CHAPTER 3 SECURITIES MARKET
1. Consider the data for a sample of 4 shares for two years, the base year and year t
Share
A
B
C
D
Price in
base year
Rs.
50
100
30
60
Price in
year t
Rs.
80
150
24
75
Number of
outstanding
shares (in million)
4
6
8
12
(i)
What is the equal weighted index for year t?
(ii)
What is the value weighted index for year t?
CHAPTER 4 RISK AND RETURN
1.The probability distribution of the rate of return on Intech Limited is as follows :
Rate of Return
Probability
10%
0.3
20%
0.5
30%
0.2
(i) What is the expected rate of return?
(ii) What is the standard deviation of the rate of return?
2. The probability distribution of the rate of return on BDM Limited is as follows:
(i)
(ii)
Rate of Return
Probability
10 %
15 %
20 %
0.3
0.3
0.4
What is the expected rate of return?
What is the standard deviation of the return?
3. The probability distribution of the rate of return on Sintech Limited is as follows:
Rate of Return
10%
20%
30%
Probability
0.2
0.3
0.5
(i) What is the expected rate of return?
(ii) What is the standard deviation of the rate of return?
4. The probability distribution of the rate of return on ABM Limited is as follows:
Rate of Return
Probability
5%
0.2
10%
0.5
15%
0.3
(i) What is the expected rate of return?
(ii) What is the standard deviation of the return?
CHAPTER 5 TIME VALUE OF MONEY
1. Your firm borrows Rs.2, 000,000 at an interest rate of 12 percent per year and the
loan is to be repaid in 5 equal annual instalments payable at the end of each of the
next 5 years.
(i) What is the annual instalment payable?
(ii) What proportion of the instalment payable at the end of year 3, represents the
principal repayment portion?
2. Your firm borrows Rs.3, 000,000 at an interest rate of 11% per year and the loan is
to be repaid in 5 equal instalments payable at the end of each of the next 5 years.
(i) What is the annual instalment payable?
(ii) What proportion of the instalment payable at the end of year 3, represents the
principal repayment portion?
3. Your firm borrows Rs.4, 000,000 at an interest rate of 12% per year and the loan is
to be repaid in 5 equal instalments payable at the end of each of the next 5 years.
(i) What is the annual instalment payable?
(ii) What proportion of the instalment payable at the end of year 3, represents the
principal repayment portion?
4. Your firm borrows Rs.5, 000,000 at an interest rate of 13% per year and the loan is
to be repaid in 5 equal instalments payable at the end of each of the next 5 years.
(i) What is the annual instalment payable?
(ii) What proportion of the instalment payable at the end of year 3, represents the
principal repayment portion ?
5. As an investment advisor, you have been approached by a client called Nitin for
advice on some financial matters. Nitin is 30 years old and has Rs.1, 000,000 in bank.
He plans to work for 25 years more and retire at the age of 55. His present salary is
Rs.1,200,000 per year. He expects his salary to increase at the rate of 10 percent per
year until his retirement.
Nitin has decided to invest his bank balance and future savings in a balanced
mutual fund scheme which he believes will provide a return of 10 percent per
year.
(i)
(ii)
Nitin seeks your help in answering several questions given below. In answering
these questions, ignore the tax factor.
Once he retires at the age of 55, he would like to withdraw Rs. 3,000,000 per year
for his consumption needs for the following 20 years (his life expectancy is 75
years). Each annual withdrawal will be made at the beginning of the year. How
much should be the value of his investments when he reaches the age of 55, to
meet his retirement need?
How much should Nitin save each year for the next 25 years to be able to
withdraw Rs.3,000,000 per year from the beginning of the 26th year for a period of
20 years? Assume that the savings will occur at the end of each year. Remember
that he already has some bank balance.
(iii) Suppose Nitin wants to donate Rs.800,000 per year in the last 5 years of his life to
a charitable cause. Each donation would be made at the beginning of the year.
Further, he wants to bequeath Rs.9,000,000 to his son at the end of his life. How
much should he have in his investment account when he reaches the age of 55 to
meet this need for donating and bequeathing? Approximate it to the nearest ‘000.
(iv) Nitin wants to find out the present value of his lifetime salary income. For the sake
of simplicity, assume that his current salary of Rs. 1,200,000 will be paid exactly a
year from now, and his salary is paid annually. What is the present value of his life
time salary income, if the discount rate applicable to the same is 13 percent?
Remember that Nitin expects his salary to increase at the rate of 10 percent per
year until retirement.
6.
As an investment advisor, you have been approached by a client called Sathya for
advice on some financial matters. Sathya is 40 years old and has Rs.3, 000,000 in
bank. He plans to work for 20 years more and retire at the age of 60. His present
salary is Rs.1, 800,000 per year. He expects his salary to increase at the rate of 15
percent per year until his retirement.
Sathya has decided to invest his bank balance and future savings in a balanced
mutual fund scheme which he believes will provide a return of 12 percent per
year.
Sathya seeks your help in answering several questions given below. In answering
these questions, ignore the tax factor.
(i)
Once he retires at the age of 60, he would like to withdraw Rs. 5,000,000 per
year for his consumption needs for the following 20 years (his life expectancy
is 80 years). Each annual withdrawal will be made at the beginning of the
year. How much should be the value of his investments when he reaches the
age of 60, to meet his retirement need?
(ii) How much should Sathya save each year for the next 20 years to be able to
withdraw Rs.5, 000,000 per year from the beginning of the 21st year for a
period of 20 years? Assume that the savings will occur at the end of each
year. Remember that he already has some bank balance. Give the answer to
the nearest ‘000.
(iii) Suppose Sathya wants to donate Rs.1,000,000 per year in the last 5 years of
his life to a charitable cause. Each donation would be made at the beginning
of the year. Further, he wants to bequeath Rs.10,000,000 to his son at the
end of his life. How much should he have in his investment account when he
reaches the age of 60 to meet this need for donating and bequeathing?
Approximate it to the nearest ‘000.
(iv) Sathya wants to find out the present value of his lifetime salary income. For
the sake of simplicity, assume that his current salary of Rs. 1,800,000 will be
paid exactly a year from now, and his salary is paid annually. What is the
present value of his life time salary income, if the discount rate applicable to
the same is 10 percent? Remember that Sathya expects his salary to increase
at the rate of 15 percent per year until retirement.
7.
Sunil Prabhu, a 35 years old software engineer, has approached you for advice on
his investments. He has Rs. 300,000 in a bank account. He plans to work for
another 25 years and retire at the age of 60. His present salary is Rs. 1,800,000 per
year. He expects his salary to increase at the rate of 20 percent per year until his
retirement.
Sunil has decided to invest his bank balance and future savings in a mix of
assets which he believes will provide a return of 10 percent per year.
Sunil seeks your help in answering the questions given below. In answering
these questions, ignore the tax factor. You may assume that the salary is paid in
one lumpsum at the end of each year.
(i)
Once he retires at the age of 60, he would like to withdraw Rs. 2,000,000 per
year for his consumption needs for the following 15 years (being of sound
health, his life expectancy is 75 years). Each annual withdrawal will be made
at the beginning of the year. How much should be the value of his
investments when he reaches the age of 60, to meet his retirement need?
(ii)
How much should Sunil save each year for the next 25 years to be able to
withdraw Rs. 2,000,000 per year from the beginning of the 26 th year for a
period of 15 years? Assume that the savings will occur at the end of each
year. Remember that Sunil already has some bank balance. Give the answer
to the nearest ‘000.
(iii) Suppose Sunil wants to give a donation of Rs. 600,000 per year for the last 5
years of his life to a charitable cause. Each donation would be made at the
end of the year. Further, he wants to bequeath Rs. 10,000,000 to his
offspring at the end of his life. How much should he have in his investment
account when he reaches the age of 60 to meet his need for donation and
bequeathing? Give the answer to the nearest ‘000.
(iv) Sunil wants to find out the present value of his lifetime salary income. For
the sake of simplicity, assume that his current salary of Rs. 1,800,000 will be
paid exactly a year from now, and his salary is paid annually. What is the
present value of his life-time salary income, if the discount rate applicable to
the same is 12 percent? Remember that Sunil expects his salary to increase
at the rate of 20 percent per year until retirement.
8.
You have been approached by a client called Edward for advice on his investments.
Edward is 25 years old and has Rs. 200,000 in a bank account. He plans to work for
30 years and retire at the age of 55. His present salary is Rs. 600,000 per year. He
expects his salary to increase at the rate of 15 percent per year until his
retirement.
Edward has decided to invest his bank balance and future savings in a mix of
assets which he believes will provide a return of 9 percent per year.
Edward seeks your help in answering the questions given below. In answering
these questions, ignore the tax factor. You may assume that the salary is paid in
one lumpsum at the end of each year.
(i)
Once he retires at the age of 55, he would like to withdraw Rs. 1,200,000 per
year for his consumption needs for the following 20 years (being of sound
health, his life expectancy is 75 years). Each annual withdrawal will be made
at the beginning of the year. How much should be the value of his
investments when he reaches the age of 55, to meet his retirement need?
(ii)
How much should Edward save each year for the next 30 years to be able to
withdraw Rs. 1,200,000 per year from the beginning of the 31 st year for a
period of 20 years? Assume that the savings will occur at the end of each
year. Remember that Edward already has some bank balance. Give the
answer to the nearest ‘000.
(iii) Suppose Edward wants to give a donation of Rs. 400,000 per year for the last
4 years of his life to a charitable cause. Each donation would be made at the
end of the year. Further, he wants to bequeath Rs. 5,000,000 to his widowed
daughter at the end of his life. How much should he have in his investment
account when he reaches the age of 55 to meet his need for donation and
bequeathing? Give the answer to the nearest ‘000.
(iv) Edward wants to find out the present value of his lifetime salary income. For
the sake of simplicity, assume that his current salary of Rs. 600,000 will be
paid exactly a year from now, and his salary is paid annually. What is the
present value of his life-time salary income, if the discount rate applicable to
the same is 10 percent? Remember that Edward expects his salary to
increase at the rate of 15 percent per year until retirement.
CHAPTER 6 FINANCIAL STATEMENT ANALYSIS
1. Determine the sales of a firm given the following information:
Current ratio
= 1.5
Acid-test ratio
= 1.3
Current liabilities
= 12,000
Inventory turnover ratio
= 5
2. Determine the sales of a firm, given the following information:
Current ratio
= 2
Acid-test ratio
= 1.2
Current liabilities
= 15,000
Inventory turnover ratio
= 6
3. Determine the sales of a firm, given the following information:
Current ratio
= 1.2
Acid-test ratio
= 0.9
Current liabilities
= 10,000
Inventory turnover ratio
= 4
4. Determine the sales of a firm given the following information:
Current ratio
Acid-test ratio
Current liabilities
Inventory turnover
=
=
=
=
2.5
1.7
25,000
7
5. The summarized Profit and Loss Account and Balance Sheet of the Great Eastern
Shipping Company Limited are given below:
Profit and Loss Account for the Year Ended March 31, 2003
 Total revenue
10156
 Operating profit (PBIT)
4527
 Interest and finance charges
390
 Depreciation
1680
 PBT
2457
 Provision for tax
292
 PAT
2165
Balance Sheet as at March 31,2003
Sources of Funds
Shareholder’s funds
12496
Loan funds
10208
Deferred tax liability
1274
23978
Application of Funds
Fixed assets
18226
Investments
1949
Current assets, loans, and advances 5928
Inventories : 537
Other
: 5391
Current liabilities and provisions
2234
Net current assets
3694
Miscellaneous expenditure
109
23978
The paid up capital of the Great Eastern Shipping Company as at March 31,2003 is
Rs.2653 million( Par value per share is Rs.10). Assume that all of it is equity.
The market price per share on March 31,2003 was Rs.54
Fill in the values below. Regard deferred tax liability as part of debt.
Fill in the values below.






.
Net profit margin
Asset turnover ratio
Financial leverage multiplier
Return on equity
Interest coverage ratio
Price – earnings ratio
Market to book ratio
-------------------------------------------------------------------------------------
Please note that in 2003, the required formats of balance sheet and profit and
loss account statement were as above.
6. The summarised Profit and Loss Account and Balance Sheet of Tata Iron and Steel
Company Limited are given below:
Profit and Loss Account for the Year Ended March 31, 2004
Rs. in million
 Total revenue
108430
 Profit before interest taxes
34130
 Interest and finance charges
1220
 Depreciation
6250
 PBT
26660
 Provision for tax
9200
 PAT
17460
Balance Sheet as at March 31, 2004
Sources of Funds
Shareholders’ funds
45160
Loan funds
33730
Deferred tax liability
8400
Other provisions
15630
102920
Application of Funds
Fixed assets
Investments
Current assets, loans, and advances
Inventories : 12490
Other
: 28340
Current liabilities and provisions
Net current assets
Miscellaneous expenditure
78580
21940
40830
39990
840
1560
102920
The paid up capital of the Tata Steel as at March 31,2004 is Rs.3680 million (Par value
per share is Rs.10). Assume that all of it is equity. The market price per share on March
31,2004 was Rs.383.50
Fill in the values below.
 Net profit margin
------------ Asset turnover ratio
------------ Financial leverage multiplier
------------ Return on equity
------------ Interest coverage ratio
------------ Price – earnings ratio
------------.
Market to book ratio
------------Please note that in 2004, the required formats of balance sheet and profit and
loss account statement were as above.
7. The Summarised Profit and Loss Account and Balance Sheet of Infosys Technologies
Limited are given below:
Profit and Loss Account for the Year Ended March 31, 2005
Rs. in million
 Total revenue
68596
 Gross profit
32047
 Profit before interest & taxes
22296
 Interest and finance charges
 PBT
22296
 Provision for taxation
3253
 PAT
19043
Balance Sheet as at March 31, 2005
Sources of Funds
Shareholders’ funds
52417
52417
Application of Funds
Fixed assets
Investments
Deferred Tax assets
Current assets, loans, and advances
Sundry debtors
: 12528
Cash and bank
: 14815
Loan and advances : 9962
Current liabilities and provisions
Net current assets
14944
13287
340
37305
13459
23846
52417
The paid up capital of Infosys as at March 31, 2005 is Rs.1353 (Par value per share is
Rs.5). Assume that all of it is equity. The market price per share on March 31, 2005 was
Rs.2252.52
Fill in the values below.
 Net profit margin
……………………..
 Asset turnover ratio
…..…..……………..
 Financial leverage multiplier
…..…..……………..
 Return on equity
……....……………..
 Interest coverage ratio
…………………..
 Price – earnings ratio
…….………………..
 Market value to book value ratio
……….……………..
Please note that in 2005, the required formats of balance sheet and profit and
loss account statement were as above.
8. The Summarised Profit and Loss Account and Balance Sheet of Reliance Industries
Limited are given below:
Profit and Loss Account for the Year Ended March 31, 2005
Rs. in million
 Total revenue
669,768
 Gross profit
142,609
 Profit before interest & taxes
105,374
 Interest and finance charges
14,687
 PBT
90,687
 Provision for taxation
14,970
 PAT
75,717
Balance Sheet as at March 31, 2005
Sources of Funds
Shareholders’ funds
404,033
Loan funds
187,846
Deferred tax liability
42,668
634,547
Application of Funds
Fixed assets
Investments
Current assets, loans, and advances
Sundry debtors
: 39,278
Inventories
: 74,129
Cash and bank balances: 36,088
Other current assets
: 20,877
Loans and advances
: 114,153
Current liabilities and provisions
Net current assets
350,822
170,515
284,525
171,315
113,210
634,547
The paid up capital of Reliance Industries Ltd as at March 31,2005 is Rs.13,931 million
(par value per share is Rs.10). Assume that all of it is equity. The market price per share
as on March 31,2005 is Rs.546.05
Fill in the values below.
 Net profit margin
 Asset turnover ratio
 Financial leverage multiplier
 Return on equity
 Interest coverage ratio
 Price – earnings ratio
 Market value to book value ratio
Please note that in 2005, the required formats of balance sheet and
profit and loss account statement were as above.
9. Complete the balance sheet and sales data (fill in the blanks) using the following
financial data. Consider an year to consist of 360 days.
Debt-equity ratio
Acid-test ratio
Total asset turnover
Days’ sales outstanding in accounts receivable
Gross profit margin
Inventory turnover ratio
:
:
:
:
:
:
0.6
0.5
2
13.5 days
37.5 percent
5
Balance Sheet
Equity capital
150,000 Fixed assets
----------
Retained earnings
100,000 Inventories
----------
Long-term debt
70,000 Accounts receivable
----------
Short-term debt
---------- Cash
----------
----------
----------
Profit & Loss
Sales
----------
Cost of goods sold
----------
10. Complete the balance sheet and sales data (fill in the blanks) using the following
financial data.
Debt-equity ratio
Acid-test ratio
Total asset turnover
Days’ sales outstanding in accounts receivable
Gross profit margin
Inventory turnover ratio
:
:
:
:
:
:
0.5
1.0
1.2
30 days
20 percent
4
Balance Sheet
Equity capital
100,000 Fixed assets
----------
Retained earnings
200,000 Inventories
----------
Long-term debt
100,000 Accounts receivable
----------
Short-term debt
---------- Cash
----------
----------
----------
Profit & Loss
Sales
----------
Cost of goods sold
----------
Please note that earlier, the formats of balance sheet and profit and loss
account statement were as above.
11. The following ratios are given for Cintex Company
Net profit margin
:
Current ratio
:
Return on net worth
:
Total debt to total assets ratio
Inventory turnover ratio
:
Complete the following statements
7 percent
2
17 percent
:
0.50
15
Marks: 7
Profit and Loss Account
Sales
…………..
Cost of goods sold
…………..
Operating expenses
800
EBIT
…………..
Interest (12 percent)
60
Profit before tax
…………..
Tax provision(30 percent) ………….
Profit after tax
…………..
Balance Sheet
Net worth
Debt
………… Fixed assets
………
………… Current assets
250
Cash
……
Receivables 40
Inventory …...
Current liabilities …….
Net current assets
……….
……….
……….
Please note that earlier, the formats of balance sheet and profit and loss
account statement were as above.
12. The following ratios are given for Axel Limited
Net profit margin
:
Current ratio
:
Return on net worth
:
Total debt to assets ratio
:
Inventory turnover ratio
:
Complete the following statements
8 percent
1.5
18 percent
0.50
16
Profit and Loss Account
Sales
…………..
Cost of goods sold
…………..
Operating expenses
900
EBIT
…………..
Interest (14 percent)
70
Profit before tax
…………..
Tax provision (30 percent) ………….
Profit after tax
…………..
Balance Sheet
Net worth
Debt
…………
…………
……….
Fixed assets
Current assets
Cash
Receivables
Inventory
Current liabilities
Net current assets
………
300
……
50
…...
…….
……….
……….
Please note that earlier, the formats of balance sheet and profit and loss
account statement were as above.
13. The following ratios are given for Syntel Limited
Net profit margin
:
3 percent
Current ratio
:
1.5
Return on net worth
:
25 percent
Total debt to assets ratio
:
0.70
Inventory turnover ratio
:
16
Complete the following statements
Profit and Loss Account
Sales
----------
Cost of goods sold
----------
Operating expenses
1200
EBIT
----------
Interest (16 percent)
80
Profit before tax
----------
Tax provision (30 percent)
----------
Profit after tax
---------Balance Sheet
Net worth
Debt
-------------------
----------
Fixed assets
Current assets
Cash
Receivables
Inventory
Current liability
Net current asset
---------500
---------60
-------------------------------------
Please note that earlier, the formats of balance sheet and profit and loss
account statement were as above.
14. The following ratios are given for Cemex Limited.
Net profit margin
:
8 percent
Current ratio
:
1.5
Return on net worth
:
20 percent
Total debt to total assets ratio
:
0.40
Inventory turnover ratio
:
15
Complete the following statements
Profit and Loss Account
Sales
Cost of goods sold
Operating expenses
EBIT
Interest (12 percent)
Profit before tax
Tax provision (30 percent)
Profit after tax
------------------1200
---------84
----------------------------
Balance Sheet
Net worth
Debt
---------_----------
----------
Fixed assets
Current assets
Cash
Receivables
Inventory
Current liabilities
Net current assets
---------600
---------80
-------------------------------------
Please note that earlier, the formats of balance sheet and profit and loss
account statement were as above.
15. The financial statements* of Infosys and Reliance Industries are given below:
Profit and Loss Account (Rs. in crores)
Infosys
For year ending
31-3-08 31-3-07
Net sales/income
15,648
13,149
Cost of goods sold/Software
8,876
7,278
development expenses
Gross profit
6,772
5,871
Operating expenses
2,355
2,115
Operating profit
4,417
3,756
Non-operating surplus
683
379
Profit before interest and tax
5,100
4,135
Interest
Profit before tax
5,100
4,135
Tax/Provision for tax
630
352
Profit after tax
4,470
3,783
As on
Balance Sheet (Rs. in crores)
Infosys
31-3-08
31-3-07
Liabilities & Equity
Share capital
Reserves & surplus
Loan funds
Deferred tax liabilities**
Assets
Net fixed assets
Investments
Deferred tax assets
Current assets, loans & advances
Inventories
Receivables
Cash & bank balance
Other current assets
Loans & advances
Less:
Current liabilities & provisions
Net current assets
*
286
13,204
286
10,876
13,490
11,162
3,931
964
99
3,107
839
79
3,093
6,429
2,292
5,470
2,705
3,731
8,496
13,490
Reliance Industries
31-3-08
31-3-07
133,443
111,693
104,197
85,876
29,246
10,787
18,459
5,629
24,088
1,077
23,011
3,552
19,459
25,817
10,586
15,231
478
15,709
1,189
14,520
2,577
11,943
Reliance Industries
31-3-08
31-3-07
3,136
78,313
36,480
7,873
125,802
1,453
62,514
27,826
6,982
98,775
84,889
22,064
71,189
16,251
1,199
14,248
6,228
4,280
73
18,058
12,137
3,732
1,835
3
12,206
1,824
7,137
11,162
24,038
18,849
125,802
18,578
11,335
98,775
The statements are based on the published annual reports of these companies. Items
**
have been suitably regrouped for analytical purposes.
Treat this as loan funds for analysis.
a. Prepare the Dupont chart for Reliance Industries and Infosys for the year ended on
31st March 2008.
2) Prepare the common size Balance Sheet and Profit and Loss Account for Reliance
Industries and Infosys for the years 2007 and 2008.
Please note that earlier, the formats of balance sheet and profit and loss
account statement were as above.
CHAPTER 7 PORTFOLIO THEORY
1. Consider two stocks, M and N
Stock M
Stock N
Expected
return
16%
18%
Standard
deviation
25%
40%
The returns of the two stocks are perfectly correlated. What is the expected return
of a portfolio constructed to drive the standard deviation of portfolio return to zero?
CHAPTER 8 CAPITAL ASSET PRICING MODEL AND ARBITRAGE PRICING MODEL
1.
The following table gives an analyst’s expected return on two stocks for
particular market returns.
Market Return
10 %
15 %
Aggressive Stock
15 %
25 %
Defensive Stock
11 %
15 %
(i)
What is the ratio of the beta of the aggressive stock to the beta of the defensive
stock?
(ii)
If the risk-free rate is 6 % and the probabilities that the market return would turn
out to be 10 % and 15 % are 0.2 and 0.8 respectively, what is the market risk
premium?
(iii)
What is the alpha of the defensive stock?
2.
The following table gives an analyst’s expected return on two stocks for
particular market returns.
Market Return
6%
20 %
Aggressive Stock
8 %
50 %
Defensive Stock
15 %
25 %
(i)
What is the ratio of the beta of the aggressive stock to the beta of the
defensive stock?
(ii)
If the risk-free rate is 4 % and the probabilities that the market return
would turn out to be 6 % and 20 % are 0.7 and 0.3 respectively, what is the
market risk premium?
(iii)
What is the alpha of the defensive stock?
3.
The following table gives an analyst’s expected return on two stocks for particular
market returns.
Market Return
8%
35 %
4.
Aggressive Stock
-8%
60 %
Defensive Stock
10 %
20 %
(i)
What is the ratio of the beta of the aggressive stock to the beta of the
defensive stock?
(ii)
If the risk-free rate is 10% and the probabilities that the market return
would turn out to be 8% and 35% are 0.4 and 0.6 respectively, what is the
market risk premium?
(iii)
What is the alpha of the defensive stock?
The following table gives an analyst’s expected return on two stocks for particular
market returns.
Market Return
5%
40 %
Aggressive Stock
-6%
70 %
Defensive Stock
8%
25 %
(i)
What is the ratio of the beta of the aggressive stock to the beta of the
defensive stock?
(ii)
If the risk-free rate is 7 % and the probability that the market return is
likely to be 5 % and 40 % is 7:3, what is the market risk premium?
(iii)
What is the alpha of the defensive stock?
5.
The rate of return on the stock of Alpha Technologies and on the market
portfolio for a period of 5 years has been as follows:
Year
1
2
3
4
5
Return on the stock of
Alpha Technologies (%)
36
24
-20
46
50
Return on the market
portfolio (%)
28
20
-8
52
36
What is the beta for the stock of Alpha Technologies (labelled as A, hereafter)?
CHAPTER 11 BOND PRICES AND YIELDS
1. A Rs.100 par bond carrying a coupon rate of 10 percent and maturing after 4
years is selling for Rs. 102.
(i)
What is the approximate YTM?
(ii) What will be the realised yield to maturity if the reinvestment rate is 8
percent?
2.
A Rs. 1,000 par bond carrying a coupon rate of 8 percent and maturing after 8
years is selling for Rs. 1,100.
(i)
What is the approximate YTM?
(ii) What will be the realised yield to maturity, if the reinvestment rate is 9
percent?
3
A Rs. 1,000 par bond carrying a coupon rate of 12 percent and maturing after 5
years is selling for Rs. 1,080.
(i)
What is the approximate YTM?
(ii) What will be the realised yield to maturity, if the reinvestment rate is 9
percent?
4.
Consider the following data for government securities:
Face value
Rs. 100,000
Rs. 100,000
Rs. 100,000
Interest rate
0
4%
5%
What is the forward rate for year 3(r3)?
Maturity (years)
1
2
3
Current price
Rs 93,800
Rs 95,000
Rs 97,000
5.
Consider the following data for government securities:
Face value
Rs. 100,000
Rs. 100,000
Rs. 100,000
Interest rate
0
5%
6%
Maturity (years)
1
2
3
Current price
94,000
96,500
97,000
What is the forward rate for year 3(r3)?
6.
Consider the following data for government securities:
Face value
Rs. 100,000
Rs. 100,000
Rs. 100,000
Interest rate
0
5%
6%
Maturity (years)
1
2
3
Current price
94,000
96,500
97,000
What is the forward rate for year 3(r3)?
7.
Consider the following data for government securities:
Face value
Rs. 100,000
Rs. 100,000
Rs. 100,000
Interest rate
0
6%
7%
What is the forward rate for year 3(r3)?
Maturity (years)
1
2
3
Current price
95,400
98,800
97,000
CHAPTER 12 BOND PORTFOLIO MANAGEMENT
1.
A Rs.100 par bond carrying a coupon rate of 10 percent and maturing after 4 years
is selling for Rs. 100. What is the duration of the bond?
2.
A Rs.1, 000 par bond carrying a coupon rate of 8 percent and maturing after 8
years is selling at par.
What is the duration of the bond?
3.
A Rs. 1,000 par bond carrying a coupon rate of 12 percent and maturing after 5
years is selling for Rs. 1,080.
(i)
What is the approximate YTM?
(ii)
What is the duration of the bond?
calculating the yield to maturity.
Use the approximate formula for
(iii) Now, assume that the market price of the above bond is Rs. 1,000. What is
the duration of the bond?
CHAPTER 13 EQUITY VALUATION
1.
The current dividend on an equity share of Sonata Limited is Rs. 6.00 on an earnings
per share of Rs. 24.00.
(i)
Assume that the dividend per share will grow at the rate of 18 percent per
year for the next 6 years. Thereafter, the growth rate is expected to fall and
stabilise at 10 percent. Investors require a return of 14 percent from Sonata’s
equity shares. What is the intrinsic value of Sonata’s equity share?
(ii)
Assume that the growth rate of 18 percent will decline linearly over a 6 year
period and then stabilise at 10 percent. What is the intrinsic value of
Sonata’s share if the investors’ required rate of return is 14 percent?
(iii) Assume that the dividend is expected to grow at a rate of 12 percent
annually forever from now on and investors require a return of 14 percent
from Sonata’s equity shares. What will be the retrospective price-earnings
ratio for Sonata?
2.
The current dividend on an equity share of Zipro Limited is Rs.12.00 on an earnings
per share of Rs. 60.00.
(i)
Assume that the dividend per share will grow at the rate of 25 percent per
year for the next 6 years. Thereafter, the growth rate is expected to fall and
stabilise at 15 percent. Investors require a return of 18 percent from Zipro’s
equity shares. What is the intrinsic value of Zipro’s equity share?
(ii)
Assume that the growth rate of 25 percent will decline linearly over a six year
period and then stabilise at 15 percent. What is the intrinsic value of
Omega’s share if the investors’ required rate of return is 18 percent?
(iii) Assume that the dividend is expected to grow at a rate of 16 percent
annually forever from now on and investors require a return of 18 percent
from Zipro’s equity shares. What will be the retrospective price-earnings
ratio (Po/Eo) for Zipro?
3.
The current dividend on an equity share of Hero Limited is Rs. 15 on an earnings
per share of Rs. 70.00.
(i)
Assume that the dividend per share will grow at the rate of 20 percent per
year for the next 4 years. Thereafter, the growth rate is expected to fall and
stabilise at 10 percent. Investors require a return of 18 percent from Hero’s
equity shares. What is the intrinsic value of Hero’s equity share?
(ii) Assume that the growth rate of 20 percent will decline linearly over a 4 year
period and then stabilise at 10 percent. What is the intrinsic value of Hero’s
share if the investors’ required rate of return is 18 percent?
(iii) Assume that the dividend is expected to grow at a rate of 14 percent
annually forever from now on and investors require a return of 18 percent
from Hero’s equity shares. What will be the retrospective price-earnings
ratio for Hero?
4.
The current dividend on an equity share of Merryl Limited is Rs. 11.00 on an
earnings per share of Rs. 40.00.
(i)
Assume that the dividend per share will grow at the rate of 18 percent per
year for the next 6 years. Thereafter, the growth rate is expected to fall and
stabilise at 12 percent. Investors require a return of 14 percent from Merryl’s
equity shares. What is the intrinsic value of Merryl’s equity share?
(ii)
Assume that the growth rate of 18 percent will decline linearly over a 6 year
period and then stabilise at 12 percent. What is the intrinsic value of
Merryl’s share if the investors’ required rate of return is 14 percent?
(iii) Assume that the dividend is expected to grow at a rate of 11 percent
annually forever from now on and investors require a return of 14 percent
from Merryl’s equity shares. What will be the retrospective price-earnings
ratio for Merryl?
CHAPTER 15 COMPANY ANALYSIS
1. The income statement and balance sheet of Vijay Corporation for the years 20X7
and 20X8 are given below.
Income Statement
 Net sales
20X7
80,000
 PBIT
15,000
 Interest
 PBT
 Tax
 PAT
 Dividends
2,000
13,000
3,900
9,100
2,200
Balance Sheet
20X8
90,000  Equity capital
(Rs.10 par)
18,000  Reserves and
surplus
2,500  Loan funds
15,500
4,650  Net fixed assets
10,850  Investments
2,850  Net current assets
20X7
7,000
20X8
7,000
15,000
23,000
12,000
34,000
22,000
6,000
6,000
14,000
44,000
31,000
3,000
10,000
34,000
44,000
(i)
Show the decomposition of ROE for the year 20X8 in terms of three factors.
(ii)
What will be the EPS for the next year (20X9) using the following assumptions.



Net sales will grow by 20 percent
PBIT/Net sales ratio will increase by 0.05 over its 20X8 value
Interest cost will increase by 10 percent
The effective tax rate will be 32 percent
2.
The income statement and balance sheet of Vikas Company for the years 20X6
Income Statement
Balance Sheet
 Net sales
20X6
45,000
 PBIT
 Interest
 PBT
 Tax
 PAT
 Dividends
6,500
1,000
5,500
1,500
4,000
1,500
20X7
51,000  Equity capital
(Rs.10 par)
7,500  Reserves and surplus
1,200  Loan funds
6,300
2,000  Net fixed assets
4,300  Investments
1,600  Net current assets
20X6
3,500
20X7
3,500
17,500
10,000
31,000
18,500
3,000
9,500
20,000
11,000
34,500
20,000
3,500
11,000
31,000
34,500
and 20X7 are given below.
(i)
(ii)
Show the decomposition of ROE for the year 20X7 in terms of three
factors.
What will be the EPS for the next year (20X8) using the following
assumptions.




Net sales will grow by 15 percent
PBIT/Net sales ratio will increase by 0.75 percent (75 basis points) over its
20X7 value
Interest cost will increase by 12 percent
The effective tax rate will be 30 percent
3. The income statement and balance sheet of Zycus for the years 20X6 and 20X7 are
given below.
Income Statement
 Net sales
 PBIT
 Interest
 PBT
 Tax
 PAT
 Dividends
 Retained earnings
20X6
20,050
2,900
498
2,402
480
1,922
500
1,422
Balance Sheet
20X7
23,180  Equity capital
(Rs.5 par)
3,260  Reserves and surplus
614  Loan funds
2,646
530  Net fixed assets
2,116  Investments
550  Net current assets
1,566
20X6
2,000
20X7
2,000
7,010
6,070
15,080
9,900
1,520
3,660
8,576
7,050
17,626
10,680
1,740
5,206
15,080
17,626
(i)
Show the decomposition of ROE for the year 20X7 in terms of five factors.
(ii)
What will be the EPS for the next year (20X8) using the following assumptions.
 Net sales will grow by 16 percent
 PBIT/Net sales ratio will increase by 1 percent over its 20X7 value
 Interest cost will increase by 12 percent over its 20X7 value
 The effective tax rate will be 20 percent
4.
The financials of Vindhya Corporation, a leading player in electronics for the past
five years, are as under:
Rs. in million
Income Statement Summary
2005
2006
2007
2008
20 0 9
 Net sales
 Profit before interest & tax
 Interest
 Profit before tax
 Tax
 Profit after tax
 Dividends

3,700
800
4,000
920
4,800
1,200
5,800
1,300
7,000
1,400
70
730
205
525
75
845
237
608
80
1,120
325
795
78
1,222
360
862
60
1,340
410
930
105
122
159
216
233
420
486
636
646
697
200
1,000
600
1,800
1,000
200
600
1,800
480
200
1,486
580
2,266
1,396
250
620
2,266
410
200
2,122
520
2,842
1,982
180
680
2,842
450
200
2,769
610
3,579
2,659
220
700
3,579
520
200
3,466
550
4,216
3,206
260
750
4,216
610
Retained earnings
Balance Sheet Summary







Εquity Capital( Rs.10 par)
Reserves and Surplus
Loan Funds
Capital employed
Net fixed assets
Ιnvestments
Net current assets
· Market price per share(year end)
The year 2009 has just ended. The market price per share at the beginning of 2005 was
Rs.430.
(a)
(b)
(c)
(d)
(e)
(f)
What was the geometric mean return for the past 5 years?
Calculate the following for the past 2 years: return on equity, book value per
share,EPS, PE ratio (Prospective), market value to book value ratio, retention ratio.
Calculate the CAGR of (i) Sales for the period 2005 – 2009 & (ii) EPS for the period
2008 – 2009
Calculate the sustainable growth rate based on the average retention ratio and the
average return on equity for the past 2 years.
Decompose the ROE for the last two years in term of five factors.
Estimate the EPS for the next year (2010) using the following assumptions.
(i)
Net sales will grow at 10% (ii) PBIT / Net sales ratio for 2010 will be 0.5% more
than its value in 2009. (iii) Interest will increase by 10 % over its 2009 value. (iv)
Effective tax rate will be 35 %.
(g) Derive the PE ratio using the constant-growth model. For this purpose use the
following assumptions.
(i) The dividend pay out ratio for 2010 will be equal to the average dividend pay out
ratio for the period 2008 to 2009. (ii) The required rate of return is estimated with
the help of the CAPM (Risk free return = 8% Market risk premium = 10 %, Beta of
Vindhya Corporation’s Stock = 1.6). (iii) The expected growth rate in dividends is set
equal to the product of the average return on equity and average retention ratio
for the previous 2 years.
5.
Karishma Limited is a diversified company with a fairly strong position in certain
segments. The financials of the company for the last five years are given below:
Income Statement Summary
 Net sales
 Profit before interest and tax
 Interest
 Profit before tax
 Tax
 Profit after tax
 Dividends
Balance Sheet Summary
 Equity capital (Rs. 5 par)
 Reserves and surplus
 Loan funds
 Capital employed
 Net fixed assets
 Investments
 Net current assets
 Total assets
 Market price per share (year end)
20X4
730
104
26
78
20
58
12
20X5
790
118
28
90
23
67
14
20X6
820
130
30
100
30
70
14
20X7
890
153
33
120
30
90
16
70
300
170
540
320
20
200
540
70
70
353
220
643
400
21
222
643
60
70
409
240
719
440
19
260
719
81
70
483
280
833
526
22
285
833
110
Rs. in crore
20X8
970
162
35
127
31
96
18
70
561
225
856
521
15
320
856
85
The year 20X8 has just ended. The current market price per share is Rs.80.
(a)
(b)
Calculate the following for the past 2 years : return on equity, book value per
share, EPS, PE ratio (prospective)
Calculate the CAGR of sales and EPS for the period 20X4 - 20X8.
(c)
(d)
(e)
(f)
Calculate the sustainable growth rate based on the average retention ratio and
the average return on equity for the past 2 years.
Decompose the ROE for the last two years in terms of five factors.
Estimate the EPS for the next year (20X9) using the following assumptions: (i)
Net sales will grow at 15%. (ii) PBIT / Net sales ratio will improve by 2% over its
20X8 value. (iii) Interest will increase by 10 percent over its 20X8 value. (iv)
Effective tax rate will be 32 percent.
Derive the PE ratio using the constant growth model. For this purpose use the
following assumptions: (i) The dividend payout ratio for 20X9 will be equal to the
average dividend payout ratio for the period 20X7 - 20X8. (ii) The required rate
of return is estimated with the help of the CAPM (Risk-free return = 9%, Market
risk premium = 10%, Beta of Karishma Limited’s stock is 1.2). (iii) The expected
growth rate in dividends is set equal to the product of the average return on
equity for the previous two years and the average retention ratio.
CHAPTER 17 OPTIONS
1.
An equity share is currently selling for Rs. 40. In a year’s time, it can rise by 25
percent or fall by 15 percent. The exercise price of a call option on this share is
Rs. 42.
(i)
What is the value of the call option if the risk-free rate is 5 percent? Use the
option-equivalent method.
(ii) Calculate the value of the call option using the risk-neutral method.
2.
An equity share is currently selling for Rs. 100. In a year’s time, it can rise by 20
percent or fall by 10 percent. The exercise price of a call option on this share is
Rs. 105.
(i)
(ii)
3.
4.
What is the value of the call option if the risk-free rate is 7 percent? Use the
option-equivalent method.
Calculate the value of the call option using the risk-neutral method.
An equity share is currently selling for Rs. 80. In a year’s time, it can rise by 30
percent or fall by 15 percent. The exercise price of a call option on this share is
Rs. 90.
(i)
What is the value of the call option if the risk-free rate is 8 percent? Use the
option-equivalent method.
(ii)
What is the value of the call option if the risk-free rate is 8 percent? Use the
risk-neutral method.
An equity share is currently selling for Rs. 80. In a year’s time, it can rise by 30
percent or fall by 15 percent. The exercise price of a call option on this share is
Rs. 90.
(i)
What is the value of the call option if the risk-free rate is 8 percent? Use
the option-equivalent method.
(ii)
What is the value of the call option if the risk-free rate is 8 percent? Use
the risk-neutral method.
5.
Consider the following data for a certain share
a. Price of the share now
= S0 = Rs. 50
b. Exercise price
= E = Rs. 54
c. Standard deviation of continuously compounded annual return = σ =
0.2
d. Expiration period of the call option = 6 months
e. Risk-free interest rate
= 5 percent
i.
What is the value of the call option? Use the normal distribution table given
along with this booklet and resort to linear interpolation.
(ii)
What is the value of a put option?
6. Consider the following data for a certain share





Price of the share now
= S0 = Rs. 300
Exercise price
= E = Rs. 320
Standard deviation of continuously compounded annual return = σ = 0.3
Expiration period of the call option = 3 months
Risk-free interest rate
= 8 percent
(i)
What is the value of the call option? Use the normal distribution table given
along with this booklet and resort to linear interpolation.
(ii)
What is the value of a put option?
7. Consider the following data for a certain share





Price of the share now
= S0 = Rs. 110
Exercise price
= E = Rs. 120
Standard deviation of continuously compounded annual return = σ = 0.2
Expiration period of the call option = 3 months
Risk-free interest rate
= 7 percent
(i) What is the value of the call option? Use the normal distribution table given
along this booklet and resort to linear interpolation.
(ii)
What is the value of a put option?
8. Consider the following data for a certain share





(i)
(ii)
Price of the share now
= S0 = Rs. 150
Exercise price
= E = Rs. 170
Standard deviation of continuously compounded annual return = σ = 0.4
Expiration period of the call option = 6 months
Risk-free interest rate
= 9 percent
What is the value of the call option? Use the normal distribution table given
along this booklet and resort to linear interpolation.
What is the value of a put option?
CHAPTER 18 FUTURES
1. The share of Avinash Limited, which is not expected to pay any dividend in the
annum. A three-month futures is selling for Rs. 62. Develop an arbitrage strategy
and show what the profit will be 3 months hence. Ignore brokerage and other such
charges.
2.
The share of Vikas Limited, which is not expected to pay any dividend in the near
future, is currently selling for Rs. 100. The risk-free interest rate is 6 % per annum.
A six-month futures is selling for Rs. 104. Develop an arbitrage strategy and show
what the profit will be 3 months hence.
3.
The share of Manas Limited, which is not expected to pay any dividend in the near
future, is currently selling for Rs. 80. The risk-free interest rate is 9 % per annum.
A three-months futures is selling for Rs. 82. Develop an arbitrage strategy and
show what the profit will be 3 months hence.
4.
The share of Siddharth Limited, which is not expected to pay any dividend in the
near future, is currently selling for Rs. 120. The risk-free interest rate is 9.6% per
annum. A three-month futures is selling for Rs. 123.4. Develop an arbitrage
strategy and show what the profit will be 3 months hence.
CHAPTER 20 INVESTMENTS IN REAL ASSETS
1. Xavier considering an investment in a commercial property costing Rs. 30 million.
Xavier can get a bank loan of Rs. 15 million at the rate of 14 percent against the
property. The loan will be repaid in 5 equal annual installments; the first
installment will fall due at the end of the first year. Xavier expects that the
property will fetch a rental income of Rs. 4 million per year. For the sake of
simplicity, assume that the rental income is receivable at the end of each year.
Xavier plans to sell the property after 5 years. The net salvage value of the
property after 5 years is expected to be Rs. 50 million. Assume that for the next
five years, (a) Xavier’s marginal rate of tax will be 30 percent, (b) Xavier will be
able to claim a standard deduction of 30 percent from the annual rental income
of Rs. 4 million, and (c) there will be no expenses on account of repairs,
maintenance, collection charges, and property taxes.
(i)
What will be the PVIFA (14%, 5), calculated to the fourth decimal point, with
the help of the formula?
(ii) What will be the annual installment payable for amortising the loan, if the
bank calculates the installment correct to the nearest hundred?
(iii) What will be the post-tax rental income per annum?
(iv) What post-tax rate of return will Xavier earn on his equity investment(s) in
the property?
2.
Kamal is considering an investment in a commercial property costing Rs. 60
million. Kamal can get a bank loan of Rs. 40 million at the rate of 12 percent
against the property. The loan will be repaid in 5 equal annual installments; the
first installment will fall due at the end of the first year. Kamal expects that the
property will fetch a rental income of Rs. 4 million per year. For the sake of
simplicity, assume that the rental income is receivable at the end of each year.
Kamal plans to sell the property after 5 years. The net salvage value of the
property after 5 years is expected to be Rs. 80 million. Assume that for the next
five years, (a) Kamal’s marginal rate of tax will be 32 percent, (b)Kamal will be able
to claim a standard deduction of 30 percent from the annual rental income of Rs. 4
million, and (c) there will be no expenses on account of repairs, maintenance,
collection charges, and property taxes.
(i)
What will be the PVIFA (12%, 5), calculated to the fourth decimal point, with
the help of the formula?
(ii) What will be the annual installment payable for amortising the loan?
(iii) What will be the post-tax rental income per annum?
(iv) What post-tax rate of return will Kamal earn on his equity investment(s) in
the property?
3.
Jayesh is considering an investment in a commercial property costing Rs. 20
million. Jayesh can get a bank loan of Rs. 12 million at the rate of 10 percent
against the property. The loan will be repaid in 4 equal annual installments; the
first installment will fall due at the end of the second year. Jayesh expects that the
property will fetch a rental income of Rs. 2 million per year. For the sake of
simplicity, assume that the rental income is receivable at the end of each year.
Jayesh plans to sell the property after 5 years. The net salvage value of the
property after 5 years is expected to be Rs. 28 million. Assume that for the next
five years, (a) Jayesh’s marginal rate of tax will be 30 percent, (b) Jayesh will be
able to claim a standard deduction of 30 percent from the annual rental income of
Rs. 2 million, and (c) there will be no expenses on account of repairs, maintenance,
collection charges, and property taxes.
(i)
What will be the PVIFA (10%, 4), calculated to the fourth decimal point,
with the help of the formula?
(ii) What will be the annual installment payable for amortising the loan, if the
bank calculates the installment correct to the nearest thundered?
(iii) What will be the post-tax rental income per annum?
(iv) What post-tax rate of return will Jayesh earn on is equity investment(s) in the
property?
4.
Satish is considering an investment in a commercial property costing Rs. 10 million.
Satish can get a bank loan of Rs. 5 million at the rate of 12 percent against the
property. The loan will be repaid in 5 equal annual installments; the first
installment will fall due at the end of the first year. Satish expects that the
property will fetch a rental income of Rs. 0.9 million per year. For the sake of
simplicity, assume that the rental income is receivable at the end of the year.
Satish plans to sell the property after 5 years. The net salvage value of the
property after 5 years is expected to be 13,768,000. Assume that (a) Satish’s
marginal rate of tax is 30 percent, (b) Satish can claim a standard deduction of 30
percent from the annual rental income of Rs. 0.9 million, and (c) there will be no
expenses on account of repairs, maintenance, collection charges, and property
taxes.
(i)
(ii)
(iii)
(iv)
What will be the PVIFA (12%, 5), calculated to the fourth decimal point,
with the help of the formula?
What will be the annual installment payable for amortising the loan?
What will be the post-tax rental income per annum?
What post-tax rate of return will Satish earn on is equity investment(s) in
the property?
Chapter 23
PORTFOLIO MANAGEMENT: IMPLEMENTATION AND REVIEW
1. Consider the following information for a mutual fund and the market.
Mean return (%)
Mutual Fund
Market
Standard deviation Beta
10 %
8%
15 %
10%
1.2
1.0
The mean risk-free return was 5 %.
(i) What is the Treynor measure for the mutual fund?
(ii) What is the Sharpe measure for the mutual fund?
(iii) What is the Jensen Measure for the mutual fund?
2.
Consider the following information for a mutual fund and the market.
Mean return (%)
Mutual Fund
Market
Standard deviation Beta
16 %
12 %
20%
15%
1.3
1.0
The mean risk-free return was 6 %.
(i) What is the Treynor measure for the mutual fund?
(ii) What is the Sharpe measure for the mutual fund?
(iii) What is the Jensen Measure for the mutual fund?
3.
Consider the following information for a mutual fund (M) and the market.
Mean return (%)
M
Market
Standard deviation
18 %
13 %
The mean risk-free return was 8 %.
(i) What is the Treynor measure for M?
(ii) What is the Sharpe measure for M?
(iii) What is the Jensen Measure for M?
30%
22%
Beta
1.2
1.0
4.
Consider the following information for a mutual fund (G) and the market.
Mean return (%)
G
Market
Standard deviation
20 %
12 %
40%
28%
Beta
1.5
1.0
The mean risk-free return was 9 %.
5.
(i)
What is the Treynor measure for G ?
(ii)
What is the Sharpe measure for G?
The return on a mutual fund portfolio during the last few years was 35 percent
when the return on the market portfolio was 32 percent. The standard deviation
of the mutual fund portfolio return was 36 percent whereas the standard
deviation of the market portfolio was 28 percent. The portfolio beta was 1.1. The
risk-free rate was 9%.
(i)
What is the impact of systematic risk?
(ii) What was the impact of imperfect diversification?
(iii)
What was the net superior return due to selectivity?
6. The return on a mutual fund portfolio during the last few years was 22 percent when
the return on the market portfolio was 20 percent. The standard deviation of the
mutual fund portfolio return was 40 percent whereas the standard deviation of the
market portfolio was 30 percent. The portfolio beta was 1.2. The risk-free return
was 10%.
(i) What was the impact of systematic risk?
(ii) What was the impact of imperfect diversification?
(iii) What was the net superior returns due to selectivity?