentioned in this presentation are for illustrative purpose, these figures does not indicates performance of scheme of DSP BlackRock Mutual Fund
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Understanding Time Value of Money through excel
Let’ understand few important terms used in excel.
FV: It is the future value, or a cash balance you want to have
after the last payment is made.
Rate is the interest rate per period. Interest is normally
given per annum. If it is quarterly we need to use rate percent/4
Nper: It is the total number of payment period in the investment
Pmt: It is the payment made in each period. It cannot change
over the life of the investment.
PV: It is the present value, or the lump-sum amount
that a series of payment is worth now
Type: Type is a value representing the timing of payment;
payment at the beginning of the period =1( e.g. SIP, premium);
payment at the end of the period =0 ( e.g. EMI of home loan).
If you don’t mention any thing then by default it will consider
payment made at end of period i.e.0
All figures mentioned in this presentation are for illustrative purpose, these figures does not indicates performance of scheme of DSP BlackRock Mutual Fund
11
Computing Future Value
If you invest Rs 5,000 today at a rate of 9% per annum, what will be its future value after 12 yrs?
PV
5000
Rate
9%
Tenor
12
FV
14,063
Type will play a role only when pmt is involved. In our
example we have to ignore it as no payment is involved.
If your yearly expenses is Rs 240,000 .How much amount would you require per month, 20 years hence to maintain the same
standard of living. Assuming inflation to be 7% p.a
PV
240,000
Rate
7%
Tenor
20
FV
Calculate?
All figures mentioned in this presentation are for illustrative purpose, these figures does not indicates performance of scheme of DSP BlackRock Mutual Fund
12
Computing PV
What is the present value of Rs 1,000,000 receivable 30 years from now, if the discount rate is 10%
FV
1000000
Rate
10%
Nper
30
PV
(57,309)
All figures mentioned in this presentation are for illustrative purpose, these figures does not indicates performance of scheme of DSP BlackRock Mutual Fund
13
Computing payment
Sheena is 3 years old. Her father wants to make a provision of Rs 30 lacs for her graduation. He wants the amount when she is
18 yrs old. You advise her father to start a systematic investment plan in a diversified equity mutual fund assuming it would give
12% as annual rate of return. How much should he invest every month?
Time to graduate ( yrs)
15
No of month
180
Rate of return per annum
12%
FV
3,000,000
PMT
(5,946)
In SIP the time of the payment is at the beginning of the term, hence “Type” is 1
All figures mentioned in this presentation are for illustrative purpose, these figures does not indicates performance of scheme of DSP BlackRock Mutual Fund
14
Computing payment
You have taken a home loan for Rs 3,843,000 for a period of 20 years and rate of interest is 8%. What will be your EMI?
PV
3,843,000
Nper
240
Rate of Interest
8%
Pmt
32,144
In home loan, EMI starts after 30 days from the date of disbursement of loan. Hence type is “0” signifying the payment is
made at the end of the period.
All figures mentioned in this presentation are for illustrative purpose, these figures does not indicates performance of scheme of DSP BlackRock Mutual Fund
15
Computing “rate” using excel
A finance company advertised that it will pay a lump sum of Rs 44,650 at the end of 5 years to investors who deposit Rs 6000
annually for 5 years. What is the rate implicit in this offer?
FV
44650
Pmt
-6000
Nper
5
Rate
20%
All figures mentioned in this presentation are for illustrative purpose, these figures does not indicates performance of scheme of DSP BlackRock Mutual Fund
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Snapshot
Terms
What they mean?
Annualized Returns
It is a comparable one year return on an investment made for any period, other
than a year
Yield
It is the income generated by an asset divided by the market price of the asset or
the purchase price of the asset
Total Return
It captures the return generated by an asset from both capital appreciation/loss and
interest/dividend earned, if any
CAGR
It is the year-over-year growth rate of an investment for any period greater than a
year.
XIRR
It’s the internal rate of return for a series of cash flows that may or may not be
periodic in nature
IRR
Expected Portfolio Return
Time Value of Money
It’s the internal rate of return for a series of cash flows that are periodic in nature
It is the sum of weighted average of the expected return on individual securities in
the portfolio
It tells you the present value of future income/payments discounted at a particular
rate. It can also be used to compute the future value of cash flows based on a rate
of interest.
Case Study-1
Mr. Bade Miyan aged 40 and his wife Hina aged 38 are living in Mumbai for the last 10 years. They have 2 children Rohan
(7) and Arti (4). Both of them are studying in school. His take home salary is Rs. 45,000 p.m. He has found out that his
monthly expense is Rs. 22,000. He pays his home loan EMI every month. He had bought a 2 BHK flat when he came to
Mumbai 10 years back. They have taken a home loan of Rs. 6,00,000 for which he pays an EMI of Rs. 5,000. He wants to
buy a car worth Rs. 8,00,000 today, at the time of his retirement.
His current portfolio comprises of the following:
He has a life insurance policy with a sum assured of Rs. 7,00,000. He has sufficient health insurance for his family and
himself. He wants to build a retirement corpus and they have a life expectancy of 75 years.
Questions
1. He would like to send his children to an overseas university when they reach 21 years of age. He estimates that in today’s value the education fund for one
child required is Rs. 8,00,000. He assumes that the inflation rate is 10% and the rate of return on his investment is 12%. Calculate how much education fund is
required for the university education when his child reaches 21 years of age.
2. Mr. Bade Miyan purchased a flat of Rs. 15,00,000. He expects the property to appreciate by average rate of 12% p.a. compounded annually. He wants to
sell the property for Rs. 20,00,000. How long in years he has to wait before the flat is worth Rs. 20,00,000.
3. Mr. Bade Miyan is planning to retire at the age of 60 years. His life expectancy is 85 years. He wants to have a corpus so as to be able to withdraw Rs.
1,00,000 from the account at the beginning of the year after his retirement till age 85. He also wants to have a corpus of Rs. 20,00,000 left in the account at the
time of his expected death. He plans to accumulate the corpus by making annual contributions for the next 20 years. He expects to earn 12% p.a. before his
retirement and 8% p.a. post his retirement. He will put his investments in safe instruments. What equal annual deposits should he make each year to reach his
retirement goal? Inflation is taken as 5%.
All figures mentioned in this presentation are for illustrative purpose, these figures does not indicates performance of scheme of DSP BlackRock Mutual Fund
18
Case Study 2
Mr. Aspiring (35) is into business of textile garments. His family includes his wife (30) & a son (5). Till now he has
invested all his business profits into business working capital & purchasing a flat, where he is living. He is now
seeking advice to invest his yearly savings of about Rs. 12 Lakhs into various assets other than business, which will
enable him to meet his financial goals in life. After understanding his financial goals you have proposed the below
investment portfolio
Asset Class
Annual Investments (Lakh RS.)
Expected Rate of return
2.7
15%
ELSS
1
15%
Stocks
2
15%
Liquid Funds
3
5%
Bonds
1.8
7%
Bank FD
0.5
7%
Gold
0.6
10%
Medi Claim
0.05
-
Life Insurance
0.35
-
Equity MF
Net Annual Investments
12
Questions
1. If Aspiring invests as per the advised portfolio what will be the average annual returns of the portfolio at the end of the 10th year? (Consider investments of
the first year only for this purpose)
All figures mentioned in this presentation are for illustrative purpose, these figures does not indicates performance of scheme of DSP BlackRock Mutual Fund
Case Study 2
2. Aspiring is considering the following investment projects:
Cash Flows
Projects
C0
C1
C2
C3
1
-10,000
+10,000
NIL
NIL
2
-10,000
+7,500
+7,500
NIL
3
-10,000
+2,000
+4,000
+12,000
4
-10,000
+10,000
+3,000
+3,000
Assuming the projects are independent and mutually exclusive, advice Aspiring which project he should opt for on the basis of
IRR.
All figures mentioned in this presentation are for illustrative purpose, these figures does not indicates performance of scheme of DSP BlackRock Mutual Fund
Disclaimer
This presentation shall not constitute any offer to sell or solicitation of an offer to buy units of any of the Schemes of the
DSP BlackRock Mutual Fund
All figures mentioned in this presentation are for illustrative purpose, these figures does not indicates performance of
scheme of DSP BlackRock Mutual Fund
Mutual Fund investments are subject to market risks, read all scheme related documents carefully.