# Ch 9-The Cost of Capital by IM Pandey

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## Full text

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### LEARNING OBJECTIVES

 Explain the general concept of the opportunity cost of capital

 Distinguish between the project cost of capital and the firm’s cost of capital

 Learn about the methods of calculating component cost of capital and the weighted average cost of capital

 Recognize the need for calculating cost of capital for divisions

 Understand the methodology of determining the divisional beta and divisional cost of capital

 Illustrate the cost of capital calculation for a real company

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## and Values

 The required rate of return (or the opportunity cost of capital) is shareholders is market-determined.

 In an all-equity financed firm, the equity capital of ordinary shareholders is the only source to finance investment projects, the firm’s cost of capital is equal to the opportunity cost of equity capital, which will depend only on the business risk of the firm.

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## Opportunities

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### Opportunity Cost of Capital

 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.

 The opportunity cost of retained earnings is the rate of return, which the ordinary shareholders would have earned on these funds if they had been distributed as dividends to them

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## Cost of Capital

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### 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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## COSTS OF CAPITAL

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### Tax adjustment

0 d B INT i k   n d n t d t n 1 t 0 ) k 1 ( B ) k 1 ( INT B       ) T 1 ( k debt of cost tax After  d12

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## Cost of the Existing Debt

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### Redeemable Preference Share

0 p P PDIV k  n p n t p t n 1 t 0 ) k 1 ( P ) k 1 ( PDIV P       15

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## Example

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### Zero-growth

) g k ( DIV P e 1 0 

### 

         n 1 t n e n e 1 n t e t s 0 0 ) k 1 ( 1 g k DIV ) k 1 ( ) g 1 ( DIV P 0) g (since P EPS P DIV k 0 1 0 1 e   17

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## COST OF EQUITY CAPITAL

### Earnings–Price Ratio and the Cost of Equity

g P DIV k 0 1 e   0) (b P EPS br) (g br P ) b 1 ( EPS k 0 1 0 1 e       18

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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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### 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 ()

j f m f e

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## Example

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### application in practice

 It assumes that the dividend per share will grow at a constant rate, g, forever.

The expected dividend growth rate, g, should be less than the cost of equity, ke, to arrive at the simple growth formula.

 The dividend–growth approach also fails to deal with risk directly.

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## Cost of equity under CAPM

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### DIVIDEND–GROWTH MODEL

CAPM has a wider application although it is based on restrictive assumptions.

 The only condition for its use is that the company’s share is quoted on the stock exchange.

 All variables in the CAPM are market determined and except the company specific share price data, they are common to all companies.

 The value of beta is determined in an objective manner by using sound statistical methods. One practical problem with the use of beta, however, is that it does not probably remain stable over time .

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### 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.

E D E k E D D ) T 1 ( k k w k w ) T 1 ( k k e d o e d d d o         26

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### calculating WACC

 Firms in practice set their target capital structure in terms of book values.

 The book value information can be easily derived from the published sources.

 The book value debt-equity ratios are analysed by investors to evaluate the risk of the firms in practice.

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### questioned on theoretical grounds;

 First, the component costs are opportunity rates and are determined in the capital markets. The weights should also be market-determined.

 Second, the book-value weights are based on arbitrary accounting policies that are used to calculate retained earnings and value of assets. Thus, they do not reflect economic values

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### to book-value weights:

 They reflect economic values and are not influenced by accounting policies.

 They are also consistent with the market-determined component costs.

### The difficulty in using market-value weights:

 The market prices of securities fluctuate widely and frequently.

 A market value based target capital structure means that the amounts of debt and equity are continuously adjusted as the value of the firm changes.

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### AND INVESTMENT ANALYSIS

A new issue of debt or shares will invariably involve flotation costs in the

form of legal fees, administrative expenses, brokerage or underwriting commission.

 One approach is to adjust the flotation costs in the calculation of the cost of

capital. This is not a correct procedure. Flotation costs are not annual costs; they are one-time costs incurred when the investment project is undertaken and financed. If the cost of capital is adjusted for the flotation costs and used as the discount rate, the effect of the flotation costs will be compounded over the life of the project.

 The correct procedure is to adjust the investment project’s cash flows for

the flotation costs and use the weighted average cost of capital, unadjusted for the flotation costs, as the discount rate.

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### COST OF CAPITAL

The pure-play approach for calculating the divisional cost of capital involves the following steps:

 Identify comparable firms

 Estimate equity betas for comparable firms:  Estimate asset betas for comparable firms:  Calculate the division’s beta:

 Calculate the division’s all-equity cost of capital  Calculate the division’s equity cost of capital:  Calculate the division’s cost of capital

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## Example

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### The Cost of Capital for Projects

 A simple practical approach to incorporate risk differences in projects is to adjust the firm’s WACC (upwards or downwards), and use the adjusted WACC to evaluate the investment project:

 Companies in practice may develop policy guidelines for incorporating the project risk differences. One approach is to divide projects into broad risk classes, and use different discount rates based on the decision maker’s experience.

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### Low risk projects

discount rate < the firm’s WACC

### Medium risk projects

discount rate = the firm’s WACC

### High risk projects

discount rate > the firm’s WACC

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## References

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