Cost Of Capital

Chapter 13

COST OF CAPITAL

Alex Tajirian

Cost of Capital

13-2

1 OBJECTIVE #

Managing the right-hand-side of the B/S

#

By now, for valuation analysis, we know: ! ! ! !

#

criteria: NPV, IRR, payback what the relevant CFs are how to compute net CFs how to introduce forecast error in CFs (WHAT IF,. . . )

Sources of financing: Debt, equity, retained earnings, preferred stock, warrants, venture capital, and bank loans, strategic alliances.

#

#

!

Bank loans, venture capital, and warrants not discussed

!

To simplify, we concentrate only on debt, equity, and retained earnings.

Cost of financing = cost of capital = ? !

Definition:

!

What is the cost of each source of financing?

!

What is a project's cost of capital?

The rate that must be earned to satisfy the required rate of return of the firm's investors.

Why might cost of capital in Japan be lower than in U.S.?

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Alex Tajirian

Cost of Capital

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2 MOTIVATION 2.1

WHY IS COST OF CAPITAL IMPORTANT? If financing cost is reduced Y NPV increases Y more projects end up with NPV > 0 Y more wealth created to shareholders.

2.2 SOME PRELIMINARIES ! Minimum required return / cost of capital= that particular discount rate “k” that makes NPV = 0. !

The return generated by a security is the cost of that security to the company that issued it. ]

cost of capital to the firm = reward to investors. !

The cost of capital depends primarily on the use of funds, i.e., the risk of the CFs, not on the source. Q risk of CFs (systematic risk) Q company capital structure

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Alex Tajirian

Cost of Capital

13-4

2.3 COST COMPONENTS Case 1

Assume firm has no debt & has retained earnings.

Remember from the chapter on Performance Measures: Net Income = total dividend + retained earnings If a company cannot find profitable projects, i.e., projects with return at least equal to ks , then the firm should distribute retained earnings to shareholders as dividends. Thus, if the company is retaining your money, then the minimum acceptable reward to you (an average investor) is the required return on equity Y required return on retained earnings = ks / required return on equity. But reward to investor = cost of capital to the firm. ˆ

required return on equity = cost of retained earnings.

Case 2 Now suppose firm needs to issue new equity for an expansion project. Obviously ke > ks ] (cost of new equity) > (cost of retained earnings) ] (required return on new equity) > (required return on retained earnings) since some transactions (floatation) costs have to be paid to investment banks for assisting firm in selling the new securities.

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Cost of Capital

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Case 3 If a company has a "good" project (NPV > 0), should it be financed using equity? Not necessarily, firm should consider using debt.

2.4

OUTLINE Given a company's target capital structure, Step 1: Estimate cost of each component Step 2: Calculate the cost of the combination of financing sources, i.e., company WACC

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In general, WACC ' sum of weighted rewards to firm ) s capital providers ' w d(cost of debt) % w s(cost of equity) Debt Debt ' where, wd ' Assets Debt % Equity Equity , and w d % ws ' 1 ws ' Debt % Equity where, WACC

=

Weighted Average Cost of Capital.

Debt

=

Market value of the company’s debt

Equity

=

market value of the company’s equity

wi

=

the weights (proportions) of each source of capital, based on the company’s optimal/target financing mix (capital structure). Notes. (a) It is not the source of financing that determined the cost of capital. (b) B/S weights need not be reflective of market values. (c) Weights are based on the optimal company’s source of financing; the topic of next chapter.

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Alex Tajirian

Cost of Capital

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CALCULATING COST OF EACH COMPONENT We first start with the cost of each source of new capital, then take their weighted average. Note, the weights are given by the optimal capital structure.

2.5 COST OF RETAINED EARNINGS, ks L

Cost of retained earnings = required rate of return on equity

?

What are possible approaches to estimate ks

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Cost of Capital

13-8

Example: Calculating Cost of Retained Earnings Given: kRF = 7% Dividend0 = $4.19 kM - kRF = 8.5% P0 = $50 $ = 0.847 g = 5% ks = ? Solution:

L

Two approaches when company stock is trading on an exchange:

#

2.5.1

CAPM Approach

ks ' k RF % (k M & k RF)$s ' 7.0% % (8.5%)(.847) ' 14.2%

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Alex Tajirian

Cost of Capital

#

2.5.2

13-9

DCF Approach:

Given: Dividend0 = $4.19, g = 5%, p0 = $50 ks = ? Solution:

From equation (4) chapter 7, we have:

ks '

'

'

Dividend1 P0

% g

Dividend0 × (1 % g) P0

7

% g

4.19 × (1.05) % .05 $50

' 0.088 % 0.05 ' 13.8%

ˆ

You can use the average of these two approaches = 14%.

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Cost of Capital

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2.6 COST OF NEWLY ISSUED COMMON STOCK, ke #

Floatation costs (F) are not part of capital budgeting CFS. Thus, if existing shareholders finance projects using new equity, they require a higher return to cover this cost Y ke > ks .

#

If P0 = $50 and F = 15% of issue price, then additional cost per share = (50)(15%) = $7.5.

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Cost of Capital

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Example: Calculating Component Cost of New Equity Given: F = 15% of issue price, Dividend0 = 4.19 , g = 5% , P0 = $50 ke = ? Solution: Using equation (4), Chapter 7, and including F, we have:

#

Accounting vs. Financial/Economic Valuation

ke ' '

'

'

'

Dividend1 net value of new equity per share Dividend1

issue price & floatation cost Dividend1 P0 & (P0)(F)

% g

Dividend0 × (1% g) P0(1& F)

% g

% g

$4.19 × (1.05) % .05 ' 15.4% $50(1& .15)

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Alex Tajirian

% g

Cost of Capital

13-12

2.7 COST OF PREFERRED STOCK, kps Given: Dividendps = $10 annually, perpetually paid price (Pps) = $113.1 per share (market price) F = floatation cost = $2.00 per share Solution: Using equation (3), from Chapter 7, and including F, we have: kps '

Dividend ps

P ps& F $10 $10 ' ' 0.09 ' 9.0% ' $113.1& 2.00 $111.1

Note.

No tax adjustment is needed since preferred dividends are paid from after-tax income.

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Cost of Capital

13-13

2.8 COST OF DEBT = kd (1-T) kd is the interest paid to new bond holders. But since interest is tax deductible Y

effective cost of debt = after-tax cost of debt = before tax cost - tax benefit = kd - T × kd = kd(1 - T) Example: Calculating Component Cost of Debt Given: Semiannual bond; coupon rate = 12%; years to maturity = 15; price of a similar bond = $1,153.72; T = 40% kd(1-T) = ?

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Cost of Capital

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Solution: Based on formula for PV of bonds Step 1: Calculate semi-annual coupon Step 2: Use Trial & Error methods Trial & Error Method: coupon '

coupon interest × par value 12% × $1,000 ' ' 60 2 2

PV ' SUM of discounted CFs Y $1,153.75 ' 60(PVIFAk d ,30 ) % $1,000(PVIFk d ,30) 2

2

Try k d ' 6% 2

Y 60(PVIFA6,30) % 1,000(PVIF6,30) ' 60(13.7648) % 1,000(.1741) ' 825.88 % 174.1 ' 999.98 < price ' $1,153.72 You have to try a number < 6%, say k d ' 4% 2

Y 60(17.2920)% 1,000(.3083) ' 1,346.35 > price

If you try kd/2 = 5%, you will get it right. ˆ kd = 5% x 2 = 10% Y kd(1-T) = 10%(0.6) = 6%

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Cost of Capital

13-15

Example: Calculating Company WACC Given: ! optimal proportions are: 30% Debt, 10% Preferred, 60% common equity ! Retained Earnings = $300,000 ! T = 40% ! Value of k from above examples is used. ! $ financing needed = $200,000 Solution: If retained earnings are to be used to finance projects, as in this example, WACC ' w dk d(1& T) % w psk ps % w sk s % w ek e ' 0.3(10%)(0.6) % 0.1(9%) % 0.6(14%) % 0 ' 1.8% % 0.9% % 8.4% ' 11.1%

?

What is the amount raised of each component?

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Alex Tajirian

Cost of Capital

?

13-16

What is the maximum amount of financing that can be sustained without issuing new equity?

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Cost of Capital

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Where do the weights come from? #

#

Possibilities include: ! proportional current book value of each component

!

proportional current market value of each component

!

target capital structure

Should short-term debt be included in wd?

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Alex Tajirian

Cost of Capital

3

?

13-18

WHAT IS A PROJECT'S COST OF CAPITAL Suppose debt = 0 and project is financed through 100% equity. Should firm use ks? If you use ks, then you are implicitly assuming that the risk of projects = risk of company

L

Remember: discount rate reflects risk of CFs. If company has no debt, then kproject = kRF + (km - kRF)$project

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Alex Tajirian

Cost of Capital

13-19

USING COMPANY k Vs. Project k k Project risk < firm’s

Project risk > firm’s

firm’s k riskReject good projects free

Accept Bad Projects

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Cost of Capital

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3.1 Project Required Return (k project) and NPV. if project risk

$ Company risk

and Y

(kproject - WACC)

NPVproject

NPVWACC

yes

+

-

+

accepting bad projects

yes

+

+

+

no problem

No

-

+

-

rejecting good projects

No

-

-

-

no problem

NPVproject = NPV using k project as the discount rate NPVWACC = NPV using company WACC as the discount rate

L

implication of using NPVWACC

use k = kproject to appropriately incorporate project CF-risk © morevalue.com, 1997

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Cost of Capital

13-21

3.2 PROJECT COST OF CAPITAL IN PRACTICE. !

To incorporate risk of CFS, companies have adopted a "crude" way of calculating kproject. The "hurdle rate" is one such method. It reflects both project risk and cost of capital. hurdle rate = company WACC ± risk premium

!

Assume company WACC = 15%,

hurdle rates project category

discount rate (k)

risk premium

speculative venture

30%

15%

new product

25%

10%

expansion of existing business

15%

0

cost of improvement, known technology

10%

-5%

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Cost of Capital

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PROJECT COST OF CAPITAL Does Firm Have Debt? No

Yes

Is Project Same Risk As Firm? Yes

Use Firm K

Is Project Same Risk As Firm?

No

Use k Reflecting Project Beta

Yes

Use Firm WACC

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Alex Tajirian

No

Use “Hurdle Rate”

Cost of Capital

4

13-23

COST OF CAPITAL (k) IN JAPAN & U.S.?

Unlike U.S. firms, Japanese firms have traditionally relied more on bank loans as a source of financing. This has enhanced firm monitoring by creditors (banks). Recently, debt and equity financing has increased. German firms have also traditionally relied more heavily on bank loans. ?

Why might the cost be lower in Japan?

#

Keiretsu (Companies aligned with financial giants) ! Agency problem lower, thus, k is lower ! Floatation cost is low

#

Government loans and subsidies, especially for R&D.

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5

T

From P0 '

SUMMARY

Dividendps Dividend Y k ps ' P ps k

Including Floatation costs Y kps ' T

From P0 '

Dividend1 k& g

Yk '

Dividend1 P0

including Floatation costs Y k e '

Dividend ps P ps& F % g Dividend1 P0(1& F)

% g

T Long-term financing used for long-term projects. Short-term financing is used only if there is a temporary mismatch between timing of inflows and outflows.

T WACC ' wdkd(1& T) % weke % wpskps % wsks Note. Only debt is tax deductible. The weights are determined by the target capital structure. The target proportions are not book values.

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Cost of Capital

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6 QUESTIONS I. Agree/Disagree-Explain 1

If a manager, with no finance background, uses the firm's WACC as the cost of project finance, then he/she would be accepting bad projects.

2

A project's cost of capital > company WACC.

3

kd is the cost of debt financing to a firm.

4

Consider the simple case of only two sources of financing, debt and equity. If the target (Debt/Asset) = 0, then a company's WACC = ks.

5

Floatation costs are irrelevant to capital budgeting.

II. What Happens to kd(1-T) and WACC if: a. firm incurs more debt b. interest rates increase c. inflation increases d. company undertakes risky projects e. tax rates are increased

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III. NUMERICAL. 1

WAK Inc. has a cost of equity of 15%, before-tax cost of debt of 10%, and a marginal tax rate of 40%. Its equity and debt are trading at book value. (a) Using its balance sheet data below, calculate WAK's WACC. Assets

Liabilities and Equity

Cash

$500

Accounts receivable

300

Inventories

800

Long-term debt

$500

Plant and equipment

400

Equity

1,500

Total assets

2,000.00

Total liabilities and equity

2,000.00

(b)

How would you calculate WACC if equity and debt were not trading at book values? Also assume that the firm is currently at its target capital structure.

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ANSWERS TO QUESTIONS I. Agree/Disagree-Explain 1

Disagree. It depends on the project's risk. See p. 20.

2

Disagree. Only if the project is more risky than the company.

3

Disagree. Interest is deductible. Thus cost of debt is kd(1-T).

4

Agree. Assuming that the only two components of assets are debt and equity, at (Debt/Asset) = 0, the WACC would have wd = 0 and ws = 1. Thus, WACC = ks.

5

Disagree. Although floatation costs are not part of the relevant CFs, they are part of the cost of capital (k). Thus, they do impact capital budgeting decisions.

II. What Happens to kd(1-T) and WACC if: a. firm incurs more debt b. interest rates increase c. inflation increases d. company undertakes risky projects e. tax rates are increased

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Cost of Capital

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III. Problems. 1. Step 1: Step 2:

Calculate weights: proportions of each source of capital substitute in WACC equation

Amount

Capital Sources Long-term debt Equity

500 1,500 2,000

wd '

Debt 500 ' ' .25 Asset 500% 1,500

ws ' 1& wd ' .75 Y WACC ' wdkd(1& T) % wsks ' .25(.10)(.6) % .75(.15) ' 12.75% (b)

What happens if stock is not trading at book value, i.e., book value is different from market value?

Calculate market values of debt and Equity. Debt = Market value of Debt = sum of [(market price of each bond)(# of bonds outstanding)] Equity = Market value of Equity = (price of stock)(# of shares outstanding) Thus, the proportions have to be based on market-value proportions, not book value proportions.

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Alex Tajirian