LECTURE SIX: COST OF CAPITAL6.0 INTRODUCTION

When funds are obtained by selling an ownership interest (equity) or a through a loan, the cost to the issuer or loanee (demander) is commonly called the required rate of return. Objectives At the end of the lecture students should be conversant with: 1.Sources and costs of long term capital 2. Weighted average cost of capital (WACC) and weighted marginal cost of capital (WMCC) 3. Financing and investment decisions using IOS and WMCC schedules1.

6.1 COST OF CAPITALCost of capital acts as a major link between the firms investment decision and the wealth of the owners of a firm. It is the magic number that is used to decide whether a proposed corporate stock price. Our concern is with long-term sources, which supply the permanent financing. Definition Cost of capital can be defined as the rate of return that a firm must earn on its project investments to maintain the market value of its shares. Or, As the minimum rate of return required by suppliers of capital firm to attract their funds to the firm. If risk is held constant, projects with rate of return above the cost of capital will increase the value of the firm, vice versa.

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Cost of capital and risk The following equation explains the general relationship between risk and financing costs.

k = r + bp + fp Ki f i i

1

6.1

Where:

k r bpi f

=

specific cost of the type of long term financing risk free cost of the given type of financing business risk premium of firm i financial risk premium faced by firm i

=

i

= =

fp

i

The equation indicates that the cost of each type of capital depends on the risk free cost of that type of funds, the business risk of the firm and the financial risk of the firm. Business risk is the risk to the firm of being unable to cover operating costs. Financial risk is the risk of the firm of being unable to cover required

6.2 SPECIFIC SOURCES OF CAPITALThe right hand side of the balance sheet comprises current liabilities, long-term debt, preferences shares capital, and ordinary share capital. Our concern is only with the longterm sources of funds because they supply the permanent financing. 6.2.1 Cost of Debt Before tax cost of debt The before tax cost of debt can be derived by solving for the discount rate

k

d

, that

equates the market price of the bond with present value of cash flows from the bond over its life (interest plus principal payments). This is the same as funding the internal rate of return (IRR) on the bonds cash flows.

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This cost, k d , also know as the yield to maturity can be calculated by using the formula

Bo = t =1

n

I +P (1+ k d )t t

t

6.2

Where B0 , is the current market price of bold (net proceeds (minus any flotation costs).

P

t

and

I

t

are the payment of principal and interest in period t .

If principal payment occurs only at maturity and if the interest payments are constant the relationship would simplify to: n

Bo = t =1

It

(1+ k d ) (1+ k d )

+

Mn

Where M is the payment at maturity and I is the periodic interest payment. By solving for k d , the discount rate the equates the present value of cash payments to suppliers of debt to current market price of debt, we find the rate of return required by the lenders. Example A company intends to sale a bond to raise capital. The features of the bond are: Par value Kshs. 1,000 Coupon rate 9% Discount on issue Kshs. 20 Flotation cost 2% of par value Find the cost of debt financing Soution

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Net proceeds of from sale of bond = 1000 20 2% x 1000 = 960 The cash flows associates with ABC Companys bond issue are as follows End of year 0 1 20 20 CF +960 -90 -1000

We work out the cost of debt k d , through trial and error. The discount rate must be higher than the 9% (because 960 < 1000, the par value. The present value at a 9% is Sh. 1000, same as par value. Lets try 10%. The present value of cash flows is given by 90*

k

d

of

PVIFA

10%, 20 yrs

+ 1000 * PVIF 10%, 20 yrs =Sh. 915.26.

Because 960 is between 1000 and 915.26 the however 9% to the nearest whole %,

k

d

must be between 9% and 10%. It is

By using interpolation the bonds before tax cost is 40 = 9.47% 85 = 9.47

9% +

k

d

After tax cost of debt The specific cost of financing must be selected on an after tax basis. Because interest on debt is tax deductible it reduces taxes by an amount equal to the product of the interest payment and firms tax rate. The after-tax cost of debt will be substantially lower than the before tax cost and will be given by k i = k d (1 T )

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Where

k

d

is the before tax cost of debt and is T is the firms tax rate.

If the ABC Co is in the 40% tax bracket, the after tax cost of debt will be 9.47 x (1-0.4) = 9.47 x 0.6

= 5.68% Typically the explicit of debt is less than the cost of alternative forms of long term financing primarily because of the tax deductibility of interest. The higher the rate of corporation tax is, the greater the tax benefits in having debt finance when compared with equity finance. In the example above, if the rate of tax had been 50%, the cost of debt would have been 9.47(1-.5) =4.74%

Example: Owen Allot plc has in issue 10% debentures of a nominal value of Sh.1000. the market price is Sh.900 ex interest. Calculate the cost of this capital if the debenture is: a. b. Solution The cost of irredeemable debt capital is I I Irredeemable; Redeemable at par after 10 years.

Ignore taxation. 100 = 11.1% 900

B

=0

The cost of redeemable debt capital. The best trial and error figure to try first is, 12%. Year Cash flow Discount PV Discount PV 5

Factor 12% 0 Market value (900) 1-10 Interest 100 10 Capital repayment 1000

factor 11%

(90.00) 5.889 58.89 35.20 40.90

1.000 (900.00) 1.000 5.650 565.00 0.322 322.00 0.352 (13.00)

The approximate cost of debt capital is, therefore 12

13.00 = 11.76% 40.90 + 13.00

The cost of debt capital estimated above represents the cost of continuing to use the finance rather than redeem the securities at their current market price. It would also represent the cost of raising additional fixed interest capital if we assume that the cost of the additional capital would be equal to the cost of that already issued. If a company has not already issued-any fixed interest capital, it may estimate the cost of doing so by Approximating before tax cost of debt Therefore tax cost of debt using following equation: 1000 N d 6.3

k

d

, for a bond with Kshs.1000 par value center approximate

k

d

=

I+

n + 1000 Nd 2

Where I = annual interest payments

N

d

= net proceeds from sale of debt

n = number of years to bonds maturity Substituting in previous example:

6

k

d

=

90 +

1000 960 20 960 + 1000 2

= 9.4%.

6.2.2 Cost of Preferred Stock

The cost of irredeemable preferred stock,

k

p

is the ratio of the preferred stock

dividend to the firms net proceeds from sale of the preferred stock ( Market price minus any flotation costs and discounts).

k

p

=

D Npp

(6.4)

Where k p cost of preferred stock,

D

p

annual dividend, and

N

p

the net proceeds from

sale of preference shares, excluding any flotation costs. Because preferred stock dividend are paid out of the firms after tax cash flows, a tax adjustment is not required as was in the case of debt. Example ABC Co is contemplating issuance of a 10% preferred stock expected to sell for its Kshs.87 per share par value. The cost of selling the stock is expected to be Shs.5 per share. Find the cost of preferred stock

D N

p

=

10% x 87

=

Kshs.8.70

p

=

87 5

=

Kshs. 82

k

p

=

8.70 = 10.6% 82

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6.2.3 Cost of Ordinary Share Capital

The cost of equity is the return required on by investors in the market place. The cost,

k

s

, is the rate at which investors discount the expected dividends of the firm to determine its share value. There are 2 forms of equity financing 1. Retained earnings 2. New issues of equity.

In the context of the dividend discount model approach the cost of equity

k

s

can be

thought of as the discount rate that equates the present value of cash flows with the current market price of the share. Recall from valuation.

P0 = t =1

D (1+ k s)t

t

(6.5)

Where P0 = current market price per share, end of period t and

D

t

is dividend expected to be paid at the

k

s

is discount rate, the cost of equity.

In estimating future dividend, assumptions necessary. The most frequently used assumptions are zero growth in dividends, constant growth in dividends, and variable growth rates. Constant Growth Rate If future dividends are expected to grow at a constant rate, the expression to use in estimating cost of equity is

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P

0

=

D (1 + g ) = D k g k g0 1 s s

(6.6)

Therefore, cost of equity is Example

ks =

D (1 + g ) + g = D P P0 0

1

+g

(6.6)

0

ABC dividends are expected to grow at a constant rate of 5% into the foresable future. The company has just paid dividend of Shs.3.80 and is share is selling at a market price of Shs.50 calculate of cost of equity.

ks =

3.80 (1 + 0.05) + 0.05 = 3.99 + 0.05 = 12.98%50 50

Growth Phases If growth in dividends is expected to vary in future a modification in the dividend model will be in order. Usually above normal growth is followed by normal growth. For instance, if dividend were expected to growth 15% compound rate for 5 years, at 10% for next 5 years, and the gowth at 5% rate into the firescible future the equation would be: -

D (1+ 0.15 + D (1+ 0.10) + D * 1 P = k 0.05 (1+ k s) (1+ k s) (1+ k s)5 t 0 10 t 5 11 0 t =1 t t =6 t s

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If current dividend paid is 2/= and current market price is Sh.70, the 10.42%. Cost of Retained Earnings

k

s

would be

The cost of retained earning, Kr, to the firm is the same as the cost of equity. 9

k

r

=

k

s

It is not necessary to adjust the cost of retained earnings for flotation costs because retention is an internal financing received without incurring these costs. The cost of retained earnings for ABC Co as calculate above for Ks. Cost or retained earnings is always lower than cost of a new issue due to absence of flotation costs when financing projects with retained earnings. Cost of new issues

The cost of new issue of equity

k

n

is determined by calculating the cost of equity net of

any discounts and associated flotation costs. Because of flotation costs and discounts the proceeds from an issue will be less than current market price of the stock and hence its cost will be more expensive. The cost of new issues can be calculated by modifying equations as follows. If net proceeds =

N

n

i.e.

( Price - Flotation cots). The cost of equity,

under the two assumptions of no growth. and constant growth will be

No Growth

k

n

=

D

N

n

With constant growth = k n =

D N

1 n

+g

Example:

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The Co estimates that to sell a new issue the shares will have also to be priced at Sh.47, and in addition flotation costs of Sh..2.50 per share will be incurred. What is cost of new issue if the company has and will experience a constant growth in dividend of 5%, and is currently selling at a price of Sh.50. Dividend next year is expected to be Sh. 4.00 per share.

k

n

=

4.00 + 0.05 = 14% 47 2.50

This is the value to be used in subsequent calculations of a firms cost of capital.

6.3 WEIGHTED AVERAGE COST OF CAPITALWACC reflects the expected average future cost of funds over the long run; found by weighing the cost of each specific source of capital by its proportion in the firms capital structure. The calculation of the WACC is performed by multiplying the specific cost of each form of financing by its proportion in the firms capital structure and summing the weighted values

k (WACC ) = wi * k i + w p * k p + ws * k s Where

(6.7)

w w w

i

= = =

proportion of long term debt in capital structure proportion of preference stock in capital structure proportion of equity in capital structure

p

s

11

w

i

+

w

p

+

w

s

= 1

the firms equity weight ws is multiplied by either the cost if retained earnings of new equity

k

r

or cost

k

n

, which cost is used depend on whether the firms equity will come

from retained earnings on new issues.

Example: ABC Co costs of various types of capitals are

Cost of debt

k

i

=

5.6%

Cost of preference

k k

p

=

10% 13% = 14%

Cost of retained earnings Cost of new equityn

k

r

=

The Co target capital structure proportions are: Weight Debt Preferred stock Equity 40% 10% 50% 100% The company has a sizable amount of retained earnings that it intends to use for future investments. Find companys WACC Weight Debt Preferred stock 0.4 0.1 Cost 5.6% 10.6 Weighted Cos 2.2% 1.1

12

Equity

0.5

13.0

6.5 9.8

WACC

=

9.8%

Arguments for using WACC The weighted average cost of capital is recommended for use in investment appraisal on the assumptions that: a. Net investments must be financed by new sources of funds; retained earnings, new share issues, new loans and so on; b. The cost of capital to be applied to project evaluation must reflect the marginal cost of new capital; and c. The weighted average cost of capital reflects the companys long-term future capital structure, and capital costs. If this were not so, the current weighted average cost would become irrelevant because eventually it would not relate to any actual cost of capital.

It has been argued that the current weighted average cost of capital should be used to evaluate project, because a companys capital structure changes only very slowly over time; therefore the marginal cost of new capital should be roughly equal to the weighted average cost of current capital. If this view is correct, then by undertaking investments, which offer a return in excess of the WACC, a company will increase the market value of its ordinary shares in the long run. This is because the excess returns would provide surplus profits and dividends for the shareholders.

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Arguments against using the WACC The arguments against using the WACC as the cost of capital for investment appraisal are based on criticism of the assumptions that are used to justify use of the WACC. The main arguments against the WACC are as follows. a. New investments undertaken by a company might have different business risk characteristics from the companys existing operations. As a consequence, the return required by investors might go up (or down) if the investments are undertaken, because their business risk is perceived to be higher (or lower). b. The finance that is raised to fund a new investment might substantially change the capital structure and the perceived financial risk of investing in the company. Depending on whether the project is financed by equity or by debt capital, the perceived financial risk of the entire company might change. This must be taken into account when appraising investments. c. Many companies raise floating rate debt capital as well as fixed interest debt capital. With floating rate debt capital, the interest rate is variable, and is altered every three or six months or so in line with changes in current market interest rates. The cost of debt capital will therefore Floating rate debt is difficult to fluctuate as market conditions vary.

incorporate into a WACC computation, and the best that can be done is to substitute an equivalent fixed interest debt capital cost in place of the floating rate debt cost.

6.4 WEIGHTING SCHEMEWeights can be calculated base on book value or market value and using historic or target proportions.

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Book value vs. Market value Book value weights use historical accounting values to measure the proportion of each type of capital in the firms financial structure. Market value weights measure the proportion of each type of capital at its current market value. Market value weights are appealing, because the market value of securities closely approximate the actual shilling amounts to be received from their sale. In addition the long term cash flows from investments to which cost of capital is applied are estimated in terms of current as wells future Market values. Historic versus Target Historic weights are either book or market value weights based on desired optimal capital structure proportions. From a purely theoretical point of view the preferred weighting is target market value proportion.

6.5 WEIGHTED MARGINAL COST OF CAPITALAs volume of financing increase the cost of various types of financing will increase, raising the firms WACC. Therefore, it is useful to calculate WMCC, which is the firms WACC associated with its next shilling of total new financing. The marginal cost is the WACC relevant to current decisions. As larger amounts of financing are raised the greater the risk to the funds providers. Therefore the WMCC is an increasing function of the level of total new financing. Another factor that causes WACC to increase is that as retained earnings are exhausted equity will have to be sourced through more expensive new issues.

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Finding Breaking points To calculate WMCC, we must calculate the breaking points, which reflect the level of total new financing at which cost of one of the financing components rises. following general equation can be used to find breaking points. BPj = Afj Wj Where: BPj AFj Wj = = = breaking point for financing source j amount of funds circulable from source j at a given cost (before BP) capital structure weight for financing source j. The

Example ABC Co has Kshs.300,000 of retained earnings available whose cost is 13%. If it exhausts the returned earnings it must use more expensive new issue of equity whose cost is 14%. The firm expects that it can borrow only Kshs.400,000 of debt at the 5.6% cost, additional debt will have an after tax cost of 8.4%. Unlimited amounts of funds can be raised by issuing preferred stock at cost of 10.6% The company target capital structure proportions are:

Weight Debt Preferred stock Equity Required: 40% 10% 50% 100%

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-

Determine the breaking points Calculate the WMCC after each breaking point Draw WMCC schedule.

Solution (a) Breaking points: Two breaking points exist (1) When the Kshs.300,000 of retained earnings is exhausted and (2) When the Kshs.400,000 of debt costing 5.6% is exhausted. BP equity = AF Ws BP debt = AFj Wj = = 300,000 0.5 400,000 0.4 = Sh.1,000,000 = Sh.600,000

No breaking is caused by increase use of preference shares. (b) Calculating WMCC Next we calculate the WACC between breaking points. First find WACC between total financing of Sh.0 Sh.600,000, then WACC from Sh.600,000 Sh.1,000,000 then above Sh.1,000,000. WACC for ranges of total financing:

Sh.0 600,000 Sh .600,000 1,000,000 Sh.1,000,000 and above (c) WMCC graph (c) 12

0.4 (5.6) + 0.1 (10.6) + 0.5 (13) 0.4 (5.6) + 0.1 (10.6) + 0.5 (14.0) 0.4 (5.6) + 0.1 (10.6) + 0.5 (14.0)

= = =

9.8% 10.3% 11.5%

17

11.5% 10.3% 10 9.8%

0

600,000

1,000,000 Total new finances

6.6 INVESTMENT OPPORTUNITY SCHEDULE (IOS) AND THE WMCC SCHEDULEThe investments made by firm depend on two things. The returns on investment opportunities The cost of financing the opportunities.

The firms IOS is a ranking of investment possibilities from best to worst (lowest return). As the cumulative amount of money invested in a firms capital project increase, its IRR on the projects will decrease. The first project selected will have the highest return, followed by the second highest and so on until the funds available are exhausted. We can use the concept of the investment opportunity schedule and the WMCC schedule to simultaneously illustrate the interdependence of the investment and the financing decisions. Lets go back to the preceding example of ABC company. Suppose ABC has the following investment opportunities available during a given year. Investment opportunit y A Opportunitys Initial IRR 15% Investment Sh. 000 100 18

B C D E F G

10.0 12.0 11.0 14.0 13.0 14.5

100 300 200 400 100 200

The following IOS can be prepared ranking the projects according to their IRRs from the most to the least preferable. company has prepared the following investment opportunity schedule:

Investment opportunit y A G E F C D B

Opportunitys Initial IRR 15% 14.5 14.0 13.0 11.0 11.0 10.0 Sh. 000 100 200 400 100 300 200 100

Cum. Sh. 000 100 300 700 800 1100 1300 1400

Investment investment

We can plot the project returns against the cumulative investment on the same axes as the WMCC schedule the firm should accept projects up to the point at which the marginal return on its investment equals its weighted marginal cost of capital.

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A

15 14 13 12.5 12 F 11.5WMCC

G

E

11 C 10.5

10

D

IOS

9.5

* 200 400 600 800 1000 1200 1400

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By using the WMCC and IOS schedules the firms optimal capital budget is determined as (1,100,000). By raising Kshs. 1100,000 of new financing and investing in projects AGEF and C the firm should maximize shareholder width. Review Questions

1. 2.

A cost of capital can be said to consist of three elements. What are they? What is the dividend valuation model formula for the cost of equity:

(a) with no dividend growth? (b) with dividend growth? 3. How is the after-tax cost of debt of debt capital calculated? 4. Why should a weighted average cost of capital be used as the discount rate, instead of the cost of the funds that are specifically used to finance each new investment? 5. On what assumption is it appropriate to use the weighted average cost of capital as the discount rate for investment evaluation? 6. Should weightings be based on the market values or the book values of the sources of capital? What are the argu

Problems 6.1 Explain and distinguish between: a) Weighted average cost of capital, and b) Marginal weighted average cost of capital. Nyuki Ltd is a company operating in eh telecommunications industry. The companys balance sheet as at 31 March 2007 is as below:

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Liability and Owners Equity Current liabilities 18% debentures (sh. 000) 10% preference shares Ordinary shares (sh.10 par) Retained earnings Sh 000 12,500 16,000 6,250 12,500 28,125 75,375 Current assets Net fixed asset Sh 000 32,500 42,875

75,375

Additional Information 1. 2. The debentures are selling at Sh. 950 in the market and will be redeemed 10 years from noon. By the end of last financial period the company had declared and paid sh.500 as dividend per share. The dividends are expected to grow at an annual rate of 10% in the forecast future. Currently the companys share are grading at sh.38 per share at the local stock exchange. 3. 4. 5. Required: i) ii) The market weights average cost of capital for the firm. Why are markets value weights preferable to book value weight when determining the weighted average cost of capital for a firm. The preference shares were floated in 2002 and their prices have remained constant. Most Banks are lending out money at a interest rate of 22% per annum. The corporation tax rate is 40%.

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