Shares, Ownership & Indices

Question 1

(a) Outstanding = Issued − Treasury = $5{,}000{,}000 - 200{,}000 = 4{,}800{,}000$ shares. (2) Why: outstanding excludes shares the company holds itself; authorized is irrelevant here.

(b)

• Dividend yield $= \dfrac{3.20}{80} = 0.04 = 4\%$. (2)
• Declared dividend rate (on face value) $= \dfrac{3.20}{10} = 0.32 = 32\%$. (2)

(c) (4)

• Yield uses market price as the denominator; the declared rate uses face value, a fixed accounting figure. (1)
• Since market price (\80$)$\gg$face value ($$10$), the yield ($4%$) is far below the declared rate ($32%$). (1)
• A "32% dividend" sounds huge but tells you nothing about your real return on the money invested. (1)
• A value/income investor should watch the dividend yield, because it reflects income per rupee actually invested. (1)

Question 2

(a) (4)

• $3:2$ split → shares multiplied by $3/2$: $600 \times \frac{3}{2} = 900$ shares. (1)
• New price = 150 \times \frac{2}{3} = \100$. (1)
• Before: 600 \times 150 = \90{,}000$; After:$900 \times 100 = $90{,}000$. Unchanged. (2)

(b) (4)

• $1:4$ bonus = 1 free share per 4 held → holding multiplied by $5/4$: $900 \times \frac{5}{4} = 1125$ shares. (2)
• Theoretical price = 100 \times \frac{4}{5} = \80$. (1)
• Check value: 1125 \times 80 = \90{,}000$. Unchanged. (1)

(c) (4)

• Wealth is unchanged: value stays \90{,}000$ throughout — more shares at a proportionally lower price. (2)
• The claim is false; the pie is merely re-sliced. (1)
• Real difference: a bonus issue capitalises reserves (transfers from reserves to share capital, increasing paid-up capital) whereas a stock split merely reduces face value with no accounting transfer between reserves and capital. (1)

Question 3

(a) TERP (4)

• Ratio $1:4$ → for every 4 old shares (value $4\times40 = 160$) add 1 new (paid $25$). (1)
• Total value = 160 + 25 = \185$for$5$ shares. (2)
• TERP = 185/5 = \37$. (1)

(b) (4)

• Rights entitlement $= 800/4 = 200$ new shares. (1)
• Cost of new shares = 200 \times 25 = \5{,}000$. (1)
• Old cost basis assumed at market: original value 800 \times 40 = \32{,}000$; total outlay$= 32{,}000 + 5{,}000 = $37{,}000$for$1000$ shares. (1)
• Average cost = 37{,}000 / 1000 = \37$ per share (equals TERP). (1)

(c) A rights issue increases the number of outstanding shares (new shares created), while a buyback decreases it (shares retired/held as treasury). (2)

Question 4

(a) Price-weighted index (3)

• Sum of prices $= 200 + 500 + 100 = 800$. (1)
• Index $= 800/3 = 266.67$. (2)

(b) New divisor after B's $5:1$ split (4)

• New price of B $= 500/5 = 100$. New price sum $= 200 + 100 + 100 = 400$. (1)
• Index must be continuous: $\dfrac{400}{D_{new}} = \dfrac{800}{3}$. (2)
• $D_{new} = \dfrac{400 \times 3}{800} = 1.5$. (1)

(c) Free-float market-cap index (5)

• Market caps: A $= 200\times50 = 10{,}000$; B $= 500\times10 = 5{,}000$; C $= 100\times80 = 8{,}000$ (crore). (2)
• Total $= 23{,}000$ crore. Weights: A $\approx 43.5\%$, C $\approx 34.8\%$, B $\approx 21.7\%$. (1)
• In the price-weighted index, B (price 500) dominates with weight $500/800 = 62.5\%$; in the cap-weighted index, A dominates. (1)
• Price-weighting is misleading because a high-priced but small company can drive the index despite little economic size — weight tracks share price, not value. (1)

Question 5

(a) Sectoral — restricted to one industry (banking). (2) (b) Broad-market — 50 large firms across many sectors representing the overall market. (2) (c) Thematic — cuts across multiple sectors united by a single theme (EV transition), not one industry. (2)

[
  {"claim":"Q1 dividend yield 4% and declared rate 32%","code":"y=Rational(320,100)/80; r=Rational(320,100)/10; result=(y==Rational(1,25)) and (r==Rational(32,100))"},
  {"claim":"Q2 final holding 1125 shares, value unchanged at 90000","code":"sh=600*Rational(3,2)*Rational(5,4); price=150*Rational(2,3)*Rational(4,5); result=(sh==1125) and (sh*price==90000)"},
  {"claim":"Q3 TERP is 37 and average cost 37","code":"terp=(4*40+25)/5; avg=(800*40+200*25)/1000; result=(terp==37) and (avg==37)"},
  {"claim":"Q4 new price-weighted divisor is 1.5","code":"idx=Rational(800,3); Dnew=400/idx; result=(Dnew==Rational(3,2))"},
  {"claim":"Q4 cap-weighted: A has largest weight","code":"caps={'A':200*50,'B':500*10,'C':100*80}; result=(max(caps,key=caps.get)=='A')"}
]