cost of capital questions financial management

Cost of capital numerical

1. 1111.tlbadon-18
r
The following is the capital structure and the firms expected after tax component co .
various source of finance.
sts Of the
Sources of Finance
Equity Share Capital
Retained
Earnings
Amount
6,50,000
2,50,000
Preference Share Capital
1,50,000
Debt Capital
4,50,000
Calculate the weighted average
cost of capital.
Expected After tax co~(%)
20
20
15
12

2. 501,,t1on:
Calculation of Weighted
Average Cost
source of Funds Amount
Proportion
After t.ax cost Product
(f)
w
X xw
Equity share capital 6,50,000
43.33 20
866.6
p.etainecl Earnings 2,50,000
16.67 20 333.4
preference Share Capital 1,50,000
10 15 150
oebt capital 4,50,000

30
12 360
Total 15,00,000
100 1710
.
:EXW 1,710
Weighted average cost of capital= :EW =
100
= 17.1 o/o
~-11
A company has the following capital structure.
Find out the weighted average cost of capital.
-securities
Book Value
After t.ax cost
--Equity
10,00,000 12%
Retained earnings
4,00,000 8%
Preference capital
4,00,000 14%
Debentures
8,00,000 5%
26,00,000
-
Statement Showing Weighted Average Cost
of capital
securities Proportion Aftertax
Weighted Average Cost
Equity 38 12% (38x.12)
= 4.56
Retained earnings 15 8% (15x.08)
= 1.20
Preference Shares 15 5% (lSx.05)
= 0. 75
Debentures 32 5% (32x.0S) = 1.60
100 8.11
Weighted Average cost= 8.11 %
~
A firm has the following capital structure
and after tax cost for different sources of funds used.
Source of Funds Amount After
Tax Cost
Debt
15,00,000 5%
Preference Shares
12,00,000 10%
Equity Shares
18,00,000 12%
Retained Earnings 15,00,000
11 %
Total
60,00,000
You are required to compute the weighted
average cost of capital.

3. Solution:
calculation of Weighted Average Cost
Source of Funds Amount Proportion
After Tax Cost Product
((')
w
X xw
Debt 15,00,000 25
5 125
Preference Shares 12,00,000 20
10 200
Equity Shares 18,00,000 30 12 360
Retained Eamings 15,00,000 25 11 275
-
Total 60,00,000 100 960
. 1:XW 960
We,ghtedaveragecostofcapital= 1:W =
100
=9.6%

4. zzsr:·srv
~ . .
~Y has on Its books tllefollowing amounts and specific costs of each type of capital.
rypeofCiJpital Book Value MarketValue SpedficCosts(%)
oebt
4,00,000
3,80,000
preference 1,00,000
1,10,000
EQUltY
6,00,000
12,00,000
Retained Earnings 2,00,000
13,00,000 16,90,000
oetermlne the weighted average cost of capital using:
~) eook Value Weights and
5
8
15
13
{ ,) Market Value Weights
How are they differing? Can you think of a situation where the weighted average cost of capital
would be the same using either of the weights?
Computation of Weighted Average Cost of Capital
using Book
Value Weights
Type of capital Amount Proportion (w)
Specific Cost(%) (x)
Debt 4,00,000 30.77
5
Pre.ferenCe Shares 1,00,000 7.69
8
Equity Shares 6,00,000 46.15 15
Retained Earnings 2,00,000 15.39 13
13,00,000 100
LXW 1,108
Welghtedaveragecostofcapital = "i.W =
100
= 11.08%
Computation of Weighted Average Cost of Capital
using Market Value Weights
Tn,e dOJpital Amount Proportion (w) SpedficCost(%) (x)
Debt 3,80,000 22.5 5
P:nlaaa Shares 1,10,000 6.5 8
--Shares
9,00,000 53.25 15
.._lid Earnings 3,00,000 17.75 13
16,90,000 100
"f,XW ~195
'lllll4liCl~ecostofcapltal = r.w = 100 = 11.95%
Product xw
154
62
692
200
1108
Product xw
113
52
799
231
1195

5. T Ltd. has the followi ng capital structure:
Equity Snares cap:tai (10 laKhsshares)
Retained Eamf.1gs
14
% Debentures (70,000 Debentures)
16% Term Loan
f (lakhs)
100
130
70
--~
40Q
--
.
rhl shares is t' 25. The next expected dividend per share ls~ 2 an~
The marl<e'" pnce pay per eou, ... ,
' '
Th d b tu'"eS are redeemable after six years at par and the current market
expected to
grow at 8%. e e en . .
ooA
ta
tfon rs r 90 per debenture. The
tax rate applicable to the firm rs 5 o.
QUO
.
. •
hted average cost of capital of the company using market values
You are reouired ~.o compute werg
as weignts.
Solutfon:
~ c:; (2/25}+8%=8%+8%=
16%
K =Ke= 16%
~1 (Debenture)= [14(1-0.5) + (100-90)/6] + (100 + 90)/2 = 9.12%
Kd
7 (Term Loan)= 16%(1-0.5) = 8%
Statement Showing WACC
CiJpital Structure
I
Amount I Weights(W)
Costof WACC-LK-
w
'
(rln /akhs) I
Capltal(K)
-
Equity
100 I 0.25
16% 4%
Reserves
130 I 0.325
16% 5.2%
I
9.12% 1.596%
Debentures
70 j 0.175
I
0.25 8% 2%
Tenn Loan
100 I
Total
400 1.00
- 12.796%
IU..,alfon~at
Swan Ltd. has assets off 3,20,000 whidt has been financed
with t' 1,04,000 of debt, t' 1,80,000 of
equity and a genera/ reserve
oft' 36,000. The company's
total profit after interest and taxes for the year
ended 31.3.2021 were r 27,000. It pays 8% interest on borrowed funds and
is In the 30% tax bracket. rt
has 1800 equity shares of r 100 per share presently selling at a market price oft' 120 per share. What ;
5
the weighted average cost of capita/ of Swan Ltd.
Solution:
EPS =PAT/No.of equity shares= 27,000/1800 = f 15
Therefore, Cost of Equity= (EPSJMPS) = 15/120 = 12. 5%
Cost of Debt= Interestrate(l -Tax Rebate)= 8%(1-0.30) = 5.6%
Cost of Retained Earning = Cost of Equity= 12.5%

6. Statement showing WACC under Book Value
sources Amount(r)
Weights(W) Cost of WACC-. W.K
Capiti3I (K)
equltY 1,04,000
0.325 12.5%
4.06%
Retained Earning
36,000
0.113 12.5% 1.41%
oebt capital
1,80,000
0.562 5.6% 3.15%
rotal 3,20,000
1.00
- 8.62%
Statement of WACC under Market Value
sources Amount(()
Weights(W)
Costof WACC= W.K
Capital (K)
- 2,16,000 6.25% EqUitY
0.50 12.5%
Retained Earning
36,000
0.08 12.5 1.00%
pebt capital
1,80,000
0.42 5.6% 2.35%
Total
4,32,000 1.00
- 9.60% -
Note: Since market value of equity shares becomes~
2,16,000 (120 x 1800). So, increase in the value of equity shares by f 1, 12,000(2, 16,000 -1,04,000)
shall be treated as securities premium and
hence may be added to the value of reserves and surplus. Hence, the market value of Equity
Shares
and reserves & surplus may be taken as f 1,04,000 and~ 1,48,000 respectively while calculating
WACC
and Its weights(W) may change accordingly. But
as Ke and Kt are equal here, so overall cost of capital
(WACC) at market value is unaffected and remain 9.60%.
-•tM&
The capital structure of Bombay Traders Ltd. as on 31.3.2021 is as follows:
Equity capital: 100 lakh equity shares off 10 each
Retained earnings
14% debentures
~ incrores
10
2
3
For the year ended 31.3.2021 the company has paid a equity dividend at 20% and the growth rate
Is 5% every year. The equity shares are traded
at ~ 80 per share in the stock exchange.
Tax rate
applicable to the company is 40%. Calculate the current weighted average cost of capital.
Solution:
(a) Cost of equity capital
01 = 20(1 + 0.5)
Ke =
01
x 100 + G =
21
x 100 + 5 =26.25+5=31.250/o
MP 80
(b} Cost of debentures (after Tax)
Kd = J:....(1 -t) = 14 (1-0.4) = 8.4%
a NP
(c) Cost of retained earnings
Kr =k (1-t )(1-b)=31.25(1-04)(1-0)=31.25(0.6)=18.75
e P

7. Oomputatlon
of WACC
V" !IC
Wd{lht
r re-.
R (am 'lv
]4~0~!K'
t ~
JO
0 61
2
0 13
J
02
1S
~-·~-·. Kl !'l n um.:u~d wzs.~ to ralse edd ttonal finance oft' 20 lakh ror meeting Its
in
has,
4 70 000
tn the ram,
0
1 r:ctal!led cam ngs aV"a1lablc for Investment purpose 1
..,~unl!nt
, ,
s. hct P~
m ave? .lah;.c
Ollo""'ng <I!.
1, Oclr. /equJy mtx 30%: 70%
~
2. Cost of dclJt u:tu>, 3,60,000 - 10% (Before tax)
Costa' deot beyond, 3,60,000-16%
(Before tax)
3 E.am ngs per share: 4
,=, Oh dend payo;;t~ 50% of earnings
S E.Xt>ectedgrowttirateo1dMdend:
10%
6. Cument market p:i.ce: 44
7. Tax rate: 50%
Yov are required:
n) lo determine the
pattern for raisfng the additional finance.
b) To determine the post-tax average cost of additional cost.
c}
lo determine the cost of retained
earnings and cost of equity.
d) Compute the overall weighted average
after tax cost of additional finance.
Solution:
a) Pattern for raising the addltlonal finance
Dcbitors 30% off 20,00,000
= 6,00,000
Equlty70%
oft 20,00,000
= 14,00,000
20,00,000
The pattern of finanang
with costs
Sources
Amount(()
Debt
Debt
Retained earnings
Equity (14,00,000-4,20,000)
b) Poat tax average cost of additional debt:
Formula: Kd (1-t)
Kd • 3,60,000@ 10%
= 36,000
=
2.40,000@ 16% = 38,400
6,00,000
74,400
3,60,000
2,40,000
4,20,000
9,80,000
20,00,000
Cost
10%
16%

8. Cost II:?
7
4,1100
f>,oo,
000 x Joo 12..'1%
PoS
t
-tax aver c.1ge cost of debt • 12.4 (1-0 r>) 6. I%
c) cost of retained earn Inga:
D1
Ke"" R +g
o 10% Hcnc.~,atttie
The dividend
pay out ratio is 50% of~ 4 i.e. ~ 2.00 per share. Growth rate being .
end of the year, dividend wtll be-= t
2
+ l0% -~
2
.
20
2.20
Kr= 44 +O.lO==o.so+o.10-o.1sor1S%
d) weighted Average After tax cost of Add"tl
I
fl
1 ona nance:
-
sources Amount
Proportion
-
oebt 6,00,000 30.0%
Retained Earnings 4,20,000 21.0%
equity 9,80,000 49.0%
-
20,00,000 100
-
~n-27
MN Ltd. has the following capital structure:
Equity share capital (20,000) shares , 40,00,000
10% Preference share capital
t 10,00,000
14% Debentures
t 30,00,000
80,00,000
WACC
After tax cost
0.3 X 6.2-l.86
6.2%
15.0%
0.21
X 15=3.15
15.0%
0.49
X 15""'7.35
12.36
The share of the company sells fort 20. It is expected that the company will pay next year a
dividend oft 2 per share which will grow at 7% forever. Assume 50% tax rate.
a) Compute the weighted average cost of capital based on the existing capital structure.
b) Compute the new Weighted Average Cost of capital if the company raises an additional t
20,00,000 debt by issuing 15% debentures. This would increase the expected dividend to~ 3 and
leave the growth rate unchanged but the price of share will fall tot 15 per share.
Solution:
(a) WACC: Existing Capital Structure:
After-tax cost Weights Weighted Cost
Ordinary 0.17* 0.500 0.0850
10% Preference 0.10 0.125 0.0125
14% Debentures 0.07 0.375 0.0262
WACC 0.1237
or12.37%
*Cost of ordinary share is:
ke = (DIVl/Po) + g = (2/20) + 0.07 = 0.17

9. (b) W~CC: NewC.pltalStnlcture:
After- Weights
Weight;;
tax cost
Amounts
______ J--:-:-:-:::::--t--;:;:-:;:;;:--1-~~1--~Cost
Ordinary 40,00,000 0.27* 0.40
0,108
10% Preference
10,00,000
O.lO
O.lO 0,01
0
14% Debentures
30,00,000
o.o
7 o.
3
o 0,02
1
~----1:.::.S...:%:...:D:::.:e::b.:en:t:ure=.s
__ ..L_...:2::.:o::,o:....o.:..,o_o_o_...1---o-._o
7
_
5
_
__._ ___ o_._
20
_t-__ o.a15
WACC
0,1S4
--------------------------..L-._o_r1s,4%
*Cost of ordinary
share Is.
ke = (DIVl/Po) + g = (3/15) + 0.07 = 0.20 + 0.07 = 0.27
m,,~
Klshan Limited wishes to raise additional finance of?
20 lakh for meeting its investment
pl
ans It
has, 4,20,000 In the form of retained earnings available for Investment purposes.
The following d ·
are available.
etaus
1. Debt/ equity mix 30%: 70%
2. Cost of debt upto t 3,60,000-10% (Before tax)
Cost of debt beyond t 3,60,000 -16% (
Before tax)
3. Earning per share: 4
4.
Dividend payout:
50% of earning
5. Expected growth rate of dividend:
10%
6. Current market price:
44
7. Tax rate: 50%
You are required:
a) To determine the pattern for
raising the additional finance.
b) To determine the post-tax
average cost of additional cost.
c) To determine the cost of retained earnings
and cost of equity.
d) Compute the overall weighted average after tax cost
of additional finance .
•
Solution:
a) Pattern for raising the additional finance:
Debitors 30% on 20,00,000
Equity 70% on 20,00,000
The pattern of financing
with costs
Source
Debt
Debt
Retained earnings
Equity (14,00,000 -4,20,000)
Amount(()
3,60,000
2,40,000
4,20,000
9,80,000
20,00,000
= 6,00,000
= 14,00,000
20,00,ooo
-
Cost
10%
16%

10. b) Post tax average cost of additional debt:
Formula: Kd (1-t)
Kd = 3,60,000@
10% = 36,000
= 2,40,000 @
16% = 38,400
6,00,000
74,400
74,400
Cost= G,O0,000 X 100 = 12.4%
Post-tax average cost
of debt = 12.4 (1-0.5) = 6.2 %
c) Cost of retained earnings:
D1
Ke= Po+g
Toe dividend pay
out ratio is 50% oH 4 i.e., 2.00 per share. Growth rate being 10%.Hence,
at the
end of the year, dividend will
be=, 2+10% = 2.20
2.20
Kr=
44
+0.10 = 0.50+0.10 = 0.15 or 15%
d) Weighted Average
After tax cost of Additional finance:
sources
Amount Proportion
A~er tax cost
WACC
Debt
6,00,000 30.0% 6.2% .3x6.2=1.86
Retained Earnings 4,20,000 21.0% 15.0% .21x15=3.15
Equity
9,80,000 49.0% 15.0% .49x15=7.35
20,00,000 100 12.36
As a financial analyst of a large electronics company, you are required
to determine the weighted
average cost of capital (WACC)
of the company using
(a) book value weight and(b)
market value
weights. Toe following
information
is available for your perusal:
The company's present books value capital structure is
Preference shares
Cf 100 per share) f 2,00,000
Equity shares
c, 10 pershare) , 10,00,000
Debentures
(f 100 per share) f 8,00,000
Anticipated external financing opportunities are:
(I) , 100 per debenture redeemable
at par; 10 years maturity,
13% coupon 4% flotation costs, sale
price~ 100
(ii) , 100 preference shares redeemable
at par; 10 years maturity; 14% dividend rate,
5% floation
costs, sale price t 100.
(iii) Equity shares;, 2 persharefloation
costs, sale price
att' 22.
In addition, the dividend expected on
the equity shares at the end of current year is f 2 and the
eamingsareexpected
to increase by7% p.a. The firm has policy of paying all its ea ming sin the form of dividends. the company's corporate tax rate is 50%.

11. Solllf:ion:
f
I{i-t)-il_
Cost of debt (kd) = F·, · S'J
2
4
13{1-0.5)-;-;;-
L ~ 6.5-0~ -~
iOO -96
2
i(d = 7.04%
F
D-~
Cost of pref shares (kp) = Fv -SV
2
Kp= 14.87%
= 58 -98
= 100-95
2
3-·G -
2 -0 07 = o.:-0.07
Cost of Equity (ke) = Po -F -- (22 -2; ·
Ke = 0.17 or 17%
WACC using book value weight
Capital
Cost
Boolc-1a i..S
I
8,0G,000
Debt entry 7.04%
8,00,000
7.04X 2C.C0,03:
2,c:,eoo
Shares 14.87% 2,00,000
14
·
82 x 2C.GC,ODO
:0,00,000
Equity Shares 17% 10,00,000 17 x 20,00,oon
WACC using book value is 12.803
-
= 2.6:5
=: .!-S/
=55
WAW using market value weight cannot
be calculated as mari<e: va, ... e o--:ec-e-:-_:'E =-:
preference shares is not available in the question.
Illustration -30
From the following capital structure
of a company, calailate the overall
cost of ca:,~ -S -; :
i) Book value weights and
ii) Market value weights.
Source Book value
Man<.e~ r'c.t. e
Equity share
capita1 (~ 10 shares) ~ 45,000 ? 9C.J00
Retained earnings
~ 15,000 ~ :.
Preference share capital ~ 10,000 f 10,00J
Debentures
t 30,000 ~ 30,000
The after tax cost of different source of finance is as follows : Equity snare ca:,i taf l .!% ~er= -e,.:
earnings 13% preference capital 10%. Debentures 5%

12. SOiution:
I) overall cost of ca
1
P tal using Book value weights
securities
Equity
Retained earnings
preference share capital
Debentures
Weighted average cost
Proportion
45
15
10
30
After tax(%)
14
13
10
5
II) overall cost of capital using Market value weights
securities Proportion
~~~ 69
Retained earnings
preference share capital
Debentures
~~•31
7.6
23
After tax(%)
14
13
10
5
WACC
45 X 0.14 ==
6.3
1Sx0.13 ==
1,95
10 X 0.10 ==
1
30 x0.05 ==
LS
10.75
WACC
9.66
0.76
1.15
11.57
Alpha Ltd. has the following capital structure as per its Balance Sheet as at 31.3.2021:
Equity share capital (fully paid share of~ 10 each)
18% Preference share capital (fully paid share oft 100 each)
Reserves and surplus
12.5% debentures (fully paid debenture oft 100 each)
12% term loans
Additional information:
Inlakhs
8
6
2
16
8
40
a) The current market price of the company's share is ~ 64.25. The prevailing default risk free
interest rate on 10 yearGOI treasury bonds isS.5%. The average market risk premium is 8%. The
beta of the company ls 1.1875.
b) The preference shares of the company which are redeemable after 10 years are currenty se11ing
at 90 per preference share.
c) The debentures of the company which are redeemable after 5 years are currently quoted at 90 per
debentures.
d) The corporate tax rate is 30%.
Rtquireci:
Calculate weighted average cost of capital using
I) Book Value Weights,
Market Value Weights

13. Solution:
w ( ACC using
book value weights)
Sources of
Amountof Proposition
After tax cost
Cap{t.a/
Sources of sources
of sources
A
B C
D
Equity share capital
8 0.20
0.1500
Reserve and Surplus
2 0.05
0.1500
18% Preference shares
6 0.15 0.2000
12.5% Debentures
16 0.20 0.1000
12% Term loan
8 0.20 0.0840
40 1.00
-Weighted average cost of capital - 0.1243 or 12.43%
(WACC using market value weights)
Sources of Amountof Proposition After tax cost
Capital
Sources of sources of sources
A
B C D
Equity share capital 51.40 0.6425 0.1500
18% Pref. share capi tal 5.40 0.0675 0.2000
12.5% Debentures 15.20 0.1900 0.1000
12%
Term loan 8.00 0.1000 0.0840
80 1.00
Therefore, 13.72%
(i) Cost of equity (ke) = Ri + ~ (Average market risk)
= 5.5% + 1.875 (8%) = 15%
(ii) Cost of retained earnings (kr) =Ke= 15%
(iii) Cost of 18% preference share
= Preference dividend +(Reedemable value -Net sale proced)/w
(Redeemable value + Net sale proced)/2
18 + (100 -90) / 10 18 + 1
= (100-+ 90) I 2 = 95 = 0.20 or20%
(iv) Cost of 12% term loan
Interest
(1-Tax rate)
= Net
sale proceeds
96,000 (1 -0.30)
= 8,00,000 = o.oa
4
Product
E=CxD
0.0300
0.0075
0.0300
0.0400
0.0168
Product
~
E=CxD
0.09637
~
0.0135
0.0190
0.0084
You are required to determine the weighted average cost of capital of M/s Vinayaka Enterpri ses
Ltd., Bengaluru using
(i) Book Value Weights
(ii) Market Value Weights. The company's present book value capi
tal structure is

14. Amount (t')
Debenture (t 100 per debenture) 16,00,000
preference shares
(t 100 per share)
4,00,000
Equity shares(? 10 per share) 20,00,000
All these securities are traded in the capital markets. Recent prices are Debentures
at f 110,
preference shares at t 120 and equity shares at' 22. Anticipated external financing opportunities are
i)
t 100 per debenture redeemable
at par, 10 years maturity,
8
% coupon rate,
4% floatation cost,
sale pricer 100.
fi) t 100 preference shares, redeemable
at par, 15 years maturity, l0% dividend rate, 5% floatation
cost, sale price t 100.
i
ii) Equity shares'
2
per share floatation cost, sale price
t 22. In addition the dividend expected on
equity share
at the end of the year t 2 per share, the anticipated growth rate in dividends is
5%.
The tax rate is 50%.
soJution:
1
Kd==
8
+
20 (100 -96) 8.2
.!:_ (100 - 96) = 98
2
x
l00 = B.36% = 4.18% aftertax
10 + 0.33
10 + is (100 -95)
Kp== ! (100 + 95)
=---= 10.5%
2
2
Ke
- -X 100 + 5 = 15%
-20
sources
Debtors
Preference Shares
Equity Shares
Sources
Debtors
Preference Shares
Equity Shares
97.S
Book Value
Amount Proportion
6,00,000 40%
4,00,000
10%
20,00,000 50%
40,00,000
Market Value
Amount Proportion
8,80,000 15.9
2,40,000 4.3
44,00,000 79.7
55,20,000
After tax cost
11
10.5
15
WACC
After tax cost
4.18
10.5
15
WACC
Weighted cost
1.672
1.05
7.5
10.22%
Weighted cost
0.66
0.45
11.9
13.065%