Module 3

Cost Of Capital

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INTRODUCTION

The project’s cost of capital is the minimum required rate of return on funds committed to the project, which depends on the riskiness of its cash flows.

The firm’s cost of capital will be the overall, or average, required rate of return on the aggregate of investment projects

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THE CONCEPT OF THE OPPORTUNITY COST OF CAPITAL

The opportunity cost is the rate of return foregone on the next best alternative investment opportunity of comparable risk.

Opportunity cost of capital is given by the following formula:

where Io is the capital supplied by investors in period 0 (it represents a net cash inflow to the firm), Ct are returns expected by investors (they represent cash outflows to the firm) and k is the required rate of return or the cost of capital.

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Weighted Average Cost of Capital vs. Specific Costs of Capital The cost of capital of each source of capital is known as

component, or specific, cost of capital. The overall cost is also called the weighted average cost of

capital (WACC). Relevant cost in the investment decisions is the future cost or

the marginal cost. Marginal cost is the new or the incremental cost that the firm

incurs if it were to raise capital now, or in the near future. The historical cost that was incurred in the past in raising

capital is not relevant in financial decision-making.

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COST OF DEBT

Debt Issued at Par

Debt Issued at Discount or Premium

Tax adjustment  

Pikd

INT

SVNPikd /

INT

)1(debt ofcost tax After Tkd

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COST OF REDEEMABLE DEBT

Before Tax

After Tax  

)(2/1

)(/1INT

SVRV

SVRVnkd

)(2/1

)(/1)1INT(

NPRV

NPRVntkd

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EXAMPLE7

a) X Ltd issues Rs 50,000 8% debentures at par. The tax rate applicable to the company is 50%. Compute the cost of debt capital.

b) Y Ltd issues Rs 50,000 8% debentures at a premium of 10%. The tax rate applicable to the company is 60%. Compute the cost of debt capital.

c) A Ltd issues Rs 50,000 8% debentures at a discount of 5%. The tax rate applicable to the company is 50%. Compute the cost of debt capital.

d) B Ltd issues Rs 100,000 9% debentures at a premium of 10%. The cost of floatation are 2%. The tax rate applicable to the company is 60%. Compute the cost of debt capital.

-> NP = 110,000 - (.02x110,000)

EXAMPLE8

A company issues Rs 10,00,000 10% redeemable debentures at a discount of 5%. The cost of floatation amount to Rs 30,000. The debentures are redeemable after 5 years. Calculate before tax and after tax cost of debt assuming a tax rate of 50%.

-> RV = 10,00,000-> NP = (10,00,000-50,000-30000)

A 5 year Rs 100 debenture of a firm can be sold for a net price of Rs 96.50. Coupon rate of interest is 14% and it will be redeemed at 5% premium on maturity. The tax rate is 40%. Compute after tax cost of debenture.

-> RV = 105-> NP = 96.5

EXAMPLE9

Assuming that a firm pays tax at 50% rate, compute the after tax cost of debt capital in the following cases:

a) A perpetual Rs 100 bond sold at par, coupon rate being 7%

b) A 10year, 8% Rs 1000 bond sold at Rs 950 less 4% underwriting commission.

-> Redeemable Or Irredeemable-> RV = 1000 -> NP = 912

COST OF PREFERENCE CAPITAL

Irredeemable Preference Share  

Redeemable Preference Share  

NPk p

PDIV

)(21

NPMV

nNPMV

DKp

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Example11

Example

A company issues 10,000 10% Preference Shares of Rs 100 each. Cost of issue is Rs 2 per share.

Calculate the cost of preference shares if it is issued

A) at par

B) at a premium of 10%

C) at a discount of 5%

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Example

A company issues 10,000 10% Preference Shares of Rs 100 each redeemable after 10 years at a premium of 5%. Cost of issue is Rs 2 per share.

Calculate the cost of preference share capital.

13

)(21

NPMV

nNPMV

DKp

-> MV = 10,50,000

-> NP = 980,000

Example

A company issues 1000 7% Preference Shares of Rs 100 each at a premium of 10% redeemable after 5 years at par. Calculate the cost of preference share capital.

14

)(21

NPMV

nNPMV

DKp

-> MV = 100,000

-> NP = 110,000

COST OF EQUITY CAPITAL

NPKe 1DIV

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a) Dividend Yield Method:

b) Dividend Yield Plus Growth:

MPKe 1DIV

GNP

Ke 1DIV

Example

A company issues 1000 Equity Shares of Rs 100 each at a premium of 10%. They have been paying 20% dividend and will continue to do so. Calculate the cost of equity share capital. Will it make any difference if the market price is Rs 160?

a) Ke = 20/110 = 18.18%

b) Ke = 20/160 = 12.5%

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NPKe 1DIV

MPKe 1DIV

Example

A) A company issues 1000 Equity Shares of Rs 100 each at par. Floatation cost are expected to be 5% of the share price. They have been paying Rs10 dividend per share and the growth in dividend is expected to be 5%. Calculate the cost of equity share capital.

->NP = (100-5)

B) If the current market price is Rs 150, calculate the cost of equity.

->MP = 150

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GMP

Ke 1DIV

GNP

Ke 1DIV

COST OF EQUITY CAPITAL

Earnings–Price Ratio and the Cost of Equity

P

EPS

0

1ek

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Example: EPS

A firm is currently earning Rs 100,000 and its share is selling at a market price of Rs 80. The firm has 10,000 shares outstanding and has no debt. The earnings of the firm are expected to remain stable, and it has a payout ratio of 100 per cent. What is the cost of equity?

We can use expected earnings-price ratio to compute the cost of equity. Thus:

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THE CAPITAL ASSET PRICING MODEL (CAPM) As per the CAPM, the required rate of return on

equity is given by the following relationship:

Equation requires the following three parameters to estimate a firm’s cost of equity: The risk-free rate (Rf)

The market risk premium (Rm – Rf) The beta of the firm’s share ()

)( fmfe RRRk

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Example

Suppose in the year 2012 the risk-free rate is 6 per cent, the market risk premium is 9 per cent and beta of L&T’s share is 1.54. The cost of equity for L&T is:

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Example

1) T-Bill return is 8%, Systematic risk of ABC Ltd is around 1.125 and Market/Index return of 12%. Calculate the cost of ABC equity.

2) T-Bill return is 10%, XYZ ltd Beta is 1.10 and Index return is of 18%. Compute the cost of equity.

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THE WEIGHTED AVERAGE COST OF CAPITAL

The following steps are involved for calculating the firm’s WACC: Calculate the cost of specific sources of funds Multiply the cost of each source by its proportion in the

capital structure. Add the weighted component costs to get the WACC.

WACC is in fact the weighted marginal cost of capital (WMCC); that is, the weighted average cost of new capital given the firm’s target capital structure.

ED

Ek

ED

DTkk

wkwTkk

edo

eeddo

)1(

)1(

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The Cost of Capital for Projects For example, projects may be classified as:

Low risk projects

discount rate < the firm’s WACC Medium risk projectsdiscount rate = the firm’s WACC High risk projectsdiscount rate > the firm’s WACC

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Example

Source Of Funds:Debt - 15,00,000 - 5% cost

Preference Share - 12,00,000 - 10% cost

Equity Shares - 18,00,000 - 12% cost

Retained Earnings - 15,00,000 - 11% cost

Total - 60,00,000

Solve Weighted Average Cost Of Capital.

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Example

Source Of Funds:Debt - 18,00,000 - 10% cost

Preference Share - 22,00,000 - 14% cost

Equity Shares - 18,00,000 - 12% cost

Retained Earnings - 10,00,000 - 10% cost

Total - 68,00,000

Solve Weighted Average Cost Of Capital.

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CAPITAL STRUCTURE

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Capital Structure Theories:

Net operating income (NOI) approach.

Traditional approach and Net income (NI) approach.

MM hypothesis with and without corporate tax.

Miller’s hypothesis with corporate and personal taxes.

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Net Operating Income (NOI) Approach

According to NOI approach the value of the firm and the weighted average cost of capital are independent of the firm’s capital structure. In the absence of taxes, an individual holding all the debt and equity securities will receive the same cash flows regardless of the capital structure and therefore, value of the company is the same.

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Net Income (NI) Approach

According to NI approach both the cost of debt and the cost of equity are independent of the capital structure; they remain constant regardless of how much debt the firm uses. As a result, the overall cost of capital declines and the firm value increases with debt. This approach has no basis in reality; the optimum capital structure would be 100 per cent debt financing under NI approach.

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Traditional Approach

The traditional approach argues that moderate degree of debt can lower the firm’s overall cost of capital and thereby, increase the firm value. The initial increase in the cost of equity is more than offset by the lower cost of debt. But as debt increases, shareholders perceive higher risk and the cost of equity rises until a point is reached at which the advantage of lower cost of debt is more than offset by more expensive equity.

ke

ko

kd

Debt

Cost

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Relationship between capital structure and the firm value :

First stage: Increasing value Second stage: Optimum value Third stage: Declining value

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Criticism of the Traditional View The contention of the traditional theory, that moderate

amount of debt in ‘sound’ firms does not really add very much to the ‘riskiness’ of the shares, is not defensible.

There does not exist sufficient justification for the assumption that investors’ perception about risk of leverage is different at different levels of leverage.

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MM Approach Without Tax: Proposition I MM’s Proposition I is

that, for firms in the same risk class, the total market value is independent of the debt-equity mix and is given by capitalizing the expected net operating income by the capitalization rate (i.e., the opportunity cost of capital) appropriate to that risk class.

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MM’s Proposition I: Key Assumptions Perfect capital markets Homogeneous risk classes Risk No taxes Full payout

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The cost of capital under MM proposition I

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Criticism of the MM Hypothesis Lending and borrowing rates discrepancy Non-substitutability of personal and corporate

leverages Transaction costs Institutional restrictions Existence of corporate tax

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MM show that the value of the firm will increase with debt due to the deductibility of interest charges for tax computation, and the value of the levered firm will be higher than of the unlevered firm.

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MM Approach With Tax: Proposition II

LEVERAGE

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Operating Leverage

One potential “effect” caused by the presence of operating leverage is that a change in the volume of sales results in a “more than proportional” change in operating profit (or loss).

Operating Leverage Operating Leverage -- The use of -- The use of fixed operating costs by the firm.fixed operating costs by the firm.

Degree of Operating Leverage (DOL)

DOLDOL

Degree of Operating Leverage Degree of Operating Leverage -- The percentage change in a firm’s operating profit (EBIT) resulting from a 1 percent change in output (sales).

=

Percentage change in operating profit (EBIT)

Percentage change in output (or sales)

Financial Leverage

Financial leverage is acquired by choice. Used as a means of increasing the return to

common shareholders.

Financial Leverage Financial Leverage -- The use of -- The use of fixed financing costs by the firm. The fixed financing costs by the firm. The British expression is British expression is gearinggearing..

Degree of Financial Leverage (DFL)

DFLDFL

Degree of Financial Leverage Degree of Financial Leverage -- The percentage change in a firm’s earnings per share (EPS) resulting from a 1 percent change in operating profit.

=

Percentage change in earnings per share (EPS)

Percentage change in operating profit (EBIT)