BK SCHOOL & IDSR

MBA (EXECUTIVE) – SEMESTER – II

FINANCIAL MANAGEMENT
Unit 3 COST OF CAPITAL

Specific Cost: for different source different cost

Combined Cost = aggregate of all specific cost

According to Khan and Jain: “It is defined as the minimum rate of return that a
firm must earn on its investment for the market value of the firm to remain
unchanged.”
In the words of I. M. Pandey, ‘The cost of capital is simply the rate of return the
funds used should produce to justify their use within the firm in the light of
the wealth maximization objective.

WACC: weighted average cost of capital

The composite or overall cost of capital of a firm is the weighted average costs of
various sources of funds.
Weights are taken to be the proportion of each source of funds in the capital structure.
While making financial decisions this overall or weighted cost is used.

While valuing weighted average cost of capital we get the choice of taking book value
weight or market value weight. Both these methods have their own merits. There are
practical difficulties in its use as calculating the market value of securities may present
difficulties, particularly the market values of retained earnings. Moreover, weights based
on market values are likely to fluctuate widely.

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WACC ( Book Value) WACC ( Market Value )
Source of Book Specific Weighted Source of Market Specific Weighted
Finance Value Cost Book Finance Value Cost Market
(%) Value (%) Value
Equity Ke Equity Ke
share share
Preference Kp Preference Kp
Share Share
Debenture Kd Debenture Kd
Bond Kb Bond Kb
Long term Kl Long term Kl
Loan Loan
Retained Kr Retained Kr
Earning Earning
Total Xxx Xxx Total Xxx xxx
𝑻𝒐𝒕𝒂𝒍 𝑾𝒆𝒊𝒈𝒉𝒕𝒆𝒅 𝑩𝒐𝒐𝒌 𝒗𝒂𝒍𝒖𝒆 𝑻𝒐𝒕𝒂𝒍 𝑾𝒆𝒊𝒈𝒉𝒕𝒆𝒅 𝑴𝒂𝒓𝒌𝒆𝒕 𝒗𝒂𝒍𝒖𝒆
WACC ( BV) = ×100 WACC ( MV) = ×100
𝒕𝒐𝒕𝒂𝒍 𝑩𝒐𝒐𝒌 𝒗𝒂𝒍𝒖𝒆 𝒕𝒐𝒕𝒂𝒍 𝑴𝒂𝒓𝒌𝒆𝒕 𝒗𝒂𝒍𝒖𝒆

MARGINAL COST OF CAPITAL:

 Marginal Cost of Capital is the cost of raising an additional rupee of capital.
 It is derived when the average cost of capital is computed with marginal weights. The
weights represent the proportion of fresh funds the firm intends to employ.
 When funds are raised in the same proportion as at present and if the costs remain
unchanged, there will be no difference between average cost of capital and marginal
cost of capital. As the level of Capital Employed increases, the costs of all the source
may start increasing. In such a case both the WACC and marginal cost of capital will
increase. But marginal cost of capital will rise faster.

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 Cost of Debt (Debenture, Bond , Term Loan)(Kd, Kb, Kt)
Irredeemable Debenture Redeemable Debenture
Before Tax Before Tax
Kd= × 100 Kd= × 100
I= interest I= Interest, SV= issue price / sale value,
RV= Redeemable Value, n= time period
P= issue Price
After tax After tax
Kd= Kd(1-t) Kd= Kd(1-t)
T= tax rate

Cost of Preference Share (Kp)

Irredeemable Preference share Redeemable Preference share
Kp= × 100 Kp= × 100
D= Dividend D= Dividend, SV= issue price / sale
value,
RV= Redeemable Value, n= time period
P= issue Price

Cost of Equity: (Ke)

Dividend Approach Earning Approach CAPM ( Capital asset Pricing Model)
No Growth Growth 𝑬
Ke= × 𝟏𝟎𝟎 Ke= 𝑹𝒇 + 𝜷(𝑹𝒎 − 𝑹𝒇 )
𝑷
𝑫
Ke= × 𝟏𝟎𝟎 Ke=(
𝑫𝟏 E= Earning Per
+ 𝒈) × 𝟏𝟎𝟎
𝑷 𝑷𝟎
share
D1= Expected P= market price of
Dividend/next year share
dividend
D1=D0(1+g)
D0= Current year or
past year dividend
P0= current price
G= Growth

Cost of Retained earnings:

Kr=Ke(1-b)(1-t)
B= brokerage
T = tax

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CAPITAL ASSETS PRICING MODEL
Shape’s model
The CAPM explains the behaviour of security prices and provides a mechanism whereby
investors could assess the impact of proposed security investment on their overall portfolio
risk and return.
The systematic/non - diversifiable risk is attributable to factors that affect all firms. like
interest rate changes, inflation or purchasing power change, changes in investor
expectations about the overall performance of the economy and political changes, and so
on.
As unsystematic risk can be eliminated by an investor through diversification, the
systematic risk is the only relevant risk. Therefore, an investor (firm) should be concerned,
according to CAPM, solely with the non - diversifiable (systematic) risk. Such
unsystematic risk do affect the market sentiment and it may affect the value of the portfolio
of the investor.
According to CAPM, the non - diversifiable risk of an investment/security/asset is assessed
in terms of the beta coefficient. Beta is a measure of the volatility of a security's return
relative to the change in market sentiment.
Beta coefficient of 1 would imply that the risk of the specified security is equal to the
market sentiment; the interpretation of zero coefficient is that there is no market - related
risk to the investment.
A negative coefficient would indicate a relationship in the opposite direction. With
reference to the cost of capital perspective, the CAPM describes the relationship between
the cost of equity capital, and the non - diversifiable or relevant risk, of the firm as reflected
in its index of non - diversifiable risk, that is, beta. Symbolically,

Ke = Rf + β (Rm - Rf)
Where Ke = Cost of equity capital
Rf =the rate of return required on a risk - free asset/security/ investment
Rm = the required rate of return on the market portfolio of assets.
𝜷 = the beta coefficient (risk of investment in relation to portfolio)
Alternatively, this notation may be expressed as follows :
Return from investment = Risk free return + β (Market return – Risk free return)

 Systematic ( non- diversified risk)( market risk) 𝛽

 Unsystematic (diversified) ( diversified portfolio)

Business risk / financial risk

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E.g:
Beta 𝛽 ( CAPM) (capital asset pricing model)
Ke= Rf+𝛽 (Rm-Rf)
Rf= 6%
Rm=15%
𝛽 = 1.5
6+1.5(15-6)
6+1.5(9)
6+13.5
19.5

Practice Sums:
Calculate after tax cost of capital in the following situations:
1) 10% Debenture of 100 each issued @ 5% discount and 3% flotation cost, tax 40%.

I=100*10%=10
P=
100
-disc 5
95
-FC 3
P 92

T= 40%=0.40

Kd= × 100
= × 100
=10.87%

After tax
Kd(1-t)=10.87 (1-0.40)=6.52%

2) A company issues 14% redeemable debentures of Rs. 1,000 each aggregating Rs.
10,00,000 @ 10% premium. After 5 years, the company will redeem debentures at
par. The company tax rate is 35%. Determine the cost of Debt.

n=5
i=1000*14%=140
RV=1000

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SV=1000+ 100(1000*10%)=1100
T=35%=0.35

Kd= × 100

Kd= × 100

= × 100
=11.43%
Kd(1-t)=11.43(1-0.35)=7.42%

3) A 10% debenture of Rs.1,000 face value to be redeemed after 8 years. The

debenture is expected to be sold at 10% discount and flotation cost 3%. Tax rate
50%.
n=8
i=1000*10%=100
RV=1000
SV=1000-130=870
T=0.50

Kd= × 100

Kd= × 100

.
= × 100
=12.43%
After tax kd= 12.43(1-0.5)=6.215%

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 4) Abascus Limited issued 15 year 14 percent bonds. The bond which has a face value
of ₹ 100 is currently selling for ₹ 108. What is the pre-tax cost of debt? What is the
after-tax cost of debt? (Assume a 35 percent tax rate)
N=15
I=14%=100*14%=14
Fv=100
Sv=108
Rv=100
T=35%
Before tax

Kd= × 100

Kd= × 100
.
Kd= × 100
Kd=12.9488
After tax
Kd(1-t)=12.9488 (1-0.35)=8.41%

5) Omega Enterprises issued 10 year, 9 percent preference shares. The preference

share which has a face value of ₹ 100 is currently selling for ₹ 92. What is the cost of
preference shares?
N=10
D=9%=100*9%=9
Fv=100
SV=92

Kp= × 100

Kp= × 100
=9.8/96
10.20%

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 6) Rao Corporation has a target capital structure of 60 percent equity and 40 percent
debt. Its cost of equity is 18 percent and its pre-tax cost of debt is 13 percent. If the
relevant tax rate is 35 percent, what is Rao Corporation’s WACC?

Post tax cost of debt

Kd(1-t)=13 (1-0.35)= 8.45%

Source Weights Specific Cost WACC

Equity 0.6 18% 10.8
Debt 0.4 8.45% 3.38
Total 14.18

7) A company has on its books the following amounts & specific costs of each type of
capital
Specific costs
Type of capital Book value Market value
(%)
Debt 5,00,000 4,20,000 10
Preference 1,00,000 1,60,000 12
Equity 6,00,000 16
12,00,000
Retained earnings 2,00,000 14

Total 14,00,000 17,80,000

Determine the weighted average cost of capital using book value & market value weights.

Specific costs Weighted Book

Type of capital Book value
(%) value
Debt 5,00,000 10% 50000
Preference 1,00,000 12% 12000
Equity 6,00,000 16% 96000
Retained earnings 2,00,000 14% 28000

Total 14,00,000 186000

WACC (BV)= × 100 = × 100 = 𝟏𝟑. 𝟐𝟖%

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600000:200000
6:2
Equity =1200000 × = 900000
Retained 1200000 × = 300000

Specific costs Weighted

Type of capital Market value
(%) Market value
Debt 4,20,000 10 42000
Preference 1,60,000 12 19200
Equity 9,00,000 16 144000
Retained earnings 3,00,000 14 42000

Total 17,80,000 247200

WACC (MV)= × 100 = × 100 = 𝟏𝟑. 𝟖𝟖%

8) Following details are available about Pinkal Ltd :

Type of capital Book value
Rs.
Equity share capital (each share of Rs. 10) 10,00,000
11% preference share capital (each share of Rs. 100) 2,00,000
Reserves and surplus 18,00,000
15% Debentures (each debenture of Rs. 100) 20,00,000
Total 50,00,000

On equity shares, the next year’s expected rate of dividend is 25%. The growth rate of the
earnings of the company is 10%. The average current market price of equity share is Rs. 25.
Assume that the cost of retained earnings is 4% less than the cost of equity capital. The
current market price of preference shares and debentures are Rs. 80 and Rs. 70
respectively. The tax rate applicable to company is 50%. Ascertain the average cost of
capital of the company on the basis of Market value Weights.
Solution:

Equity
D1=25%=10*25%=2.5
g=10%
P0=25

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Ke=( + 𝑔) × 100

.
=( + 0.1) × 100
=(0.1 + 0.1) × 100
=20%

Retained
Kr=20-4=16%

Cost debt
Before tax
I=15%=100*15%=15
P=100
Kd= × 100 = × 100 = 15%
After tax
Kd(1-t)=15(1-0.5)=7.5%

Cost preference share

D=11%=100*11%=11
P=100

𝑫 𝟏𝟏
Kp= × 𝟏𝟎𝟎 = × 𝟏𝟎𝟎 = 𝟏𝟏%
𝑷 𝟏𝟎𝟎

Source of capital Market Value Specific Cost Weighted Market

Value
Equity 25,00,000 20% 500000
(1000000/10=1000000*25)
Retained earning 18,00,000 16% 288000
15% debt 14,00,0000 7.5% 105000
(2000000/100=20000*70)
11% pref share 160000 11% 17600
(200000/100=2000*80)
Total 5860000 910600

WACC (MV)= × 100 = 𝟏𝟓. 𝟓𝟒%

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 9) The R Ltd. has a following Capital structure as on 31.3.04
Equity Capital Rs. 1,50,000@ 10
Reserves Rs. 1,20,000
12% Preference Shares Rs. 30,000 @ 100
15% Debentures Rs. 1,50,000@ 100
Rs. 4,50,000
The company falls in 40% tax bracket. The current earnings of the company are Rs.
1,50,000 with market price of equity Rs. 50.
The company is considering to raise Rs. 1,50,000 which is planned to be financed through
20% from Internal Accruals and balance by issue of 17% Debenture. Cost of Reserves is 2%
less than that of Equity Cost. Calculate WACC.

Cost of Equity
No of shares = 150000/10=15000
E= EPS= Earning per share =150000/15000=10
P=50
𝑬 𝟏𝟎
Ke= × 𝟏𝟎𝟎 = × 𝟏𝟎𝟎 = 𝟐𝟎%
𝑷 𝟓𝟎
Cost of retained earning =20-2=18%

Cost of preference share

Kp = × 100 = × `100 = 12%

Cost of debenture
Kd= × 100 = × 100 = 15%

After tax
Kd(1-t)=15(1-0.4)=9%

Additional Debenture
Kd= × 100 = × 100 = 17%

After tax
Kd(1-t)=17(1-0.4)=10.2%

WN
ADDITIONAL
Reserves =150000*20%=30000
Debenture =150000-30000=120000

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Source of Capital Book value Specific Cost Weighted Book Value
Equity 150000 20% 30000
Retained Earning 150000 18% 27000
(120000+30000)
12% pref share 30000 12% 3600
15% debenture 150000 9% 13500
17% debenture 120000 10.2% 12240
Total 600000 86340

WACC (BV)= × 100 = 𝟏𝟒. 𝟑𝟗%

10) Assuming that a firm pays tax at a 50 per cent rate, compute the after-tax cost of
capital in the following cases:
i) A 8.5 per cent preference share sold at par.
D= 8.5%=100*8.5%=8.5
P= par =100
.
Kp= × 100 = × 100 = 𝟖. 𝟓%

ii) A perpetual bond sold at par, coupon rate of interest being 7 per cent.
P=100
I=100*7%=7
Kd= × 100 = × 100 = 7%
After tax
Kd(1-t)=7(1-0.5)=3.5%

iii) A ten-year, 8 per cent, `1000 par bond sold at `950 less 4 per cent underwriting
commission.

iv) A preference share sold at Rs.100 with a 9 per cent dividend and a redemption
price of Rs.110 if the company redeems it in five years.
N=5
D=100*9%=9
FV=100
RV=110
SV=100

Kp= × 100

Kp= × 100

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Kp= × 100 = 𝟏𝟎. 𝟒𝟕%

v) An ordinary share selling at a current market price of `120, and paying a

current dividend of `9 per share, which is expected to grow at a rate of 8 per
cent.
P=120
D=9
G=8%

D1=D0(1+g)=9(1+0.08)=9(1.08)=9.72

Ke=( + 𝑔) × 100
.
Ke=( + 0.08) × 100=(0.081+0.08)*100=16.1%

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