16 Shares and Debentures

8/2/2019 16 Shares and Debentures

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16.1 BASIC FACTS(i) The capital of a company is called the Stock, e.g. 5% stock at 97 J!leans that if a person invests

Rs 97, he can buy stock worth Rs 100 and his annual income is Rs 5.(ii) The convenient unit in which the capital stock of a joint stock company is divided, is called a

Share. These shares are generally worth Rs 10 and Rs 100 each. The company raises its capitalby means of selling such shares.

(iii) .The persons who purchase shares are called Share Holders.(iv) The part of the profit of a company which is divided among the share holders is called Dividend.

For example, a 20% dividend means that on a share of Rs 100, the share holder gets Rs 20; ona share of Rs 10, he gets Rs 2 and so on.

(v) The value at which a company issues shares is called the Nominal Value, Face Value or ParValue of the share. This value is printed on the share certificate.

(vi) The value at which a share is available in market is known as Market Value of the share.(vii) If the Market Value = Face Value, share is at par.(viii) If the Market Value> Face Value, share is at premium or above par.(ix) If the Market Value < Face Value, share is at discount or below par.(x) When a company likes to borrow money from the shareholders or public for a Fixed Period at

a Fixed Rate of Interest, the company issues Debentures. So, debentures are a Debt for acompany.

(xi) A debenture-holder receives interest on the face value of debentures at a rate fixed by the com-pany. The interest does not vary.

(xii) Dividend on Shares is calculated on Face value(xiii) Interest on Debentures is calculated on Face value.(xiv) Shares and Debentures, are generally sold or purchased in a market known as Stock Exchange

through authorised persons known as Share-brokers (Brokers).(xv) Broker's commission is called Brokerage.(xvi) Brokers charge commission from the purchasers and also from the sellers.(xvii) Brokerage is calculated on Market Value of ShareslDebentures.(xviii) Share Purchaser has to pay (Market Value + Brokerage)(xix) Share Seller will get (Market Value - Brokerage)


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16-2 Qua ntita tiv e A ptitu de fo r C ompe titiv e E xamin atio ns16.2 APPROACH TO PROBLEMS ON STOCKFor example,(a) 3%Rs 100 stock at Rs 96 By investing Rs 96, one can purchase stock of Rs 100.Hence, market price of the stock = Rs 96. . income = Rs 3 from an investment of Rs 96.So, to obtain Re 1 income from the stock, the person is to invest = Rs 963 = Rs 32(b) 3%stock yielding Rs 240 a year He earns an income = Rs 3 from Rs 100 stock

Rs 240 is earned from 100 x 240 = Rs 8,000 stock3~ amount of stock purchased = Rs 8,000

(c) Investment ofRs 1,125 in 3%stock at 112~a stock of Rs 100So, an investment of Rs 1,125 will allow the purchase of stock worth 100 x (1l2~ )112-2

= Rs, 1,000

#Byinvesting Rs 1121., a person gets2

amount of stock purchased = Rs 1,000

(1125) x 3 = Rs 3011212

(d) Saleproceeds fromRs 4,000 stock at92 By selling Rs 100 stock, cash realised = Rs 92

So, annual income after purchase of stock =

92Sale proceeds from Rs 4,000 stock = - x 4,000100= Rs 3,680

16.3 APPROACH TO PROBLEMS ON SHARE(a) Face value is the value of share printed by the company. Market value is the value of share available

in the market. It varies from time to time. If the share is at par, then market value = face value If the share is at premium, then market value = face value + premium If the share is at discount, then market value = face value - discount

(b) Brokerage is expressed as the percentage of market value of share.(c) During purchase of each share, the share holder has to pay the brokerage percentage as a commission

to the broker. ThereforePurchase value of 1 share = market value + (% brokerage x market value)

= market value (1 + % brokerage)But, in case a person purchases directly from the company, he need not to pay brokerage, then,purchase value of 1 share = market value


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M EM O RY T ABL ES

Table 16.1 Form ulae on StockPart vJJ I1 IV

Purchase Cost'M .V .+ brokerage

Total Stock100

Sale RealisationM.V. - brokerage

Annual IncomeRate %

. . . .a'IIW

No. of Stock =

*Purchase Cost = Total InvestmentNB: Equate any of the TWO PARTS to find out the unknown as per the data available.

T able 16.2 Fo rm ulae o n S hares a nd D eb en tu resPart I /I /II IV

Investment (or Purchase Cost)M.V. (1 + %brokerage)

Sale Realisation Annual Income x 100Dividend % x Face ValueNo. of Shares = M.V. (1-% brokerage)

NB: Equate any of the TWO PARTS as per the requirements of the given problem.M.V. stands for Market Value of one share/debenture/stock.


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~~~~ :__ - --~~~--~-----~-

16-4 Q uantitative A ptitude for C om petitive Exam inations(d) During sale of each share, the share holder has to again pay the % brokerage as a commission to the

broker. Therefore,Sale value (or sale earning) of 1 share = market value - (% brokerage x market value)

= market value (1 - % brokerage)(e) Investment is the total amount invested in purchasing a certain number of shares at the market value.

It implies that if a person purchases 'n' shares, then his investment= n x purchase value of 1 share(0 A company pays dividend (share of the profit) to each shareholder. The dividend is normally a

certain percentage of the face value of each share or a certain amount for each share.The dividend has no relation with the market value of the share. In fact, this dividend is the annual

income or the return on investment for the shareholder. HenceAnnual income on one share = face value x % dividend

Total income on 'n' no. of shares = n x face value x % dividend(g)

. incomeActual rate per cent on investment = -.-~--'----investmentFrom (e) and (D , it can be concluded that:

x 100

'f

Number of shares = n = investment- - - - - - - - - - - - - - - - - - - =purchase value of one shareannual income---(face value x % dividend)

annual income of one shareSolved Example.

E-l Find the cost of2(a) Rs 5,000, 83 % stock at 951(b) Rs 3,000, 72:% stock at par

(c) Rs 2,500, 7% stock at 10 premium(d) Rs 1,000, 3t % stock at 8 discount(e) Rs 2,200, 6% stock at par

(brokerage 111%)(D Rs 2,000, 5 t % stock at 5 premium

( brokerage 1%)(g) Rs 1,000, 6% stock at 6 discount

( brokerage 1%)


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Shares and Debentures 16-5S-1 While finding the purchase cost, neglect the rate % data

Market Value(a) Cost of purchase = Amount of stock x 100 [Refer Parts II and illin Table J 195

= 5,000 x 100 = Rs 4,750.(b) Since it is at par, .. Cost of purchase= Amount of stock = Rs 3,000.(c) Here, the stock is at 10 premium.

.. Market Value = (100 + Premium) = 110Market Value. . Cost of purchase = Amount stock x 100

110= 2500 x 100 = Rs 2,750.(d) Here, stock is at 8 discount, .. Market Value = 100 - discount

(100 - discount):. Cost of purchase = Amount of stock x 10092= 1,000 x 100 = Rs 920.

(e) Brokerage is added while purchasing the stock(brokerage +Market Value). . Purchase Cost = Amount of stock x 100

(Since it is at par Market Value = 100)2,200 ( 1 )= 100 - x 100 + 11

1,101= 22 x -- = Rs 2,202.11(1 ) Market Value= 100 + Premium = 100 + 5

(Market Value + brokerage)Purchase Cost = Amount of stock x 100

100+S+!= 2000 x 100 = Rs 2,110.(g) Market Value = 100 - discount = 100 - 6

(Market Value + brokerage)Purchase Cost = Amount of stock x 100100-6+}

100 = Rs 945.1,000 xE-2 Find the cash realised by selling Rs 2,000, 5% stock at 6 premium (brokerage 1%).S-2 Brokerage is subtracted when stock is sold.


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[Refer Parts II and V in Table l}

16-6 Quantitative Aptitude for Competitive Examinations(Market Value - brokerage). . Sale Realisation = Amount of stock x 100

(100+6-1)=2,000 x = Rs 2,110.100

E-3 How much stock should be sold to realise Rs 1,221 from 5% stock at2 premium (brokerage 1%).

S-3 Amount of stock = Sale Realisation~~--~~~~~--~ x 100(Market Value - brokerage)1,221

[Refer Parts II and N in Table l}

1 I x 100 = Rs 1,200.100+2---4 2E-4 How much 6% stock at 8 discount can be purchased by investing

Rs 1,850 (brokerage 1%).S-4 Since Market Value = 100 - discount

Purchase Cost. . Amount of Stock =. x 100(100 - discount + brokerage)1,850 1 x vl00 = Rs 2,000.100-8+-

2Hence stock being at 8% discount, by investing Rs 1,850, one can purchase stock of Rs 2,000 (whichis more than Rs 1,850).

E-5 Find the annual income derived from Rs 2,800, 4% stock at 122?S-5 Annual Income = Total Amount of stock x % rate of stock= 2,800 x .04 = Rs 112.E-6 Find the annual income derived by investing Rs 2,800, in 4% stock at 112?S-6 Note, here total investment is Rs 2,800

But amount of stock purchased is not known.Investment x % rate of stock:. Annual Income =

(Market Value + brokerage) 100= 2,800 x 4 = Rs 100.112

E-7 What rate % is obtained by investing in 7% stock at 5 discount (brokerage %).S-7 Amount of rate per cent = Income by investment of Rs 100

Annual Income = Investment x % rate of stock(Market Value + brokerage)[Refer Parts ill and V in Table 1]


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Shares and Debentures 16-7

= __ =-=100:....:...._,,----7 = 100 x 7 7351 1-0.05 + 0.0025 =1-%5+-% 4735Rate % obtained = 100 = 7.35%.

E-8 Find the market value of a 6% stock in which an income of Rs 244 is derived by investing Rs 1,220,brokerage being %.Annual Income8-8 Rate % Investment= ~ ~ -- ~ ~ ~ ~ ~ - - ~(Market Value + brokerage) [Refer Parts 1Il and V in Table IJ

244 },2206= Market Value + _ !_4

1:.Market Value + 4 = 30 ~ Market Value = 29.75.E-9 How much should one invest in 6%% stock at 110 to secure an annual income of Rs 300.

Annual Income8-9 Rate % Investment {Refer Parts 1fI and V in Table 1]Market Value +% brokerage300 201=x110

30 x 110 x 300I= 20 ~ I = Rs 4,500 The investment is Rs 4,500.E-IO Find what a purchaser would have to pay for 250 shares ofRs 20 each quoted at Rs 74. What would

be the gain to the share holder, if be had purchased the shares at par?8-10 Face Value of 1 share = Rs 20

Market Value of 1 share = Rs 74The amount paid by the buyer (purchaser) = 250 x 74 = Rs 18,500The Purchase Cost by share holder = 250 x 20 = 5,000:. Gain by the share holder = 18,500 - 5,000 = Rs 13,500.

E-11 A man invests Rs 4,220 in 6t % stock at 105. On selling the invested stock, how much will herealise? (brokerage = % ).

8-11 Here, amount of stock is not known.Purchase cost of stock = Investment = Rs 4,220

Sale Realisation Purchase CostMarket Value - brokerage Market Value + brokerage

[Refer Pans III and N in Table 1]Sale Realisation

1105--2

= 4,220105 + t


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4,220 x 104.25~ Sale Rea1isaton = 105.5 = Rs 4,180.E-12 Find the purchase cost of 80 shares of Rs 10 each at ~ discount, brokerage being ~ per share.8-12 Since Market Value = Face Value - discount

16-8 Quantitative Aptitude for Competitive Examinations

Cost of 1 share = Face Value - discount + brokerage= 10- 1+1= 91+1= 9& = Rs918 8 8 8 8 4

3Cost of 80 share = 80 x 94"

8-13 (Market Value - brokerage)Sale Realisation = 100120= 100 x 4,500 = Rs 5,400

Income before selling = Total Amount of stock x % rate of stock5= 4,500 x 100 = 225

x Amount of stock

= (80 x 9) + ( ~ x 80) = Rs 780.E-13 A man seils Rs 4,500, 5% stock at 120 and invests the proceeds partly in 3% stock at 99 and partly

in 8% stock at 132. He thereby increases his income by Rs 75. How-much of the sale proceeds wereinvested in each stock?

Income after sale from two stocks = 225 + 75 = Rs 300Now, let, Rs x of sale proceeds be invested in 3% stock at 99 and Rs (5,400 - x) be invested in8% stock at 132.. . Income from I stock + Income from II stock = 300

xx3 (5,400-x) x 8-- + = 30099 112.. x = Rs 900 invested in 3% stock at 99and 5,400 - x = Rs 4,500 invested in 8% stock at 132.

E-14 A man invested Rs 2,592. When he bought shares of a company at Rs 108 each, the face value ofa share was Rs 100. The company paid 1 2 t % dividend. Find the dividend earned (income derived)at the end of the year.8-14 Dividend is always calculated on Face Value. Equating Parts II and IV of Table 2,

Annual Income x 100 Investment= ~~~~~~~~~----~we get, Dividend % x Face Value Market Value (1+% brokerage)Annual Income x 100

25 x 1002Income derived = 2 ; i o o x i~~2,592 = Rs 300.

2,592= 108


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E-15 Find the income derived from 88 shares of Rs 20 each at 5 premium (Brokerage per share), therate of dividend being 4 %. Also find the rate of interest on this investment.

% rate of dividendS-15 Dividend earned (income) = -------:-1-=-00-=---- x Face Value x Number of shares[Refer Parts I and IV of Table 2J

174 x 100 x 20 X 88 = Rs 74.80Purchase Cost of one share = Face Value + Premium + brokerage

= 20 + 5 + = 25% Rate of interest on the investment,

= % rate of dividend x -Face ValuePurchase Cost17 20= 4" X 101 = 3.37%.

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A man invested Rs 4,444 in the shares of face value Rs 100 and at 15% dividend, his income wasRs 600. Find the quoted price (Market Value) of each share if brokerage is 1 %.Brokerage is always calculated on Market Value.Let the market value of each share = Rs M

Investment-------------=~~-~---~-Market Value (1+% brokerage) Dividend % x Face Value[Refer Parts II and IV of Table 2J

Annual Income x 1004,444 600 x 100

M (1 + 1%) 15 x 100M = Rs 110.

.. Market Value of each share = Rs 110.E-17 A man has income of Rs 1,500 by investing in 15 % debentures of face value of Rs 100 and

available for Rs 104. If the brokerage is 1%, what is his investment?S-17 Refer Parts II and IV in Table 2Investment Annual Income x 100

Dividend % x Face Valuearket Value (1 +% brokerage)Investment104 (1+1%) =

1,500 x 10015 x 100 ~ Investment = 100 x 104 x ( l Q ! _ ). 100

. . Investment = Rs 10,504.E-18 Which is a better investment?

(i) 15 % debentures at 8 % premium or,(ii) 14 % debentures at 4 % discount


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S-18 Simple method *Investment % Market Value(i) 15Xl08 (cross multiply)(Ii) 14 96


Hence, (i)(ii)

15 x 96 = 1,44014 x 108 = 1,520 :. (ii) > (i)

R EG ULA R P RO BLEM S

. . (ll) investment is better.* This method is also applicable in case of share investment.

(1) Find the purchase cost of(a) Rs 2,000, 4% stock at 5 discount

7 1(b) Rs 1,500,4% stock at 97 " 8 and brokerage 8%1 1(2) How much 4"2% stock at 97"2 can be purchased for Rs 390.

Investment x 100Hint: Amount of stock = M.V. of one stock

(Market value + brokerage) [Refer Memory Table 1]

(3) Rs 800 stock of a company costs Rs 750 including ~% brokerage. Find the market value of Rs 100stock.Hint: 800 = 100750 Cost price of stock. . Market value = Cost price - brokerage.

Cost price = 9314

3 1 5= 93 - - - = 93 - .4 8 8(4) Find the cash realised by-selling Rs 4,000, 6 % stock at 5 premium (brokerage %).

(100 + Premium - brokerage)Hint: Sale Realisation = Amount of stock x 100(5) Find the cash required to purchase Rs 1,500, 4% stock at 105 (brokerage ~%).(6) Find the annual income derived from Rs 2,500, 4% stock at 100.(7) Find the annual income by investing Rs 3,150, 4% stock at 105 .

Hint: Income = _ _ x 3,150.105(8) Find the annual income by investing Rs 9,550 in 4% stock at 95 (brokerage % ).

Hint: IncomeInvestmentRate % of stock


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(9) What rate % is obtained by investing in 9t % stock at 90 (brokerage %).Hint: Rate % obtained = % rate of stock x 100.

Market value + brokerage(10) Find the market value of a 8% stock in which an income of Rs 125 is derived by investing Rs 1,000,( brokerage %) .

(11) What rate % is obtained if by investing Rs 1,000, one gets annual income of Rs 125.Hint: Rate% obtained = IncomeInvestment x 100.

(12) What is the better investment?(i) 4 % stock at 95 or(ii) 4% stock at 105

Hint: Test which is greater, 4 x 105 or 4 _ ! _ x 952C D (m

= 420 or 427.5.. IT is greater than I So IT is better investment, also refer E-l8.

(13) How much money must I invest in 7% stock at 105 to secure an annual income of Rs 400?(14) A man invests Rs 8,100 partly in 7% stock at 147 and partly in 6% stock at 144. If his income is

same, fmd his two investments.Hint: Since income from both investment is same, so, divide 8,100 in the ratio of 147 : 144.7 6

(15) Find the income derived from 600 shares, if the face value of one share is Rs 10 and dividend is 16%.(16) A man sold 500 shares with face value Rs 100 and market value as Rs 740. How much did he gain

if he had purchased the shares at 100% premium.Hint: Gain = 500 (740 - 200).

(17) A man purchased 300 shares of the face value of Rs 100 each from the market at Rs 800 per share.If a dividend of 24% is declared, find his earning per cent on the investment.

Face ValueHint: % earning on investment = % dividend x %Market Value= 24 x 100 = 3%.800

(18) How many shares of market value of Rs 12.50 can be purchased for Rs 12,625, (if the brokerage is1%).


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(19) A broker sold Rs 5,000 stock at 94% . If the brokerage is i % fmd the amount of brokerage and saleproceeds of the stock holder.

(20) A man invested Rs 3,300 when he bought Rs 100 shares at Rs 110. If 15% dividend is declared, findhis annual income.H i n t : Refer Table 2.

(21) A man invested Rs 12,000 in 11.5% debentures of face value Rs 100 and available market value isRs 120. Find his annual income.H i n t : See E.17.

(22) Find the income per cent on 8% debenture of face value Rs 100 and available at Rs 80 each.(23) A man sold 20% debentures worth Rs 7,500 at 5% premium. Find the cash released from this sale,

if brokerage is 2%.(24) A man buys 500 debentures of face value Rs 100 each at Rs 95 and sells the same when the price

rises to Rs 98. If brokerage is 2% find his gain or loss.H i n t : Purchase cost = Market value,. (1 + % brokerage)

Sell cost = Market value 2 (1 - % brokerage). . Gain/Loss per share = Purchase Cost - Sell Cost.

Answers1. (a) Rs 1, 900 (b) 1, 470 2 400 3. 93 ~ 4. Rs 4,190 5. 1,580 6. 100 7. 120 8. Rs 4508

19. 10-%216. Rs 2,70,00023. Rs 7,717.50

11. 12'!_ % 12. (ii) 13. Rs 6,000 14. Rs 3,780, Rs 4,320 15. Rs 960217. 3% 18. 1,000 19. Rs 625, Rs 4,725 20. 450, 21. 1,150 22. 1024.430

10. 63.75

REAL PROBLEMS I(1) The cost of Rs S, p% stock at Rs M is

MS(a) 100 (b) MS (d) psMc) ~ x 100 (e) ps100(2) The cost of Rs 1,500, 5 stock at 98, is

(a) Rs 1,550 (b) Rs 1,470 (c) Rs 1,420 (d) Rs 1,440 (e) Rs. 1,580( brokeragei) is

(e) Rs 1,564(3) The cash required to purchase Rs 1,600, 5t% stock at 3 premium.

(a) Rs 1,656 (b) Rs 1,650 (c) Rs 1,662 (d) Rs 1,590(4) The cash realised by selling Rs 2,500, 5% stock at 1l0i (brokerage i% ) is (RRB '84)

(a) Rs 2,600 (b) Rs 2,650 (c) Rs 2,750 (d) Rs 2,350 (e) Rs 2,400(5) The purchase price of a Rs 100 stock at 6 discount (brokerage 1% ) is

(d) Rs 94 (e) Rs 106a) Rs 100 (b) Rs 94.50 (c) Rs 106.5


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(e) Rs 6.75(SSC, '88)


(6) The income derived from a 6t% stock at 94 is(a) Rs 6 (b) Rs 6.50 (c) Rs 6.25 (d) Rs 5.80

(7) A 3% stock yields 4%. The market value of the stock is(a) 75 (b) 133 (c) 80 (d) 120Hint: Market Value = 1 . x 100 = 75, Refer Eq. (3).4

(8) A 4t % stock should be purchased at what price to yield 5% interest?(a) Rs 80 (b) Rs 111 (c) Rs 90 (d) Rs 75

(e) 104

(e) Rs 110(9) If a man earns Rs 270 by investing Rs 7,800 in 4t% stock, brokerage being ~%, the market value

of stock is(a) Rs 130 (b) Rs 130~ (c) 12928 (d) 129~ (e) 13118

(10) To produce an annual income of Rs 600 in a 4t % stock at 94t the amount of stock needed is(a) Rs 12,600 (b) Rs 13,000 (c) Rs 12,000 (d) Rs 10,000 (e) Rs 13,200

(11) Find the rate % on investment, of a 4% stock at 79t, brokerage = ~%.(a) 4 % (b) 5 %

Hint: Rate % on investment = % rate of stockMarket Value + brokerage(12) Which is better investment, (i) 4t% stock at 90 or (ii) 4% stock at 88?

(a) i (b) ii(UDC, '81)

(c) Data insufficient (d) None of these(13) The rate % obtained from 4% stock at 88 and from 4t % stock at M are equal. The value of M

(purchase cost) is (MBA, '85)(a) 92 (b) 99 (c) 96 (d) 102 (e) 111H 88 M fi 3mt: -4 =- Re er Eq. ( ).

412(14) If the annual income from 5% stock at 112 is Rs 42 more than 4% stock at 98, then the investmentIS(a) Rs 12,000 (b) Rs 11,000

Income differenceHint: Investment = C ~ 2 - 9 ~ )(c) Rs 10,976 (d) Rs 12,032

Answers1. (a)10. (a)

2. (b)11. (b)

3. (a)12. (a)

4. (c)13. (b)

5 . ( b )14. (c)

6 . ( b ) 7. (a)

(e) Rs 11,048

8. (c) 9 . (c)

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16 Shares and Debentures