Financial Management - Cost of Capital

 

FINANCIAL MANAGEMENT

COST OF CAPITAL

 

Part A: Discussion of basic theories including different formulas and useful tables

Part B: 10 Illustrations with solutions

Part A

Definition of cost of capital

Cost of capital refers to the discount rate that is used in determining the present value of the estimated future cash proceeds and eventually deciding whether a project is worth undertaking or not. In other words, cost of capital is defined as the minimum rate of return that a firm must earn on its investments for the market value of the firm to remain unchanged.

 

Computation of specific cost of various components of capital

The specific costs have to be computed for –

1. Equity share capital,

2. Preference share capital.

3. Debt capital (including debentures and long-term bank loans), and

4. Retained earnings (i.e. Reserves and Surplus).

 

COST OF EQUITY SHARE CAPITAL

There are three approaches that can be employed to calculate the cost of equity share capital:

1. Dividend approach,

2. Earning approach, and

3. Capital asset pricing model (CAPM) approach.

 

Dividend approach

A. IN CASE OF EXISTING EQUITY SHARES

(i)         

ke	=  [D1 (1 + Td) ÷ P0] + g

 

    Where,

D1	= Expected dividend per share at the end of current year
Td	= Dividend distribution tax rate
P0	= Current market price per share (ex-dividend)
g	= Expected annual growth rate in dividend = b × r
b	= Retention Ratio
r	= Rate of Return on Equity
D1	= D0 [1 + g]
D0	= Actual dividend per share at the end of previous year

 

(ii)

ke	= [{E1 (1 – b) (1 + Td)} ÷ P0] + g

 

    Where,

E1	= Expected earnings after tax per share
b	= Expected rate of retention of earnings after tax

 

B. IN CASE OF NEW EQUITY SHARES

(I)

ke	= [D1 (1 + Td) ÷ SV] + g

 

    Where,

SV	= Proceeds from the issue of shares – Flotation cost

 

Note:    Flotation cost is calculated by applying flotation cost percentage on the face value or issue price whichever higher, if the flotation cost percentage is given instead of the absolute amount of flotation cost.

 

    (ii)

ke	= [{E1 (1 – b) (1 + Td)} ÷ SV] + g

 

Earning approach

A. IN CASE OF EXISTING EQUITY SHARES

 

ke	= (E1 ÷ P0) + g

 

    Where,

g	= Expected annual growth rate in earnings

 

B. IN CASE OF NEW EQUITY SHARES

 

ke	= (E1 ÷ SV) + g

 

    Where,

g	= Expected annual growth rate in earnings

 

Capital asset pricing model (CAPM) approach

 

ke	= Rf + β (Rm – Rf)

 

    Where,

Rf	= The rate of return on a risk-free capital asset or investment    like the Treasury Bill / Government Bonds
Rm	= The expected rate of return on the market portfolio of capital asset/security/investment (i.e. average rate of return on all the capital assets/securities/investments in the market portfolio)
β	= The beta coefficient

 

Note – What is beta (β):

Beta is a measure of the volatility of a security’s return relative to the returns of a broad-based market portfolio. Alternatively, it is an index of the degree of responsiveness or co-movement of return on an investment with the market return.

 

The beta for the market portfolio, as measured by the broad-based market index, equals 1. A beta coefficient of 1 of a security would imply that the risk of the specified security is equal to the risk of the market. The interpretation of zero beta coefficients is that there is no market-related risk to the specific investment. A negative beta coefficient would indicate a relationship in the opposite direction.

 

COST OF PREFERENCE SHARE CAPITAL

Cost of preference share capital may be calculated for two different types of preference shares:

1. For perpetual preference shares, and

2. for redeemable preference shares

 

For perpetual preference shares

A. IN CASE OF EXISTING PREFERENCE SHARES

 

Kp	= d (1 + Td) ÷ MV

 

    Where,

d	= Annual dividend per preference share
MV	= Current market price per preference share (ex-dividend)

 

B. IN CASE OF NEW PREFERENCE SHARES

 

Kp	= d (1 + Td) ÷ SV

 

    Where,

SV	= Proceeds from the issue of preference shares – Flotation cost

 

For redeemable preference shares

A. IN CASE OF EXISTING PREFERENCE SHARES

 

Kp	[d (1 + Td) + 1/N (RV – MV)] ÷ [½ (RV + MV)]

 

    Where,

N	= Number of years in which preference shares are to be    redeemed
RV	= Redemption value i.e. amount payable at the time of    redemption

 

B. IN CASE OF NEW PREFERENCE SHARES

 

Kp	= [d (1 + Td) + 1/N (RV – SV)] ÷ [½ (RV + SV)]

 

COST OF DEBT CAPITAL

Cost of debt capital may be calculated for two different types of debentures:

1. For perpetual debentures, and

2. for redeemable debentures

 

For perpetual debentures

A. IN CASE OF EXISTING DEBENTURES

 

(i)	ki	= (I ÷ MV)                         (Before tax cost of debentures)
(ii)	kd	= (I ÷ MV) x (1 – Tc)           (After tax cost of debentures)

 

    Where,

I	= Annual interest payment
MV	= Current market price of the debentures (ex-interest)
Tc	= Corporate tax rate

   

B. IN CASE OF NEW DEBENTURES

 

(i)	ki	= (I ÷ SV)                          (Before tax cost of debentures)
(ii)	kd	= (I ÷ SV) x (1 – Tc)            (After tax cost of debentures)

 

    Where,

I	= Annual interest payment
SV	= Proceeds from the issue of debentures – Flotation cost
Tc	= Corporate tax rate

 

For redeemable debentures

A. IN CASE OF EXISTING DEBENTURES

 

(i)	ki	= [I + 1/N (RV – MV)] ÷ [½ (RV + MV)]    (Before tax cost of debentures)
(ii)	kd	= [I (1 – Tc) + 1/N (RV – MV)] ÷ [½ (RV + MV)]    (After tax cost of debentures)

 

    Where,

N	= Number of years in which debentures are to be redeemed
RV	= Redemption value i.e. amount payable at the time of redemption

 

B. IN CASE OF NEW DEBENTURES

 

(i)	ki	= [I + 1/N (RV – SV)] ÷ [½ (RV + SV)]    (Before tax cost of debentures)
(ii)	kd	= [I (1 – Tc) + 1/N (RV – SV)] ÷ [½ (RV + SV)]    (After tax cost of debentures)

 

COST OF RETAINED EARNINGS

 

kr	=  ke (1 – Tp) (1 – C)

 

    Where,

Tp	= Personal income tax rate
C	= Commission, brokerage, etc. for reinvesting the dividends by the    shareholders (expressed as percentage)

 

    Note:

   Here, k_e represents cost of existing equity shares. If k_r is calculated on the basis of cost of new equity shares, k_e will represent cost of new equity shares ignoring flotation cost, if any.

 

Computation of overall cost of capital

(Also called weighted average cost of capital)

Computation of overall cost of capital (k _o)

Sources of capital	Market value (Rs)	Weight (W)	Specific cost (K)	Weighted cost (W x K)
1. Equity Share Capital
2. Preference Share Capital
3. Debt Capital
4. Retained Earnings
TOTAL		1.00		Ko =

 

Note:

In the above table market values have been used as weights. If the market values are not available, book values may be used as the weights.

 

Marginal cost of capital

Marginal cost of capital refers to the weighted average cost of new/additional/incremental capital, where the weights will be represented by the percentage share of different financing sources the firm intends to raise/employ. Specific costs of different sources of capital, however, will remain same as used in calculating the overall cost of capital, provided nothing has been mentioned in the given problem regarding any change in any of the specific costs of different sources of capital.

Part B

 

Illustration: 1

Dr. Nandy had purchased a share of Alxa Limited for Rs 1,000. He received dividend for a period of five years at the rate of 10 percent. At the end of the fifth year, he sold the share of Alxa Limited for Rs 1,128. You are required to compute the cost of equity as per realised yield approach.

 

Solution:

Illustration: 2

Calculate the cost of equity capital of HUL Limited whose risk free rate of return equals 10%. The company’s beta equals 1.75 and the return on the market portfolio equals to 15%.

Solution:

     Cost of equity shares

     (under Capital Asset Pricing Model):

ke	= Rf + β (Rm – Rf)

 

    Where,

Rf	= The rate of return on a risk-free capital asset or investment    like the Treasury Bill / Government Bonds
Rm	= The expected rate of return on the market portfolio of capital asset/security/investment (i.e. average rate of return on all the capital assets/securities/investments in the market portfolio)
β	= The beta coefficient

 

    Here,

Rf	10% i.e. 0.10
Rm	15% i.e. 0.15
β	1.75

 

    Therefore,

ke	= 0.10 + 1.75 (0.15 – 0.10) = 0.1875 or 18.75%

 

Illustration: 3

Calculate the WACC using the following data by using:

(a) Book value weights

(b) Market value weights

The capital structure of the company is as under:

 

	Rs
Debentures (Rs 100 per debenture)	5,00,000
Preference shares (Rs 100 per share)	5,00,000
Equity shares (Rs 10 per share)	10,00,000
Total	20,00,000

 

The market prices of these securities are:

Debentures Rs 105 per debenture;

Preference shares Rs 110 per preference share

Equity shares Rs 24 each.

 

Additional information:

The company issued

(1)      Debentures @ Rs 100 per debenture redeemable at par, 10% coupon rate, 4% floatation costs, 10 year maturity;

(2)      Preference shares @ Rs 100 per preference share redeemable at par, 5% coupon rate, 2% floatation cost and 10 year maturity;

(3)      Equity shares @ Rs 24 per share, Rs 4 floatation cost.

 

The next year expected dividend is Rs 1 with annual growth of 5%. The firm has practice of paying all earnings in the form of dividend corporate tax rate is 50%.

 

Solution:

Cost of equity shares:

ke	= [D1 (1 + Td) ÷ SV] + g

 

    Where,

D1	= Expected dividend per share at the end of current year
Td	= Dividend distribution tax rate
SV	= Proceeds from the issue of shares – Flotation cost
g	= Expected annual growth rate in dividend

 

    Here,

D1	= Rs 1
Td	= 0
SV	= Rs 24 – Rs 4 = Rs 20
g	= 5% = 0.05

 

    Therefore,

ke	= [1 (1 + 0) ÷ 20] + 0.05 = 0.05 + 0.05 = 0.1 or 10%

 

Cost of preference shares:

Kp	= [d (1 + Td) + 1/N (RV – SV)] ÷ [½ (RV + SV)]

 

    Where,

d	= Annual dividend per preference share
SV	= Proceeds from the issue of preference shares – Flotation cost
Td	= Dividend distribution tax rate
N	= Number of years in which preference shares are to be redeemed
RV	= Redemption value i.e. amount payable at the time of redemption

 

    Here,

d	= Rs 100 × 5% = Rs 5
SV	= Rs 100 – Rs 100 × 2% = Rs 98
Td	= 0
N	= 10 years
RV	= Rs 100

 

    Therefore,

Kp	= [5 (1 + 0) + 1/10 (100 – 98)] ÷ [½ (100 + 98)]
⇒ Kp	= (5 + 0.20) ÷ 99 = 0.0525 or 5.25%

 

Cost of debentures:

kd	= [I (1 – Tc) + 1/N (RV – SV)] ÷ [½ (RV + SV)] (After tax cost)

 

    Where,

I	= Annual interest payment
SV	= Proceeds from the issue of debentures – Flotation cost
Tc	= Corporate tax rate
N	= Number of years in which debentures are to be redeemed
RV	= Redemption value i.e. amount payable at the time of redemption

 

    Here,

I	= Rs 100 × 10% = Rs 10
SV	= Rs 100 – Rs 100 × 4% = Rs 96
Tc	= 50% = 0.50
N	= 10 years
RV	= Rs 100

 

    Therefore,

kd	= [10 (1 – 0.5) + 1/10 (100 – 96)] ÷ [½ (100 + 96)]
⇒ kd	= (5 + 0.40) ÷ 98 = 0.0551 or 5.51%

 

Computation of WACC /

Overall Cost of Capital (k _o)

[Taking Book Value as Weight]

Sources of Capital	Book Value (Rs)	Weight (W)	Specific Cost (K)	Weighted Cost (W × K)
Equity share capital	10,00,000	0.50	0.1000	0.0500
Preference share capital	5,00,000	0.25	0.0525	0.0131
Debentures	5,00,000	0.25	0.0551	0.0138
Total	20,00,000	1.00		0.0769

 

Therefore, K _o (Taking Book Value as Weight) = 0.0769 or 7.69%

 

Computation of WACC /

Overall Cost of Capital (k _o)

[Taking Market Value as Weight]

Sources of Capital	Market Value (Rs)	Weight (W)	Specific Cost (K)	Weighted Cost (W × K)
Equity share capital	24,00,000	0.691	0.1000	0.0691
Preference share capital	5,50,000	0.158	0.0525	0.0083
Debentures	5,25,000	0.151	0.0551	0.0083
Total	34,75,000	1.00		0.0857

 

Therefore, K _o (Taking Market Value as Weight) = 0.0857 or 8.57%

 

Illustration: 4

XYZ Ltd. has the following capital structure which is considered to be optimum as on 31^st March, 2018.

	Rs
14% Debentures	30,000
11% Preference Shares	10,000
Equity Shares (10,000 Shares)	1,60,000
Total	2,00,000

 

The company’s share has a market price of Rs 23.60. Next year’s dividend per share is 50% of current year’s EPS. The following is the trend of EPS for the preceding 10 years which is expected to continue in future.

Year	EPS (Rs)	Year	EPS (Rs)
2009	1.00	2014	1.61
2010	1.10	2015	1.77
2011	1.21	2016	1.95
2012	1.33	2017	2.15
2013	1.46	2018	2.36

 

The company issued new debentures carrying 16% rate of interest and the current market price of debenture is Rs 96.

Preference share of Rs 9.20 (with annual dividend of Rs 1.10 per share) were also issued. The company is in 50% tax bracket.

i)           Calculate after tax:

a)       Cost of new debt

b)       Cost of new preference shares

c)       Cost of new equity shares

ii)           Calculate marginal cost of capital.

iii)          How much can be spent for capital investment before new ordinary shares must be sold assuming that retained earnings of 2018 will be converted into equity capital for investment purpose.

iv)         What will the marginal cost of capital when the fund exceeds the amount calculated in (iii), assuming new equity is issued at Rs 20 per share?

 

Solution:

i)       a) Cost of new debt

kd	= (I ÷ SV) x (1 – Tc)            (After tax cost of debentures)

 

    Where,

I	= Annual interest payment
SV	= Proceeds from the issue of debentures – Flotation cost
Tc	= Corporate tax rate

 

    Here,

I	= Rs 100 × 16% = Rs 16
SV	= Rs 96
Tc	= 50% = 0.50

 

    Therefore,

kd	= (16 ÷ 96) × (1 – 0.50) = 0.0833 or 8.33%

 

Note: Assumed market price is the sale value, because sale value is not given separately.

 

i)       b) Cost of new preference shares

Kp	= d (1 + Td) ÷ SV

 

    Where,

d	= Annual dividend per preference share
SV	= Proceeds from the issue of preference shares – Flotation cost
Td	= Dividend distribution tax rate

 

    Here,

d	= Rs 1.10
SV	= Rs 9.20
Td	= 0

 

    Therefore,

Kp	= 1.10 (1 + 0) ÷ 9.20 = 0.1196 or 11.96%

i)       c) Cost of new equity shares

ke	= [D1 (1 + Td) ÷ SV] + g

 

    Where,

D1	= Expected dividend per share at the end of current year
Td	= Dividend distribution tax rate
SV	= Proceeds from the issue of shares – Flotation cost
g	= Expected annual growth rate in dividend

 

    Here,

D1	= 50% of Rs 2.36 = Rs 1.18
Td	= 0
SV	= Rs 23.60
g	= 10% = 0.10 [See Working Note prepared in Excel]

 

    Therefore,

ke	= [1.18 (1 + 0) ÷ 23.60] + 0.10 = 0.05 + 0.10 = 0.15 or 15%

 

Note: Assumed market price is the sale value, because sale value is not given separately.

 

ii)     Marginal Cost of Capital

Computation of Marginal Cost of Capital

[Considering existing capital structure to be optimum]

Sources of Capital	Book Value (Rs)	Weight (W)	Specific Cost (K)	Weighted Cost (W × K)
Equity shares	1,60,000	0.80	0.1500	0.1200
11% Preference shares	10,000	0.05	0.1196	0.0060
14% Debentures	30,000	0.15	0.0833	0.0125
Total	2,00,000	1.00		0.1385

 

Therefore, Marginal Cost of Capital = 0.1385 or 13.85%

 

iii)      Retained earnings of the year 2017 – 18

= (Rs 2.36 × 10,000) × 50% = Rs 11,800

 

Present capital structure of XYZ Ltd. is considered to be optimum. Therefore, when retained earnings of Rs 11,800 will be converted into equity capital for investment purpose that will be 80% of total new capital investment.

 

∴ Capital investment possible before issue of new equity / ordinary shares

= Rs 11,800 ÷ 80% = Rs 14,750

 

iv)       For issue of new equity shares beyond capital investment of Rs 14,750, cost of new equity shares –

K_e = (1.18 ÷ 20) + 0.10 = 0.159 or 15.9%

 

Computation of Marginal Cost of Capital

[When the required fund exceeds Rs 14,750]

Sources of Capital	Optimum Weight (W)	Specific Cost (K)	Weighted Cost (W × K)
Equity shares	0.80	0.1590	0.1272
11% Preference shares	0.05	0.1196	0.0060
14% Debentures	0.15	0.0833	0.0125
Total	1.00		0.1457

 Therefore, Marginal Cost of Capital = 0.1457 or 14.57%

Working Note:

Illustration: 5

Assuming the corporate tax rate of 35%, compute the after tax cost of capital in the following situations:

i)     Perpetual 15% Debentures of Rs 1,000 sold at a premium of 10% with no flotation costs.

ii)   10-year 14% Debentures of Rs 2,000, redeemable at par, with 5% flotation costs.

 

Solution:

(I)       Cost of perpetual debentures:

kd	= (I ÷ SV) x (1 – Tc)            (After tax cost of debentures)

 

    Where,

I	= Annual interest payment
SV	= Proceeds from the issue of debentures – Flotation cost
Tc	= Corporate tax rate

 

    Here,

I	= Rs 1,000 × 15% = Rs 150
SV	= Rs 1,000 + Rs 1,000 × 10% = Rs 1,100
Tc	= 35% = 0.35

 

    Therefore,

kd	= (150 ÷ 1,100) × (1 – 0.35) = 0.0886 or 8.86%

 

(II)    Cost of redeemable debentures:

kd	= [I (1 – Tc) + 1/N (RV – SV)] ÷ [½ (RV + SV)] (After tax cost)

 

    Where,

I	= Annual interest payment
SV	= Proceeds from the issue of debentures – Flotation cost
Tc	= Corporate tax rate
N	= Number of years in which debentures are to be redeemed
RV	= Redemption value i.e. amount payable at the time of redemption

 

    Here,

I	= Rs 2,000 × 14% = Rs 280
SV	= Rs 2,000 – Rs 2,000 × 5% = Rs 1,900
Tc	= 35% = 0.35
N	= 10 years
RV	= Rs 2,000

   

    Therefore,

kd	= [280 (1 – 0.35) + 1/10 (2,000 – 1,900)] ÷ [½ (2,000 + 1,900)]
⇒ kd	= (182 + 10) ÷ 1,950 = 0.0985 or 9.85%

 

Illustration: 6

Calculate the Cost of Capital from the following cases:

i)         10-year 14% Preference shares of Rs 100, redeemable at premium of 5% and flotation costs 5%. Dividend tax is 10%.

ii)       An equity share selling at Rs 50 and paying a dividend of Rs 6 per share, which is expected to continue indefinitely.

iii)      The above equity share if dividends are expected to grow at the rate of 5%.

iv)     An equity share of a company is selling at Rs 120 per share. The earnings per share are Rs 20 of which 50% is paid in dividends. The shareholders expect the company to earn a constant after tax rate of 10% on its investment of retained earnings.

 

Solution:

I)          Cost of redeemable preference shares:

Kp	= [d (1 + Td) + 1/N (RV – SV)] ÷ [½ (RV + SV)]

 

    Where,

d	= Annual dividend per preference share
SV	= Proceeds from the issue of preference shares – Flotation cost
Td	= Dividend distribution tax rate
N	= Number of years in which preference shares are to be redeemed
RV	= Redemption value i.e. amount payable at the time of redemption

 

    Here,

d	= Rs 100 × 14% = Rs 14
SV	= Rs 100 – Rs 100 × 5% = Rs 95
Td	= 10% = 0.10
N	= 10 years
RV	= Rs 100 + Rs 100 × 5% = Rs 105

 

    Therefore,

Kp	= [14 (1 + 0.10) + 1/10 (105 – 95)] ÷ [½ (105 + 95)]
⇒ Kp	= (15.40 + 1) ÷ 100 = 0.1640 or 16.40%

 

II)       Cost of equity shares:

ke	=  [D1 (1 + Td) ÷ P0] + g

 

    Where,

D1	= Expected dividend per share at the end of current year
Td	= Dividend distribution tax rate
P0	= Current market price per share (ex-dividend)
g	= Expected annual growth rate in dividend

 

    Here,

D1	= Rs 6
Td	= 0
P0	= Rs 50
g	= 0

 

    Therefore,

ke	=  [6 (1 + 0) ÷ 50] + 0 = 0.12 or 12%

 

III)    Cost of equity shares:

ke	=  [D1 (1 + Td) ÷ P0] + g

 

Where,

D1	= Expected dividend per share at the end of current year
D1	= D0 (1 + g)
D0	= Actual dividend per share at the end of previous year
Td	= Dividend distribution tax rate
P0	= Current market price per share (ex-dividend)
g	= Expected annual growth rate in dividend

 

    Here,

D0	Rs 6
g	= 5% = 0.05
D1	= D0 (1 + g) = Rs 6 (1 + 0.05) = Rs 6.30
Td	= 0
P0	= Rs 50

 

    Therefore,

ke	=  [6.30 (1 + 0) ÷ 50] + 0.05 = 0.176 or 17.60%

 

IV)      Cost of equity shares:

ke	=  [D1 (1 + Td) ÷ P0] + g

 

    Where,

D1	= Expected dividend per share at the end of current year
Td	= Dividend distribution tax rate
P0	= Current market price per share (ex-dividend)
g	= Expected annual growth rate in dividend = b × r
b	= Retention Ratio
r	= Rate of Return on Equity
D1	= D0 [1 + g]
D0	= Actual dividend per share at the end of previous year

 

    Here,

D0	Rs 20 × 50% = Rs 10
b	= Retention Ratio = 50% = 0.50
r	= Rate of Return on Equity = 10% = 0.10
g	= b × r = 0.50 × 0.10 = 0.05
D1	= D0 (1 + g) = Rs 10 (1 + 0.05) = Rs 10.50
Td	= 0
P0	= Rs 120

 

    Therefore,

ke	=  [10.50 (1 + 0) ÷ 120] + 0.05 = 0.1375 or 13.75%

 

Illustration: 7

From the following information, determine the appropriate weighted average cost of capital, relevant for evaluating long-term investment projects of the company.

Cost of equity	0.18
After tax cost of long-term debt	0.08
After tax cost of short-term debt	0.09
Cost of Reserve	0.15

 

Sources of capital	Book Value (BV) – Rs	Market Value (MV) – Rs
Equity Capital	3,00,000	7,50,000
Reserves	2,00,000	-
Long-term debt	4,00,000	3,75,000
Short-term debt	1,00,000	1,00,000
Total	10,00,000	12,25,000

 

Solution:

Computation of WACC /

Overall Cost of Capital (k _o)

[Taking Book Value as Weight]

Sources of Capital	Book Value (Rs)	Weight (W)	Specific Cost (K)	Weighted Cost (W × K)
Equity share capital	3,00,000	0.33	0.18	0.0594
Reserves	2,00,000	0.22	0.15	0.0330
Long Term Debt	4,00,000	0.45	0.08	0.0360
Total	9,00,000	1.00		0.1284

 

Therefore, K _o (Taking Book Value as Weight) = 0.1284 or 12.84%

 

Computation of WACC /

Overall Cost of Capital (k _o)

[Taking Market Value as Weight]

Sources of Capital	Market Value (Rs)	Weight (W)	Specific Cost (K)	Weighted Cost (W × K)
Equity share capital	4,50,000	0.40	0.18	0.0720
Reserves	3,00,000	0.27	0.15	0.0405
Long Term Debt	3,75,000	0.33	0.08	0.0264
Total	11,25,000	1.00		0.1389

 

Therefore, K _o (Taking Market Value as Weight) = 0.1389 or 13.89%

 

Workings:

Market value of Eq. Share	= 7, 50,000 × [3, 00,000 ÷ (3, 00,000 + 2, 00,000)] = Rs 4, 50,000
Market value of reserves	= 7, 50,000 × [2, 00,000 ÷ (3, 00,000 + 2, 00,000)] = Rs 3, 00,000

 

Illustration: 8

In considering the most desirable capital structure of a company, the following estimates of the cost of debt and equity capital (after tax) have been made at various levels of debt-equity mix:

Debt as % of total capital employed	Cost of debt %	Cost of equity %
0	5.0	12.0
10	5.0	12.0
20	5.0	12.5
30	5.5	13.0
40	6.0	14.0
50	6.5	16.0
60	7.0	20.0

 

You are required to determine the optimal debt-equity mix for the company by calculating composite cost of capital.

 

Solution:

Proportion Of Debt	Proportion Of Equity	Cost of Debt	Cost of Equity	Overall cost Of capital (KO)
(a)	(b)	(c)	(d)	[(a × c) + (b × d)]
0.00	1.00	0.05	0.12	0.12
0.10	0.90	0.05	0.12	0.113
0.20	0.80	0.05	0.125	0.11
0.30	0.70	0.055	0.13	0.1075
0.40	0.60	0.06	0.14	0.108
0.50	0.50	0.065	0.16	0.1125
0.60	0.40	0.07	0.20	0.122

 

Minimum K_O is 0.1075 or 10.75%. Therefore, optimal capital structure of the company is 30% debt and 70% equity.

 

Illustration: 9

Determine the weighted average cost of capital using (i) book value weights; and (ii) market value weights based on the following information:

Book value structure:	Rs
Debentures (Rs 100 per debenture)	8,00,000
Preference shares (Rs 100 per share)	2,00,000
Equity shares (Rs 10 per share)	10,00,000
Total	20,00,000

 

Recent market prices of all these securities are:

Debentures: Rs 110 per debenture;

Preference share: Rs 120 per share; and

Equity shares: Rs 22 per share

External financing opportunities are:

a.   Rs 100 per debenture redeemable at par, 10 year maturity, 13% coupon rate, 4% flotation cost and sale price Rs 100;

b.   Rs 100 per preference share redeemable at par, 10 year maturity, 14% dividend rate, 5% flotation cost and sale price Rs 100; and

c.   Equity share: Rs 2 per share flotation costs and sale price Rs 22; dividend expected on equity share at the end of the year is Rs 2 per share; anticipated growth rate in dividend is 7%. Company pays all its earnings in the form of dividends. Corporate tax rate is 50%.

 

Solution:

Cost of debentures:

kd	= [I (1 – Tc) + 1/N (RV – SV)] ÷ [½ (RV + SV)] (After tax cost)

 

    Where,

I	= Annual interest payment
SV	= Proceeds from the issue of debentures – Flotation cost
Tc	= Corporate tax rate
N	= Number of years in which debentures are to be redeemed
RV	= Redemption value i.e. amount payable at the time of redemption

 

    Here,

I	= Rs 100 × 13% = Rs 13
SV	= Rs 100 – Rs 100 × 4% = Rs 96
Tc	= 50% = 0.50
N	= 10 years
RV	= Rs 100

 

    Therefore,

kd	= [13 (1 – 0.50) + 1/10 (100 – 96)] ÷ [½ (100 + 96)]
⇒ kd	= (6.50 + 0.40) ÷ 98 = 0.0704 or 7.04%

 

Cost of preference shares:

Kp	= [d (1 + Td) + 1/N (RV – SV)] ÷ [½ (RV + SV)]

 

    Where,

d	= Annual dividend per preference share
SV	= Proceeds from the issue of preference shares – Flotation cost
Td	= Dividend distribution tax rate
N	= Number of years in which preference shares are to be redeemed
RV	= Redemption value i.e. amount payable at the time of redemption

 

    Here,

d	= Rs 100 × 14% = Rs 14
SV	= Rs 100 – Rs 100 × 5% = Rs 95
Td	= 0
N	= 10 years
RV	= Rs 100

 

    Therefore,

Kp	= [14 (1 + 0) + 1/10 (100 – 95)] ÷ [½ (100 + 95)]
⇒ Kp	= (14 + 0.50) ÷ 97.50 = 0.1487 or 14.87%

 

Cost of equity shares:

ke	= [D1 (1 + Td) ÷ SV] + g

 

    Where,

D1	= Expected dividend per share at the end of current year
Td	= Dividend distribution tax rate
SV	= Proceeds from the issue of shares – Flotation cost
g	= Expected annual growth rate in dividend

 

    Here,

D1	= Rs 2
Td	= 0
SV	= Rs 22 – Rs 2 = Rs 20
g	= 7% = 0.07

 

    Therefore,

ke	= [2 (1 + 0) ÷ 20] + 0.07 = 0.10 + 0.07 = 0.17 or 17%

 

Computation of WACC /

Overall Cost of Capital (k _o)

[Taking Book Value as Weight]

Sources of Capital	Book Value (Rs)	Weight (W)	Specific Cost (K)	Weighted Cost (W × K)
Equity share capital	10,00,000	0.50	0.1700	0.0850
Preference share capital	2,00,000	0.10	0.1487	0.0149
Debentures	8,00,000	0.40	0.0704	0.0282
Total	20,00,000	1.00		0.1281

 

Therefore, K _o (Taking Book Value as Weight) = 0.1281 or 12.81%

Computation of WACC /

Overall Cost of Capital (k _o)

[Taking Market Value as Weight]

Sources of Capital	Market Value (Rs)	Weight (W)	Specific Cost (K)	Weighted Cost (W × K)
Equity share capital	22,00,000	0.66	0.1700	0.1122
Preference share capital	2,40,000	0.07	0.1487	0.0104
Debentures	8,80,000	0.27	0.0704	0.0190
Total	33,20,000	1.00		0.1416

 

Therefore, K _o (Taking Market Value as Weight) = 0.1416 or 14.16%

 

Illustration: 10

The present capital structure of a company is as follows:

	Rs (million)
Equity share (Face value = Rs 10)	240
Reserves	360
11% Preference Shares (Face value = Rs 10)	120
12% Debentures	120
14% Term Loans	360
Total	1,200

 

Additionally the following information is available:

Company’s equity beta	1.06
Yield on long-term treasury bonds	10%
Stock market risk premium	6%
Current ex-dividend equity share price	Rs 15
Current ex-dividend preference share price	Rs 12
Current ex-interest debenture market value (Face Value = Rs 100)	Rs 102.50
Corporate tax rate	40%

 

The debentures are redeemable after 3 years and interest is paid annually. Ignoring flotation costs, calculate the company’ weighted average cost of capital (WACC).

 

Solution:

    Cost of equity shares

    (under Capital Asset Pricing Model):

ke	= Rf + β (Rm – Rf)

 

    Where,

Rf	= The rate of return on a risk-free capital asset or investment    like the Treasury Bill / Government Bonds
Rm	= The expected rate of return on the market portfolio of capital asset/security/investment (i.e. average rate of return on all the capital assets/securities/investments in the market portfolio)
β	= The beta coefficient

 

    Here,

Rf	= 10% i.e. 0.10
Rm	= 10% + 6% = 16% i.e. 0.16
β	= 1.06

 

    Therefore,

ke	= 0.10 + 1.06 (0.16 – 0.10) = 0.1636 or 16.36

 

Cost of debentures:

kd	= [I (1 – Tc) + 1/N (RV – SV)] ÷ [½ (RV + SV)]    (After tax cost)

 

    Where,

I	= Annual interest payment
SV	= Proceeds from the issue of debentures – Flotation cost
Tc	= Corporate tax rate
N	= Number of years in which debentures are to be redeemed
RV	= Redemption value i.e. amount payable at the time of redemption

 

    Here,

I	= Rs 100 × 12% = Rs 12
SV	= Rs 102.50
Tc	= 40% = 0.40
N	= 3 years
RV	= Rs 100

 

    Therefore,

kd	= [12 (1 – 0.4) + 1/3 (100 – 102.50)] ÷ [½ (100 + 102.50)]
⇒ kd	= (7.20 − 0.83) ÷ 101.25 = 0.0629 or 6.29%

 

Cost of preference shares:

Kp	= d (1 + Td) ÷ SV

 

    Where,

d	= Annual dividend per preference share
SV	= Proceeds from the issue of preference shares – Flotation cost
Td	= Dividend distribution tax rate

 

    Here,

d	= Rs 10 × 11% = Rs 1.10
SV	= Rs 12
Td	= 0

 

    Therefore,

Kp	= 1.10 (1 + 0) ÷ 12 = 0.0917 or 9.17%

 

Cost of Term Loans:

Kt	= (I ÷ SV) x (1 – Tc)            (After tax cost of term loan)

 

    Where,

I	= Annual interest payment
SV	= Proceeds from the issue of debentures – Flotation cost
Tc	= Corporate tax rate

 

    Here,

I	= Rs 100 × 14% = Rs 14
SV	= Rs 100
Tc	= 40% = 0.40

 

    Therefore,

Kt	= (14 ÷ 100) × (1 – 0.40) = 0.084 or 8.40%

 

Computation of WACC /

Overall Cost of Capital (k _o)

[Taking Book Value as Weight]

Sources of Capital	Book Value (Rs ’millions)	Weight (W)	Specific Cost (K)	Weighted Cost (W × K)
Equity share capital	240	0.20	0.1636	0.0327
Reserves	360	0.30	0.1636	0.0491
Preference share capital	120	0.10	0.0917	0.0092
Debentures	120	0.10	0.0629	0.0063
Term loans	360	0.30	0.0840	0.0252
Total	1,200	1.00		0.1225

 

Therefore, K _o (Taking Book Value as Weight) = 0.1225 or 12.25%

 

Computation of WACC /

Overall Cost of Capital (k _o)

[Taking Market Value as Weight]

Sources of Capital	Market Value (Rs ’millions)	Weight (W)	Specific Cost (K)	Weighted Cost (W × K)
Equity share capital	144	0.15	0.1636	0.0245
Reserves	216	0.22	0.1636	0.0360
Preference share capital	144	0.15	0.0917	0.0138
Debentures	123	0.12	0.0629	0.0075
Term loans	360	0.36	0.0840	0.0302
Total	987	1.00		0.1120

 

Therefore, K _o (Taking Market Value as Weight) = 0.1120 or 11.20%

Workings:

Market value of Eq. Share	= (24 × 15) × [240 ÷ (240 + 360)] = Rs 144 million
Market value of reserves	= (24 × 15) × [360 ÷ (240 + 360)] = Rs 216 million