Ch.

9: The Cost of Capital

CHAPTER 9

THE COST OF CAPITAL

Problem 1

Face value (Rs) 1000

Before-tax Interest (Rs) 14% 140
Period (years) 7
Discount 3% 30
Underwriting 3% 30
Premium (Rs) 30
Tax 35%
After-tax interest (Rs) 91
Cash inflow (face value less discount & 940
underwriting commission)
Cash inflow (face value plus premium less 1000
underwriting comm.)
Yearly discount write-off 4.29
Tax saved on discount write-off 1.50
Yearly underwriting comm. write-off 4.29
Tax saved on underwriting comm. write-off 1.50
Yearly premium income 4.29
Tax on premium 1.50

ATINT Tax saved Tax saved Tax on Discount Premium

Year outflow discount on under-writing comm. Premium NCF NCF
0 940 1000
1 -91 1.50 1.50 -1.50 -88 -91
2 -91 1.50 1.50 -1.50 -88 -91
3 -91 1.50 1.50 -1.50 -88 -91
4 -91 1.50 1.50 -1.50 -88 -91
5 -91 1.50 1.50 -1.50 -88 -91
6 -91 1.50 1.50 -1.50 -88 -91
7 -91 1.50 1.50 -1.50 -1088 -1091
7 Year 7 cash flows include repayment -1,000 -1,000
After-tax cost of debenture 10.03% 9.10%

Debenture issued at discount

7

∑ (1 + k
88 t 1,000
940 = t
+
t =1 d ) (1 + k d ) 7
k d = 10.03%

Debenture issued at premium

7

∑ (1 + k
91t 1,000
940 = t
+
t =1 d ) (1 + k d ) 7
k d = 9.10%

1
I. M. Pandey, Financial Management, 9th Edition, New Delhi: Vikas.

Problem 2

Rs million
Face (and maturity) value 2.0
Net proceeds 1.8
Interest 13.5% 0.27
Period (years) 7
Tax rate 52%
Market value after 4 years 2.2
After-tax interest: 0.27 (1 - 0.52) 0.13
After-tax interest cost 8.43%
After-tax yield after 4th year 2.95%

After-tax cost of debenture:

7

∑ (1 + k ) + (1 +2k.0 )
0.13t
1 .8 = t 7
t =1 t d
After − tax cost = 8.43%

After-tax yield at the end of 4th year:

3

∑ (1 + k ) + (1 +2k.0 )
0.13t
2.2 = t 3
t =1 t d
After − tax cost = 2.95%

Problem 3

Face value 100

Dividend, DIV 9.75% 9.75
Current market price, P 80
Cost of preference capital, DIV/P = 9.75/80 12.19%

Problem 4

Current market price, P0 25

Book value, B0 18
EPS0 3.6
DIV0 1.44
Retention ratio: (EPS0 - DIV0 )/EPS0 60%
ROE: EPS0/B0 20%
Growth, Retention ratio x ROE 12%
Expected dividend: DIV1 1.61
DIV1 1.61
Cost of equity: +g= + 0.12 18.45%
P0 25

2
Ch. 9: The Cost of Capital

Problem 5

Current market price, P0 96

Book value, B0 65
EPS0 10
DIV0 7
Net issue price, I0 80
ROE, EPS0/B0 15.4%
Retention ratio: (EPS0-DIV0)/EPS0 30%
Growth: Retention ratio x ROE 4.6%
DIV1 7.32
DIV1 7.32
Cost of new issue: +g= + 0.046 13.8%
I0 80

Problem 6

DIV 3
Current market price, P0 33
Cost of equity: DIV/P0: 3/33 9.1%

It is a no-growth share.

Problem 7

Year 1 2 3 4 5 6
DIV 2.00 2.20 2.42 2.66 2.93 3.22
Growth - 0.10 0.10 0.10 0.10 0.10

Growth in dividend 10%

Current market price, P0 150
Expected dividend next year, DIV1 3.55
Issue price, I0 140
Flotation cost per share 10
DIV1 3.55
Cost of equity (including flotation cost): +g= + 0.10
(I 0 − f ) 140 − 10
12.7%
DIV1 3.55
Cost of equity (ignoring flotation cost): +g= + 0.10
I0 140
12.5%
Theoretically, it is appropriate not to adjust floating cost in the calculation of the cost of equity. Rather, this cost should
be adjusted to the initial cost of the investment project.

Problem 8

BV Weight MV Weight Cost of Weighted cost

(Rs mn.) (wb) (Rs mn.) (wm) capital Book-value Market-value
Ordinary shares 30.0 0.30 60.0 0.50 0.1500 0.045 0.075
Reserves 10.0 0.10 0.1500 0.015
Preference share 20.0 0.20 24.0 0.20 0.0976 0.020 0.020
Debt 40.0 0.40 36.0 0.30 0.1069 0.043 0.032
Total capital 100.0 1.00 120.0 1.00 WACC 0.122 0.127
12.2% 12.7%

3
I. M. Pandey, Financial Management, 9th Edition, New Delhi: Vikas.

Tax rate 35%

Face value of debenture, F 1000
Underwriting commission, c 20
Net proceeds from debenture issues, I = 1,000 - 20 980
Interest rate 16%
Interest on debenture, INT = 1,000 x 16% 160
Period (years), N 20
Before-tax cost
INT + 1 7 ( F − I) 160 + 17 (1,000 − 980) 16.45%
= 1 ( F + I)
= 1 (1,000 + 980)
2 2
After-tax cost, 0.1645(1-0.35) 10.7%
Face value of preference share, F 100
Issue price , I 120
Underwriting commission, c 7.25
Net proceeds from preference issues, I 112.75
Preference dividend rate 11%
Preference dividend, PDIV 11
PDIV 11 9.8%
Cost of pref. Share = =
I 112.75
Current price of ordinary share, P0 150
DIV1 12
Growth 7.0%
Issue price, I0 145
Flotation cost, f 5
Net proceeds, 145 - 5 140
Cost of retained earnings:
DIV1 12
+g= + 0.07 15.0%
P0 150
Cost of new issue of share:
DIV1 12
+g= + 0.07 15.6%
(I 0 − f ) (145 − 5)

Problem 9

(a) Cost of debenture:

Tax rate 35.0%

Current market price of debenture 950
Face value of debenture 1,000
Interest on debenture 10.0% 100
Remaining period (years) 5

100 100 100 100 1,100

950 = + + + +
1 2 3 4
(1 + k d ) (1 + k d ) (1 + k d ) (1 + k d ) (1 + k d )5
k d = 0.114 or 11.4%
After - tax cost of debenture = 0.114(1 - 0.35) = 0.074 or 7.4%

4
Ch. 9: The Cost of Capital

(b) Cost of preference share

Current market price of preference. P0 60

Preference dividend, PDIV 6
Cost of preference, kp =PDIV/P0 10.0%

(c) Cost of equity

Growth in dividend, g:

Annual
Year DIV Growth
1 2.00 -
2 2.16 0.080
3 2.37 0.097
4 2.60 0.097
5 2.80 0.077
6 3.08 0.100
7 3.38 0.097
8 3.70 0.095
Average 0.092

Alternatively, dividend growth can be calculated as a geometric average follows:

1/ 7
 3.70 
g=  − 1 = 0.092
 2.00 
Current market price of equity, P0 50
Current dividend, DIV0 3.70
Dividend growth 9.2%
Expected dividend, DIV1 = 3.7(1.092) 4.04
4.04 17.3%
Cost of equity: + 0.092
50

(d) Weighted average cost of capital:

(Rs 000) Weight (w) Cost (c) wxc

Debenture 500 0.333 0.074 0.0246
Preference 400 0.267 0.100 0.0267
Ordinary share 600 0.400 0.173 0.0691
Total 1500 1.000 0.1204
WACC 12.0%

Problem 10

Investor's opportunity cost

Expected return 0.18
Tax rate 0.30
Brokerage 0.03
Funds available after brokerage, (1 - 0.03) 0.97
After-tax return from reinvestment, 0.18 x 0.97 x (1 - 0.30) 0.122
Firm's opportunity cost 0.120

Since the investor’s opportunity cost is higher, dividends maybe distributed.

5
I. M. Pandey, Financial Management, 9th Edition, New Delhi: Vikas.

Problem 11

Market price of ordinary share (Rs) 25

Expected DIV (Rs) 1.50
Growth 0.10
150
.
Cost of internal equity (retained earnings): + 0.10 0.16
25
Issue price of ordinary equity (Rs) 22
150
.
Cost of equity (new issue): + 0.10 0.168
22
Issue price of preference share (Rs) 23
Flotation cost (Rs) 3
Net proceeds from pref. share issue (Rs), [23 - 3] 20
Preference dividend (Rs) 2
2
Cost of preference: 0.10
20
Cost of debt 0.17
Tax rate 0.50
After-tax cost of debt: 0.17(1 - 0.5) 0.085
Retained earnings (Rs 000) 700
Equity weight 0.7500
Investment before new equity (Rs 000), [700/0.75] 933.33
Investment planned (Rs 000) 1,000

Retained earnings New Issue

Source of capital Amount Weights (w) Cost ( c ) w x c Cost ( c ) w x c
14% Debt (Rs mn.) 93.75 0.1875 0.085 0.016 0.085 0.016
10% Preference (Rs mn.) 31.25 0.0625 0.10 0.006 0.100 0.006
Ordinary equity (Rs mn.) 375.00 0.7500 0.16 0.120 0.168 0.126
Total capital (Rs mn.) 500.00 1.0000 WACC 0.142 0.148

The firm will have to issue new equity share to finance its funds requirement in excess of Rs 933,333.

Problem 12

Current equity share price (Rs) 36

Expected dividend, DIV1 (Rs) 3.60
Growth, g 0.08
3.60
Cost of equity: + 0.08 0.1800
36
Preference dividend (Rs) 10
Market price of irredeemable preference share (Rs) 81.81
10
Cost of irredeemable preference share: 0.1222
8181
.
Market price of redeemable preference share (Rs) 93
Remaining maturity of redeemable preference share 7
Cost of redeemable preference share:
10 10 10 10 10 10 110
93 = 1
+ 2
+ 3
+ 4
+ 5
+ 6
+ 7
(1+ kp ) ( 1+ kp ) ( 1+ kp ) ( 1+ kp ) (
1+ kp ) (1 + k ) (1 + k )
p p

k f = 0.1151 or 11.51%

6
Ch. 9: The Cost of Capital

Before-tax cost of term loan 0.14

Tax rate 0.35
After-tax cost of term loan: 0.14(1 - 0.35) 0.91

Weighted average cost of capital (WACC):

Source of capital (Rs mn) Weight (w) Cost (c) WACC

Equity capital 563.50 0.3729 0.1800 0.06713
Reserve & surplus 485.66 0.3214 0.1800 0.05785
10% Irredeemable pref. share 56.00 0.0371 0.1222 0.00453
10% Redeemable pref. share 28.18 0.0186 0.1151 0.00215
12% Term loan 377.71 0.2500 0.0910 0.02275
Total capital 1511.05 1.0000 0.1544
15.44%

Problem 13

Growth in dividends:

Year Y y = (Y-5.5) EPS ln EPS y x ln EPS y2

1 1 -4.5 2.24 0.80648 -3.6291 20.25
2 2 -3.5 3.00 1.09861 -3.8451 12.25
3 3 -2.5 4.21 1.43746 -3.5937 6.25
4 4 -1.5 3.96 1.37624 -2.0644 2.25
5 5 -0.5 4.80 1.56862 -0.7843 0.25
6 6 0.5 4.40 1.4816 0.7408 0.25
7 7 1.5 5.15 1.639 2.4585 2.25
8 8 2.5 5.05 1.61939 4.0485 6.25
9 9 3.5 6.00 1.79176 6.2712 12.25
10 10 4.5 6.80 1.91692 8.6262 20.25
Avg. y = 5.5 ∑ = 8.2285 ∑ = 82.5000

ln (1+g) = 8.228/82.85 = 0.09974

(1+g) = 1.10488
g, (growth) = 1.10488 - 1 = 0.10488 or (approx.) 10.5%

Market value per equity share (Rs) 50

Equity dividend (Rs) 4
Expected equity dividend (Rs), DIV1 4.42
Cost of equity: (4.42/50) + 0.105 0.193
Face value of preference (Rs) 100
Market value per preference share (Rs) 77.50
Pref. dividend rate 0.10
Pref. dividend (Rs) 10
Cost of preference share: 10/77.5 0.129
Long-term debt interest rate 0.140
Tax rate (assumed) 0.350
After-tax cost of long-term debt: 0.14(1 - 0.35) 0.091
Debenture interest 0.130
After-tax cost of debenture: 0.13(1 - 0.35) 0.085

7
I. M. Pandey, Financial Management, 9th Edition, New Delhi: Vikas.

Weighted average cost of capital:

Amount
Source of capital (Rs 000) Weight (w) Cost (c) wxc
Equity (Rs 25 par) 66412 0.3906 0.193 0.075
Reserves 65258 0.3838 0.193 0.074
Preference (Rs 100) 3000 0.0176 0.129 0.002
Debentures 30000 0.1764 0.0845 0.015
Long-term debt 5360 0.0315 0.091 0.003
Total capital 170030 1.0000 WACC 0.170
17.0%

Problem 14

Year EPS DPS AMP ROE Retention Growth Div. yield BV

(6) (7) (5 (8) (9)
(1) (2) (3) (4) (5) [(2-3)/2] x 7) (3/5) (2/5)
1 21.55 5.28 143.04 0.209 0.755 0.158 0.0369 103.11
2 22.14 5.76 187.52 0.186 0.740 0.138 0.0307 119.03
3 26.40 5.76 312.32 0.117 0.782 0.091 0.0184 225.64
4 20.16 6.53 587.52 0.110 0.676 0.074 0.0111 183.27
5 20.40 7.68 366.72 0.095 0.624 0.059 0.0209 214.74
6 23.09 11.53 416.64 0.103 0.501 0.052 0.0277 224.17
7 22.00 7.68 355.20 0.084 0.651 0.055 0.0216 261.90
Average 22.25 7.17 338.42 0.129 0.6754 0.0895 0.0239 190.27

Calculating growth rate:

(1) Internal growth: The average growth in dividend is 8%: g = ROE x Retention = 0.116 x 0.675 = 0.08 or 8%.
(2) The regression approach: This approach applied to dividend per share (DPS), gives a growth of 10.5%.

Avg./Sum
Y (year) 1 2 3 4 5 6 7 4
(Y - 4) = y -3 -2 -1 0 1 2 3
DPS 5.28 5.76 5.76 6.53 7.68 11.53 7.68
ln DPS 1.664 1.751 1.751 1.876 2.039 2.445 2.039
y x ln DPS -4.992 -3.502 -1.751 0.000 2.039 4.890 6.116 2.800
y2 9 4 1 0 1 4 9 28.000
ln (1+g) 2.8/28.0 = 0.09999
(1+g) 1.10516
g 1.10516 - 1 = 0.10516 or approx. 10.5%

Similar approach gives a negative growth for EPS (- 4%).

(3) Geometric (average) growth:
1/ 6
 7.68 
g=  − 1 = 0.066 or 6.6%
 5.28 
Different methods give different growth rates. Since the regression approach provides objective estimates, we use
10.5% as the growth rate.

Cost of equity:
DIV1 7.68(1105
. )
ke = +g= + 0.105
P0 355.20
k e = 0.129 = 12.9%

8
Ch. 9: The Cost of Capital

Cost of debt:
Interest rate 0.11
Tax rate 0.50
After-tax cost of debt 0.11(1 - 0.5) = 0.055 or 5.5%

Weighted average cost of capital:

BV BV BV MV MV MV
(Rs weights Cost WACC (Rs weights Cost WACC
million) million)
Share capital 6,808 0.012
Reserve 34,857 0.060
Net worth 41,665 0.072 12.9% 0.009 104,726 0.163 12.9% 0.021
Long-term loans 538,220 0.928 5.5% 0.051 538,220 0.837 5.5% 0.046
Total capital 579,885 1.000 0.060 642946 0.067

Share capital 6,808

EPS in 2003 22
Number of shares: 6,808/22 309
Average market price of share in 2003 338.42
Market value of equity (Rs million) 104726

Problem 15

Div. Earn.
Year EPS DPS BV AMV ROE Payout Retention Growth yield yield
(6) (7) (8) (9) (10) (11)
1 2 3 4 5 (2/4) (3/2) (1-7) (6 x 8) (3/5) (2/5)
1 6.21 2.00 26.03 100.00 0.239 0.322 0.678 0.162 0.020 0.062
2 10.91 2.50 34.44 205.00 0.317 0.229 0.771 0.244 0.012 0.053
3 11.57 2.50 43.52 209.38 0.266 0.216 0.784 0.208 0.012 0.055
4 11.47 2.70 37.98 164.00 0.302 0.235 0.765 0.231 0.016 0.070
5 10.44 3.00 45.42 138.88 0.230 0.287 0.713 0.164 0.022 0.075
6 11.23 3.20 53.45 155.00 0.210 0.285 0.715 0.150 0.021 0.072
Average 10.31 2.65 40.14 162.04 0.261 0.262 0.738 0.193 0.017 0.065

Cost of equity:
g Avg. ke
yield
Average Growth (retention x ROE) 0.193 0.017 0.210
Growth =[( DPS91/DPS85)1/5 -1] 0.099 0.017 0.116
Growth =[( EPS91/EPS85)1/5 -1] 0.126 0.017 0.143

9
I. M. Pandey, Financial Management, 9th Edition, New Delhi: Vikas.

CASES
Case 9.1: Hindustan Lever Limited

This case illustrates the calculation of the cost of capital in a real situation. The instructor should highlight the
alternative methods of calculating cost of equity - the dividend growth model and the CAPM. The frameworks
underlying these methods, their assumptions and pros and cons should be discussed. The case would also require the
instructor to explain the sources of information needed to use the CAPM and calculation of beta. Theoretically, market
value weights should be used to calculate the WACC. The reasons for using the book value weights may be explained.

Book Market
CAPM: value value
Risk free rate 12.5% Debt (Rs million) 1866 1866
Risk premium 9% Equity (Rs million) 12615 27555
Equity beta 0.8979 Total value 14481 29421
Cost of equity 20.2% Debt ratio 12.9% 6.3%
Pre-tax cost of debt 14% Equity ratio 87.1% 93.7%
Tax rate (assumed) 35%
Post-tax cost of debt 9.1%
WACC:
Book value weights 18.8%
Market value weights 19.5%

Dividend-growth model: Payout

Payout 60% 1997 60.4%
Retention ratio 40% 1996 60.1%
Market capitalisation (Rs crore) 27,555 1995 61.0%
Market value per share (Rs) 1,383.5 1994 61.0%
Number of shares 19.9 27,555/1383.5 1993 61.6%
EPS 28.1
Net worth (Rs crore) 1,261.5
Book value per share 63.3 1,261.5/19.9
ROE 44.4% 28.1/63.3
Dividend growth 17.8% 40% x 44.4%
DPS (Rs) 17.0
Expected DPS 20.0
Current share price 1383.50
Expected dividend yield 1.4%
Cost of equity 19.2%
WACC:
Book value weights 17.9%
Market value weights 18.6%

10
Ch. 9: The Cost of Capital

Case 9.2: Solidaire Infrastructure Company

This case is intended to discuss the methodology of calculating the divisional cost of capital. The data of proxy firms
are used to calculate divisional costs of capital. The points to be highlighted are: the unlevering and relevering of beta,
determining the appropriate capital structure for the divisions and calculating divisional WACC. In this case, the Power
division does not have a comparable firm. It is assumed that firm’s unlevered beta would be equal to the weighted
average of the divisions’ unlevered betas. Thus, the Power division’s unlevered beta is calculated as the difference
between the firm’s unlereved beta and weighted betas of two divisions. Using the Power division’s target capital
structure the levered beta and the cost of equity are calculated. This approach assumes that the firm’s WACC should be
equal to the weighted average of the divisional costs. This need not be so in practice because of the positive or negative
synergies. There is a question of the appropriate weights. Theory does not provide much guidance here. Perhaps market
or book value of assests may be preferred if the information is available.

(Rs in million)
Cement Fertiliser Power Solidaire
Sales 700 450 350 1,500
PAT 29 17 24 70
Assets 550 230 420 1,200
Current assets 210 100 20 330
Equity (Market value) 1,000
Debt 1,800

(Rs in million)
Kisan Camel
Fertilisers Cement
Sales 550 850
PAT 23 41
Assets 320 700
Current assets 140 300
Market Value of Equity 150 320
Debt 220 650
Equity beta 1.2 1.36

Risk-free rate 5.6%

Risk premium 9.8%
Average market return 17.6%
Average risk-free rate 7.8%
Company
Company equity beta 1.500
Current market value debt ratio: 1.8/2.8 64.3%
Unlevered beta: Equity beta x (1-debt ratio) 0.536
Target debt ratio: 2.5/3.5 71.4%
Levered beta: Unlevered beta/(1-debt ratio) 1.875
Cost of equity: 5.6% + 9.8% × 1.875 24.0%
After cost of debt 8.0%
WACC 12.6%
Fertiliser Division
Leveraged beta of comparable firm 1.200
Debt ratio of comparable firm 59.5%
Unlevered beta for comparable firm 0.486
Fertiliser Division's target debt ratio 66.7%
Fertiliser division's levered beta 1.459
Cost of equity 19.9%
After-tax cost of debt 8.0%
WACC 12.0%

11
I. M. Pandey, Financial Management, 9th Edition, New Delhi: Vikas.

Cement Division'
Leveraged beta of comparable firm 1.360
Debt ratio of comparable firm 67.0%
Unlevered beta for comparable firm 0.449
Cement Division's target debt ratio 71.4%
Cement division's levered beta 1.570
Cost of equity 21.0%
After-tax cost of debt 8.0%
WACC 11.7%
Power Division
Power Division's unlevered beta 0.677
Target debt ratio 80.0%
Levered beta 3.383
Cost of equity 45.2%
After-tax cost of debt 8.0%
WACC 15.4%

Power Division's unlevered beta =

[Firm’s unlevered beta – (fertiliser’s unlevered beta × fertiliser’s assets/firm’s assets + cement’s unlevered beta ×
cement’s assets/firm’s assets]/ power’s assets/firm’s assets

12