WEEK 8
PGDM
SOLVED PROBLEMS – COST OF CAPITAL
Problem 1
FINANCIAL MANAGEMENT
Calculate the cost of capital in the following cases: i
ii
X Ltd. Ltd. issues issues 12% 12% Deben Debentur tures es of face face value value Rs. Rs. 100 each each and and reali realies es Rs. Rs. !" per Debenture. #he Debentures are redee$able after 10 ears at a pre$iu$ of 10%. &. Ltd. Ltd. issues issues 1'% 1'% prefere preference nce shares shares of face face value value Rs. Rs. 100 each each Rs. !2 per share. #he shares are repaable after 12 ears at par. (ote: )oth co$panies are paing inco$e ta* at "0%.
Solution
(i Co!" o# Deb" +,nt - R/ / 3 (4 1 t 5d R/ - / 3 2 ,nt t R/ ( /
6 6 6 6 6
7nnual interest to be paid i.e. Rs. 12 Co$pan8s effective ta* rate i.e. "0% or 0."0 Rede$ption value per Debenture i.e. Rs. 110 (u$ber of ears to $aturit 6 10 ears issue price per debenture $inus floatation cost i.e. Rs. !"
+12 - 110 !" 3 104 1 ." 5d 6 110 - !" 3 2 +12 - 2."40."
9.2"
6
6 "0 !9."0
ii
Co!" Co!" o# $re# $re#er ere% e%&e &e &'$i &'$i"' "'ll D - R/ / 3 ( 5p R/ - / 3 2
here; D / ( R/
Dividend on
5p 6 110 - !" 3 2 1' - .=9 15.28% 95=
Problem a 7 co$pan raised preference share capital of Rs. 1;00;000 b the issue of 10% preference share of Rs. 10 each. >ind out the cost of preference share capital when it is issued at i 10% pre$iu$; and ii 10% discount. b 7 co$pan has 10% redee$able preference share which are redee$able at th =the end of 10 ear fro$ the date of issue. #he underwriting e*penses are e*pected to 2%. >ind out the effective cost of preference share capital. c #he entire share capital of a co$pan consist of 1;00;000 e?uit share of Rs. 100 each. ,ts current earnings are Rs. 10;00;000 p.a. #he co$pan wants to raise additional funds of Rs. 2";00;000 b issuing new shares. #he flotation cost is e*pected to be 10% of the face value. >ind out the cost of e?uit capital given that the earnings are e*pected to re$ain sa$e for co$ing ears. Solution
(' Co!" o# 1)* $re#ere%&e !+'re &'$i"'l i hen share of Rs. 10 is issued at 10% $remi,m @ p 6 D 3 <0 6 10 3 11 * 100 6 !.0!% ii hen share of Rs. 10 is issued at 10% -i!&o,%" 5 p 6
Marketing Lessons From the Freedom 251 Fiasco ) Auest 7uthor; eb 1B; 201=; 0".09 < ,# •
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linkedin If you were one of those eager beavers like me who were waiting for India's $ smart !hone wonder and was madly !rancing around after seeing the 2 full !age ads in your morning news!a!er" and rushing to their website to book yourself the world's chea!est smart !hone you were in for a rude sur!rise# ecause a $ !hone was what everybody wanted and eagerly waiting for even if you were a snobbish I!hone % !lus user# ecause a $ smart !hone even for the snob is reverse snobbery at its best# &he first ad that a!!eared !romised the Indian masses that it was going to deliver them into the digital age even those who were denied of Free asics a month ago (# &he headline boldy said 'Sabka Haq' which translated into )nglish as ')veryone's birthright'# Followed by a sub head that said 'Sapne Sach Hongey ' or your dreams will come true# &he generous use of the Indian tri*colour was also mis!laced# Funnily enough it was sad that the name of the manufacturer was +inging ells ,vt Ltd because all the wrong bells were ringing for the !oor !hone manufacturer this morning# &heir baseline read ' )veryone's -ust a call away' but they were certainly not a click away# 6 10 3 ! * 100 6 11.11% b #he cost of preference share face value 6 Rs. 100 $a be found as follows: D - R/ / 3 ( 5p 6 R/- / 3 2 ,n this case D 6 R/ 6 / 6 6 5p
10 100 100 2 6 Rs. !B
10 - 100 !B 3 10
100 - !B 3 2 6
10.%
c ,n this case; the net proceeds on issue of e?uit shares are Rs. 100 10 6 Rs. !0 and earnings per share is Rs. 10. Cost of new e?uit is: 5e
6
D1 3 p0
6
10 3 !0 11.%
Problem . 7 co$pan is considering raising of funds of about Rs. 100 la5hs b one of two alternative $ethod; vi.; 1'% institutional ter$ loan or 1% nonE convertible debentures. #he ter$ loan option would attract no $aFor incidental cost. #he debentures would have to be issued at a discount of 2."% and would involve cost of issue of Rs. 1;00;000. 7dvise the co$pan as to the better option based on the effective cost of capital in each case. 7ssu$e a ta* rate of "0%. Solution
Gffective cost of 1'% loan: ,n this case; there is no other cost involved and the co$pan has to pa interest at 1'%. #his interest after ta* shield H "0% co$es to 9% onl.
Gffective cost of 1% (CD : ,n this case;
7nnual ,nterest; , /
6 6 6
Rs. 1 100 2."0 1.00 !=."0 1 1 "
5d
6 !=."0% 6
=.9'%
#he effective cost of capital is lesser in case of 1% (CD. Problem /
#he following figures are ta5en fro$ the current balance sheet of Delaware I Co. Capital hare
Rs. B;00;000 2;00;000 =;00;00 1=;00;000 ';00;00
A% '%%,'l or-i%'r0 -ii-e%- o# R!2 $er !+'re +'! Fust been paid. ,n the past; ordinar dividends have grown at a rate of 10 per cent per annu$ and this rate of growth is e*pected to continue. 7nnual interest has recentl been paid on the debentures. #he ordinar shares are currentl ?uoted at Rs. 29." and the debentures at B0 per cent. ,gnore ta*ation. 3o, 're re4,ire- "o e!"im'"e "+e 5ei6+"e- 'er'6e &o!" o# &'$i"'l (b'!e- o% m'r7er 'l,e! #or Del'5're Co2 Solution
,n order to calculate the 7CC; the specific cost of e?uit capital and debt capital are to be calculated as follows: Rs. 2 * 1.10
D1 5e 6
-g6 <0
- 10 6 1B% Rs. 29."0
#he $ar5et value of e?uit is B0;000 * Rs. 29."0 6 Rs. 22;00;000 , 5d 6
Rs. 12 6
/
6 1"% Rs. B0
#he $ar5et value of debt is ';00;000 * .B0 6 Rs. ;20;000. (ow; the 7CC is 22;00;000 3 2";20;000 * .1B - ;20;00032";20;000 * .1" 6 .19= 6 19.=% ,n this case; the dividend of Rs. 2 has Fust be en paid. o; D 0 6 Rs. 2 and the D1; i.e. dividend e*pected after one ear fro$ now will be D 0 * 1 - g 6 Rs. 2 * 1.10. Note:
Problem 9 #he following infor$ation has been e*tracted fro$ the balance sheet of >ashions Ltd. as on 1E12E1!!B:
G?uit share capital
R!2 i% L'&! '00
12% debentures 1B% ter$ loan
'00 1;200 2;00 a Deter$ine the weighted average cost of capital of the co$pan. ,t had been paing dividends at a consistent rate of 20% per annu$. b hat difference will it $a5e if the current price of the Rs. 100 share is Rs. 1=0J c Deter$ine the effect of ,nco$e #a* on the cost of capital under both pre$ises #a* rate '0%. Solution
a eighted average cost of capital of the co$pan is as follows: So,r&e! o# &'$i"'l G?uit share capital 12% debenture #er$ loan
Co!" o# &'$i"'l Pro$or"io% o# "o"'l Wei6+"e- &o!" o# &'$i"'l 20% '320 '.00 12% '320 2.'0 1B% 12320 10.B0 7CC 19.20
#herefore; weighted cost of capital without consideration of the $ar5et price of G?uit and not ta5ing into consideration the effect of ,nco$e #a* is 6 19.2% per annu$.
b hen $ar5et price of e?uit shares is Rs. 1=0 >ace value Rs. 100; the cost of capital is: D 1 20
5e
6 p 1=0 6
12."%
Wei6+"e- 'er'6e &o!" o# &'$i"'l 5ill "+ere#ore be: So,r&e! o# &'$i"'l G?uit share capital 12% debenture 1B% #er$ loan
Co!" o# &'$i"'l Pro$or"io% o# "o"'l Wei6+"e- &o!" o# &'$i"'l 12."% '320 2."% 12% '320 2.'% 1B% 12320 10.B 7CC 1".9%
#he above 7CC is without ta5ing into consideration the effect of ,nco$e #a*. c 7s interest on debenture and loans is an allowable deductible e*penditure for arriving at ta*able inco$e; the real cost to the co$pan will be interest charges less ta* benefit assu$ing that the co$pan earns ta*able inco$e. o; interest cost will be : Rate of interest 1 t 12% Debenture : 12 * 0.=0 6 9.2% 1B% #er$ loan : 1B * 0.=0 6 10.B% Problem ; #he following infor$ation is available fro$ the )alance heet of a co$pan G?uit share capital 20;000 shares of Rs. 10 each Reserves and urplus B% Debentures
Rs. 2;00;000 Rs. 1;0;000 Rs. 1;90;000
#he rate of ta* for the co$pan is "0%. Current level of G?uit Dividend is 12%. Calculate the weighted average cost of capital using the above figures. Solution
C'$i"'l !"r,&",re G?uit share capital Reserves and surplus (et worth B% debentures
C'$i"'l !"r,&",re G?uit Reserves and surplus B% debentures #otal
Amo,%" R!2 2;00;000 1;0;000 1;90;000 ";00;000
R!2
Pro$or"io% o# &'$i"'l
2;00;000 1;0;000 ;0;000 1;90;000 ";00;000
!"r,&",re '0% 2=% ==% '% 100%
Pro$or"io% (5ei6+" '0% 2=% '% 100%
A#"er "'< &o!" 12% 12% '%
Wei6+"e- &o!" 12%*'0%6 '.B0% 12%*2=%6 .12% '%*'%6 1.=% !.2B%
1. 7s the current $ar5et price of e?uit share is not given; the cost of capital of e?uit share has been ta5en with reference to the rate of dividend and the face value of the share. o; 5 e 6 123100 6 12%.
#he opportunit cost of retained earnings is the dividends foregone b shareholders. #herefore; the fir$ $ust earn the sa$e rate of return on retained earnings as on the G?uit hare Capital. #hus; the $ini$u$ cost of retained earnings is the cost of e?uit capital i.e. 5 r 6 5e. Problem =
7 Li$ited has the following capital structure: G?uit share capital 2;00;000 shares =% preference shares B% Debentures
Rs. '0;00;000 10;00;000 0;00;000 B0;00;000
#he $ar5et price of the co$pan8s e?uit share is Rs. 20. ,t is e*pected that co$pan will pa a dividend of Rs. 2 per share at the end of current ear; which will grow at 9 per cent for ever. #he ta* rate $a be presu$ed at "0 per cent. &ou are re?uired to co$pute the following: a 7 weighted average cost of capital based on e*isting capital structure. b #he new weighted average cost of capital if the co$pan raises an additional Rs. 20;00;000 debt b issuing 10 per cent debentures. #he would result in increasing the e*pected dividend to Rs. and leave the growth rate unchanged but the price of share will fall to Rs. 1" per share. c #he cost of capital if in b above; growth rate increases to 10 per cent. Solutions
a #he cost of e?uit capital is D1 5e
6
Rs. 2 -g6
- 0.09
<0 6
Rs. 20
0.1 - 0.09 6 .19 or 19%
#he cost of B% debentures; after ta* is B 1 " 6 '%
STATEMENT S>OWING WEIG>TED COST OF CAPITAL
G?uit share capital
E
A#"er?"'< Co!" .19 .0= .0'
o; eighted 7verage cost of capital @ 0 is 10.9"% b 5e 6
D1 <0
-g6
Rs. Rs. 1"
- .09
Wei6+"! ."00 .12" .9"
Wei6+"e&o!" .0B"0 .009" .01"0 .109"
6
.20 - 0.9 6 .29 or 29%
#he cost of capital of new debenture after ta* is 10% 1 E ." 6 "%
STATEMENT OF S>OWING WEIG>TED AVERAGE COST OF CAPITAL Am"2 G?uit share capital =% preference share capital B% debentures 10% debentures
c
'0;00;000 10;00;000 0;00;000 20;00;000
D1 5e 6
6
Wei6+"!
Wei6+"eCo!" .10B .00= .012 .010 .1=
.'0 .10 .0 .20
Rs. -g6
<0
A#"er?"'< Co!" .19 .0= .0' 0."
- .10 Rs. 1"
.20 - 0.9 6 .0 or 0%
STATEMENT OF S>OWING WEIG>TED AVERAGE COST OF CAPITAL Am"2 G?uit share capital =% preference share capital B% debentures 10% debentures
'0;00;000 10;00;000 0;00;000 20;00;000
A#"er?"'< Co!" .0 .0= .0' 0."
Wei6+"! .'0 .10 .0 .20
Wei6+"eCo!" .120 .00= .012 .010 .1'B
o; weighted average cost of capital 5 0 1'.B0% Problem 8 #he following is the e*tract fro$ the financial state$ent of 7)C Ltd. Kperating profit E ,nterest on debentures E ,nco$e ta* (et
Rs. 10" lacs Rs. lacs Rs. = lacs Rs. = lacs Rs. 200 lacs Rs. 100 lacs Rs. 220 lacs
#otal Rs. "20 lacs #he $ar5et price of e?uit share and debenture is Rs. 12 and Rs. !.9" respectivel. >ind out i G<; ii % cost of capital of e?uit and debentures.
Solution
(i E'r%i%6! $er !+'re
6 6 6 6 6
Rs. =;00;000 Rs. 20;00;000
(ii Co!" o# -ebe%",re!@ 7- : based on $ar5et value 5d
6
,nterest 1 t 3 ar5et value
6 6
1" 1 " 3 !.9" B%
based on >ace /alue 5d
6
,nterest 1 t 3 >ace /alue
6 6
1" 1 E ." 3 100 9."%
(iiiCo!" o# e4,i"0 &'$i"'l: 5e
6
G< 3 p0
6
1.B0 3 12 6 1"%
Problem 7s a financial analst of a large electronics co$pan; ou are re?uired to deter$ine the weighted average cost of capital of the co$pan using i boo5 value weights and ii $ar5et value weights. #he following infor$ation is available for our perusal: T+e &om$'%0! $re!e%" boo7 'l,e &'$i"'l !"r,&",re i!:
R!2 2;00;000 10;00;000 B;00;000
7ll these securities are traded in the capital $ar5et. Recent prices are: Debentures H Rs. 110 per debenture
,n order to find out the 7CC; the specific cost of capital of different sources $a be calculated as follows: Co!" "o -ebe%",re: ,nt; , / R/ t (
6 6 6 6 6
Rs. 1 100 ' 6 Rs. !! Rs. 100 ."0 10 ear +, - R/ / 3 (4 1 t
5d
6 R/ - / 3 2
+1 - 100 != 3 104 1 ." 6 100 - !" 3 2 6
=.B%
Co!" "o Pre#2 S+'re!:
6 6 6 6
Rs. 1' 100 100 " 6 Rs. !" 10 ears
D - R/ / 3 ( 5p
6
R/ - / 3 2
1' - 100 !" 3 ( 6
100 - !" 3 12 6
1'.!%
Co!" "o E4,i"0 S+'re!: <0 D1 g
6 6 6
22 2 6 20 2 .09 D1
5e
6
-g <0 2
5e
- .09
6 20 6
19%
C'l&,l'"io% o# WACC (Boo7 V'l,e So,r&e
Amo,%" Rs. 2;00;000 Rs. 10;00;000 Rs. B;00;000 Rs. 20;00;000
Wei6+" .10 ."0 .'0 1.00
CC .1'! .190 .090
W
Wei6+" .092 .== .2=" 1.000
CC .1'! .190 .090
W
o; 7CC )/ is 12.9! or 12.B% C'l&,l'"io% o# WACC (M'r7e" V'l,e So,r&e
Amo,%" Rs. 2;'0;000 Rs. 22;00;000 Rs. B;B0;000 Rs. ;20;000
o; 7CC / is 1'.2% Problem 1) #he 7)C Co$pan has the total capital structure of Rs. B0;00;000 consisting of: Krdinar shares 2;00;000 shares "0.0% 10% preference shares 12."%
1'% debentures
9."%
#he shares of the co$pan sells for Rs. 20. ,t is e*pected that co$pan will pa ne*t ear a dividend of Rs. 2 per share which will grow at 9% forever. 7ssu$e a "0% ta* rate. &ou are re?uired to:
a Co$puted a weighted average cost of capital structure.
b Co$pute the new weighted average cost of capital if the co$pan raises an additional Rs. 20;00;000 debt b issuing 1"% debenture. #his would result in increasing the e*pected dividend to Rs. and leave the growth rate unchanged; but the price of share will fall to Rs. 1" per share. c Co$pute the cost of capital if in b above; growth rate increases to 10%. Solution
(' WACC o# "+e e
D1 3 <0 -g
6
2 3 20 - 0.09
6
19%
C'l&,l'"io% o# 5ei6+"e- 'er'6e &o!" o# &'$i"'l So,r&e Krdinar shares 10%
W ."00 .12" .9" 1.000
#he 7CC of the fir$ is 12.9% (b Co!" o# &'$i"'l o# '--i"io%'l -eb" 5d 6
1" 1 E ." 6 9."%
(ew cost of e?uit share capital 5e 6
D1 3 <0 - g
6
3 1." - 0.09
6
29%
CC .19 .10 .09
W
So,r&e Krdinar shares 10%
W .'0 .10 .0 .20 1.000
CC .29 .10 .09 .09"
W
#he 7CC of the fir$ would be 1".'% ,f the growth rate in b is increased to 10% 5e 6
D1 3 <0 - g
6
3 1" - .10
6
0%
C'l&,l'"io% o# WACC o# "+e #irm So,r&e Krdinar shares 10%
W .'0 .10 .0 .20 1.000
CC .0 .10 .09 .09"
W
#he 7CC of the fir$ would be of 1=.=%. Problem 11 7)C Ltd. has the following capital structure ';000 G?uit shares of Rs. 100 each 10% preference shares 11% Debentures
Rs. ';00;000 1;00;000 ";00;000
#he current $ar5et price of the share is Rs. 102. #he co$pan is e*pected to declare a dividend of Rs. 10 at the end of the current ear; with an e*pected growth rate of 10%. #he applicable ta* rate is "0%.
i >ind out the cost of e?uit capital and the 7CC; and ii 7ssu$ing that the co$pan can raise Rs. ;00;000 12% Debentures; find our the new 7CC if a dividend rate is increased fro$ 10 to 12%; b growth rate is reduced fro$ 10 to B% and c $ar5et price is reduced to Rs. !B.
Solution
i Cost of G?uit Capital is 5e 6
D1 3 <0 - g
6
10 3 102 - .10
6 1!.B% C'l&,l'"io% o# Wei6+"e- Aer'6e Co!" o# C'$i"'l So,r&e G?uit capital 10%
Amo,%" Rs. ';00;000 1;00;000 .1 ";00;000 ." 10;00;000 1.00
W .'
CC .1!B .100 .0""
7CC 6 11.=9 KR 11.9% ii Cost of G?uit Capital is 5e 6
D1 3 <0 - g 6
12 3 !B - .0B
6
20.2%
C'l&,l'"io% o# Wei6+"e- Aer'6e Co!" o# C'$i"'l (Ne5 So,r&e G?uit capital 10%
Amo,%" Rs. ';00;000 1;00;000 ";00;000 ;00;000 1;00;000
W .0B .099 .B" .20 1.000
CC .202 .100 .0"" .0=0
W
Problem 1 7n electric e?uip$ent $anufacturing co$pan wishes to deter$ine the weighted average cost of capital for evaluating capital budgeting proFects. &ou have been supplied with the following infor$ation:
BALANCE S>EET
W
Li'bili"ie! G?uit shares capital
R!2 A!!e"! 12;00;000 >i*ed 7ssets ';"0;000 Current 7ssets ';"0;000 !;00;00 10;00;000 '0;00;000
R!2 2";00;000 1";00;000
MMMMMMMM '0;00;000
A--i"io%'l I%#orm'"io%: i 20 ears 1'% debentures of Rs. 2;"00 face value; redee$able at "% pre$iu$ can be sold at par; 2% flotation costs. ii 1"% preference shares: ale price Rs. 100 per share; 2% flotation costs iii e?uit shares: ale price Rs. 11" per share; flotation costs; Rs. " per share #he corporate ta* rate is ""% and the e*pected growth in e?uit dividend is B% per ear. #he e*pected dividend at the end of the current financial ear is Rs. 11 per share. 7ssu$e that the co$pan is satisfied with its present capital structure and intends to $aintain it.
Solution
S$e&i#i& Co!"! MMMMMMM
So,r&e! G?uit funds 1"% preference shares 1'% debentures
Wei6+"! 0."" 0.1" 0.0
S$e&i#i& &o!" Wei6+"e- &o!" 0.1B00 0.0!!00 0.1"0 0.022! 0.="" 0.01!=
o; weighted average cost of capital; 5 0; is 1'.1"%.
