Cost of Capital in management of diff firms.pptx

Cost of Debt
P = ∑ C*(1-T) + F
(1+ Kd)t (1+Kd)n
Where P = Net amount realized on debt issue
C= Annual Interest payable
T = Tax Rate
F = Redemption Price
n- = Maturity period of Debt
t=1
t=n

An Approximation
Kd = [C*(1-t) + ((F – P) /n) ] / [(F + P)/2]

Question
• Ramson Ltd., issues 10% debentures of face value Rs.100 each and
realizes Rs.90 per debenture. The dentures are redeemable after 12
years at a premium of 8%. Company is paying income tax @45%. The
cost of debt is

Answer
• Kd = [C*(1-t) + (F – P) /n] / (F + P)/2
• I = Annual Interest to be paid = Rs.10
• t = 0.45
• F = Rs.108; P = 90
• n = 12 years
• Kd = [10*(1- 0.45) + ((108 – 90) / 12) ] / [ (108 + 90)/2 ]
• = 0.0707 = 7.07%

Cost of Term Loan
Cost of Term Loan = I*(1-t)

Cost of Preference Capital
P = ∑ D + F
(1+ Kp)t (1+Kp)n
Where P = Net amount realized per preference share
D= Preference dividend per share payable annually
F = Redemption Price
n- = Maturity period of Preference Capital
t=1
t=n

An Approximation
Kp = [D + (F – P) /n] / (F + P)/2

QUESTION
A preference share issues at 12% worth Rs 60,000 at 5% discount and
after 6 years it redeem at 10% premium. The flotation cost is 5% and
tax rate is 20%. Find out the cost of preference share capital.

SOLUTION
Dividend on preference share (Dp) = 60,000*12/100 = Rs.7200
Discount = 60,000*5/100 = Rs.3000
Flotation Cost = 60,000*5/100 = Rs.3000
Net Proceeds (NP) = Rs. (60,000-3000-3000) = Rs. 54,000
Premium amount = 60,000*10/100 =Rs. 6000
Redemption Value = Rs. (60,000+6000) = Rs. 66,000
Kp = Dp+ ((RV-NP)/n)/ (RV+NP)/2
= 7200+ ((66,000-54,000)/6) / (66,000+54,000)/2
= 9200/60,000
= 15.33%

QUESTION
Company ABC a small company issued 50, 000 shares of 10 each and
pays Rs.8 per shares as dividend.
Further issue 10, 000 debentures of Rs. 100 each and the interest pays by
the company is 8%.
Company wants to expand its business by opening a new branch in
different cities. It wants to finance its expansion project through 6%
preference shares.
Find out:
a)Cost of preference share if issues 100 of Rs. 80 each at 3% discount
and redeem at 5% premium after 8 years.
b) Which one is good for the company redeemable preference share or
irredeemable preference share?
Flotation cost Rs. 10 each.

SOLUTION
Discount= 80*0.03 = 2.4
Issue price= 80-2.4 = 77.6
Net proceeds = 77.6 – 10 = 67.6
Dividend = 0.06*80 = 4.8
Premium amount = 80*0.05 = 4
Redemption value = 80 + 4 = 84
Irredeemable Preference share:
Kp = Dp/NP
= 4.8 / 67.6
= 7.10%

Redeemable Preference share:
Net proceeds = 80 – 2.4 - 10 = 67.6
Kp = Dp+ ((RV-NP)/n)/ (RV+NP)/2
= 4.8 + ((84-67.6)/8)/ (84+67.6)/2
= 4.8 + (2.05 / 75.8)
= 4.8 + 0.027
= 4.827%
The cost of redeemable preference shares is less than irredeemable
preference share by 2.27%. So, the redeemable preference share is beneficial
for the Company ABC.

Perpetual Preference Capital
P = ∑ D
(1+ Kp)t
Which is simply
Kp = D/ P
t=1
t= ∞

Cost of Equity – Dividend Capitalisation Approach
P0 = D1 / (1+Ks)1 + D2 / (1+Ks)2 + D3/(1+Ks)3 + …. D∞/(1+Ks) ∞
P0 = ∑ Dt / (1 + Ks)t
If we assume that the dividend per share remains constant every year ,
lets say i.e. D then
P0 = D/(1+ks) + D/(1+ks)2 + D/(1+ks)3 + ….. D/(1+ks)n
On Simplification
P0 = D/Ks
Or Ks = D /P
t = 1
t = ∞

Cost of Equity – Dividend Capitalisation Approach
When the dividend increases at a constant rate , the share valuation
equation becomes:
P0 = D1/(1+Ks) + D1(1+g)/(1+Ks)2 + D1(1+g)2/(1+Ks)3 + …
On simplification it becomes:
P0 = D1 / Ks –g
Or Ks = D1 / P0 + g

QUESTTION
Raj Textiles Ltd. wishes to determine its cost of equity capital, Ke. The
prevailing market price of the share is Rs. 50 per share. The firm expects to
pay a dividend of Rs. 4 at the end of the coming year 2003. The dividends
paid on the equity shares over the past six years are as follows :
Year Dividend (Rs.)
2002 3.80
2001 3.62
2000 3.47
1999 3.33
1998 3.12
1997 2.97
The firm maintained a fixed dividend payout from 1996 onwards. The annual
growth rate of dividends, g , is approximately 5 percent.

SOLUTION
P0 = D1 / Ke –g
50 = 4 / (Ke – 0.05)
Ke = (4 / 50 ) + 0.05
Ke = 0.08 + 0.05 = 13%
The 13% cost of the equity share represents the return expected by existing
shareholders on their investment so that they should not disinvest in the
share of Raj Textiles Ltd. and invest elsewhere.

Cost of Equity – CAPM
As per CAPM
Kj = Rf + Βj *(Rm – Rf)
Where Rf = Risk free rate of return
Kj = Required or Expected rate of return on security j
Βj = Beta Coefficient of security j
Rm = Expected return on the market portfolio

WACC
WACC = Wd*Kd + We*Ke + Wp*Kp + I*(1-t)

QUESTION
• A firm has the following capital structure and after tax costs for the
different sources of funds used :
Source of Funds Amount
(Rs)
Proportion (%) After tax cost
(%)
Debt 40,00,000 20 4.50
Preference Shares 20,00,000 10 9.00
Equity Shares 60,00,000 30 11.00
Retained Earnings 80,00,000 40 10.00
200,00,000 100
Calculate cost of weighted capital by using book value method.

SOLUTION
METHOD OF
FINANCING
PROPORTI
ON (%)
COST (%) WEIGHTED
COST (%)
Debt 20 4.50 0.90
Preference Shares 10 9.00 0.90
Equity Shares 30 11.00 3.30
Retained Earnings 40 10.00 4.00
9.10

QUESTION
BHARAT AGRO Ltd. has assets of Rs.2,80,000 which have been financed with
Rs.64,000 of debt and Rs.1,10,000 of equity and a general reserve of
Rs.18,000.
The firm’s total profits after interest and taxes for the year ended 31st March
2004 were Rs.25,700. It pays 13% interest on borrowed funds and is in the
60% tax bracket.
It has 1,000 equity shares of Rs.100 each selling at a market price of Rs.125
per share. The firm pays 60% of its earnings as dividends.
Calculate
a) The EPS
b) The Cost of Debt
c) The Cost of Equity
d) The Weighted average cost of Capital

SOLUTION
a) Earning Per Share = Earnings after Interest and Taxes / No. of Shares
= 25700 / 1000 = 25.7
b) Cost of debt (Kd) = I (1–t) = 13 (1–0.60) = 5.2%.

SOLUTION CONTD..
• b) Cost of debt (Kd) = I (1–t) = 13 (1–0.60) = 5.2%.

SOLUTION CONTD..
c) Cost of equity = Ke = (DPS / MP ) * 100
Where
Ke = Cost of equity capital
DPS = Dividend Per Shares; (DPS = 60% of EPS = 0.6 x 25.7 = 15.42)
MP = Market Price of Share
Ke = (15.42 / 125 ) * 100
= 12.34%

SOLUTION CONTD..
d) Weighted Average Cost of Capital
Source of Capital Amount Specific Cost Total Cost
Debt 64,000 5.2% 3,328
Equity 1,10,000 12.34% 13,574
Reserves 18,000 12.34% 2,221.20
1,92,000 19,123.20
WACC = ( 19,123.20 / 1,92,000 ) * 100 = 9.96%

WACC
Stock Information
i. Industry : Pharmaceuticals
ii. Common stock quote (March 28, 2003) : $56.96
iii. Price/earnings ratio : 24.21
iv. Earnings per share : $2.18
v. Indicated annual dividend : 0.82
vi. Yield (percent) : 1.55
vii. Beta coefficient : 0.47
viii. Shares outstanding : 2,969,972,000
The Company's marginal tax rate is estimated to be 28 percent. The
Company's cost of debt can be estimated by the average effective interest
paid on its debentures and notes payable, which is calculated to be 5.85
percent before taxes.

Risk-free rate Rf = 3.907
Firm’s beta = 0.47
Market risk premium = 5.9 percent
The Company's market value of debt as per its December 29, 2002
balance sheet includes (in millions) loans and notes payable of US$
2,117 and long-term debt of US$ 2,022, for a total of US$ 4,139 million.
Q. Calculate the WACC ?

• Ke = 3.907 + 0.47(5.9) = 6.68 percent
• The market value of equity can be calculated by multiplying the
current share price times the number of current shares outstanding,
• US$ 56.96 × 2,969,972,000 = US$ 169,169.6 million
• Thus, Wd = 2.38 percent and We = 97.62 percent.
• WACC = (1 – .28)(2.38 percent × 5.85 percent) + (97.62 percent × 6.68
percent) = 6.62 percent

(Beta for an Individual Security) = Bj = Cov (Kj , Km) / σ2
m
(Beta for a Portfolio) = Bp = Cov (Kp , Km) / σ2
m

Risk components in levered Beta
Levered beta which reflects the capital structure of the company. The levered
beta has two components of risk, business risk and financial risk.
• Business risk represents the uncertainty in the projection of the company’s
cash flows which leads to uncertainty in its operating profit and
subsequently uncertainty in its capital investment requirements.
• Financial risk represents the additional risk placed on the common
shareholders as a result of the company’s decision to use debt, i.e. financial
leverage.
• If capital structure comprised of 100% equity then beta would only reflect
business risk. This beta would be unlevered as there is no debt in the
capital structure. It is also known as asset beta.

Relationship between Levered and Unlevered
Beta
βL = βU [1 + (1 – T)D/E]
βL = levered beta (beta at the current level of debt), and
βU = unlevered beta (beta when there is no debt in the capital structure).
V = D + E
That is, the value of the firm equals the sum of values of debt and equity.
Multiplying both sides by their respective beta,
βA V = βD D + βE E

Dividing both sides by V
βA = βD * D/V + βE * E/V
That is, asset beta is the weighted average of debt and equity beta.
βL = βU [1 + (1 – T)D/E]
βU = βL / [1 + (1 – T)D/E]

How do we relever Beta in WACC?
• To obtain the equity beta of a particular company, we start with a portfolio
of assets of that company or alternatively a sample of publicly traded firms
with similar systematic risk. We will first derive the betas of these
individual assets or firms from market prices. The derived betas are levered
betas as they would reflect the capital structure of the respective firms.
They have to be unlevered so as to only reflect their business risk
components.
• From the unlevered betas, obtain a weighted average unlevered beta using
as weights the proportions of the assets in the company’s asset portfolio or
derive an average across all comparable firms. The weighted unlevered
beta thus obtained would now be relevered based on the capital structure
of the company in order to determine the equity or levered beta for the
company. This beta would reflect not only the business risk but also the
financial risk of the company.

Example
BetaCorp is a corporation that has two primary business lines –
personal hygiene and consumer off the shelf pharmaceuticals. We are
estimating its levered beta for the purpose of determining its cost of
equity. The personal hygiene subsidiary is worth USD 20 million while
the consumer pharma subsidiary is worth USD 30 million. The firm has
a debt-to-equity ratio of 1. Assume that the tax rate for all firms is 30%.
The risk free rate is 7% and the market risk premium is 6%. The
following information is for firms with comparable systematic risk:
Note that the average betas above denote the average of the levered or equity betas of these firms.
Comparable Firms Average Beta Average D/E Ratio
Personal Hygiene 0.9 20%
Medical 1.2 60%

Unlevered Beta for the personal hygiene business = 0.9 / (1+ 0.2*(1-0.3)) = 0.79
Unlevered Beta for the consumer pharma business = 1.2 / (1+ 0.6*(1-0.3)) = 0.85
The Beta for BetaCorp will be the weighted average of unlevered betas where the weights are
in proportion to the subsidiaries value in the firm, i.e.
Unlevered Beta for BetaCorp = 0.79*20m/50m + 0.85*30m/50m = 0.82
Levered Beta for BetaCorp = 0.82*(1+1*(1-0.3)) = 1.40
Cost of Equity = 7%+1.40*6% = 15.39%.

Question
Company X is a non-listed private company. Here are some details
available with you:
Total Debt $ 2 million
Total Equity $ 5 Million
Debt to Equity ratio 40%
Tax rate 30%

a comparable company which is similar in nature to the Company X is
operating in the same industry and it has the same product line and
risk profile as Company X. So, you have collected the following data
about the comparable company:
find out the beta for the Company X.
Calculated Beta 1.2
Total Debt $ 4 million
Total Equity $ 8 Million
Debt to Equity ratio 50%
Tax rate 35%

Answer
Unlevered Beta (βCompany A) = 1.2 / 1 + [ (1- 0.35) (0.5) ] = 0.91
Levered beta (βCompany X)
= Unlevered Beta * 1 + [ (1- Tax) (Debt/Equity) ]
= 0.91 * 1 + [ (1- 0.3) (0.4) ] = 1.17

Cost of Capital in management of diff firms.pptx

Cost of Capital in management of diff firms.pptx

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Cost of Capital in management of diff firms.pptx