cost of capital

Chapter 13

COST OF

CAPITAL

Alex Tajirian

Cost of Capital 13-2

© morevalue.com, 1997

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, venturecapital, and bank loans, strategic alliances.

! Bank loans, venture capital, and warrants not discussed

! To simplify, we concentrate only on debt, equity, and retainedearnings.

## Cost of financing = cost of capital = ?! Definition: The rate that must be earned to satisfy the

required rate of return of the firm's investors.

! What is the cost of each source of financing?

! What is a project's cost of capital?

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

Alex Tajirian



2 MOTIVATION

2.1 WHY IS COST OF CAPITAL IMPORTANT?

If financing cost is reduced Y NPV increases Y more projects endup 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 securityto 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

Alex Tajirian



2.3 COST COMPONENTSCase 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 returnat least equal to ks , then the firm should distribute retained earningsto shareholders as dividends.

Thus, if the company is retaining your money, then the minimumacceptable reward to you (an average investor) is the required returnon equity Y required return on retained earnings = ks / requiredreturn on equity.

But reward to investor = cost of capital to the firm.

ˆ required return on equity = cost of retained earnings.

Case 2Now suppose firm needs to issue new equity for an expansionproject. Obviously

ke > ks ] (cost of new equity) > (cost of retained earnings) ](required return on new equity) > (required return on retainedearnings)

since some transactions (floatation) costs have to be paid toinvestment banks for assisting firm in selling the new securities.

Alex Tajirian



Case 3If a company has a "good" project (NPV > 0), should it be financedusing equity?

Not necessarily, firm should consider using debt.

2.4 OUTLINEGiven a company's target capital structure, Step 1: Estimate cost of each componentStep 2: Calculate the cost of the combination of financing

sources, i.e., company WACC

Alex Tajirian



WACC ' sum of weighted rewards to firm )s capital providers

' wd(cost of debt) % ws(cost of equity)

where, wd 'Debt

Assets'

DebtDebt % Equity

ws 'Equity

Debt % Equity, and wd % ws ' 1

In general,

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 financingmix (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.

Alex Tajirian



CALCULATING COST OF EACH COMPONENT

We first start with the cost of each source of new capital, then taketheir weighted average. Note, the weights are given by the optimalcapital structure.

2.5 COST OF RETAINED EARNINGS, ksLL Cost of retained earnings = required rate of return on equity

? What are possible approaches to estimate ks

Alex Tajirian



ks ' kRF % (kM & kRF)$s

' 7.0% % (8.5%)(.847)' 14.2%

Example: Calculating Cost of Retained EarningsGiven: 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

Alex Tajirian



ks 'Dividend1

P0

% g 7

'Dividend0 × (1 % g)

P0

% g

'4.19 × (1.05)

$50% .05

' 0.088 % 0.05 ' 13.8%

## 2.5.2 DCF Approach:

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

Solution:

From equation (4) chapter 7, we have:

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

Alex Tajirian



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 requirea higher return to cover this cost YY ke > ks .

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

Alex Tajirian



ke 'Dividend1

net value of new equity per share% g

'Dividend1

issue price & floatation cost% g

'Dividend1

P0 & (P0)(F)% g

'Dividend0 × (1%g)

P0(1&F)% g

'$4.19 × (1.05)

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

Example: Calculating Component Cost of New EquityGiven:

F = 15% of issue price, Dividend0 = 4.19 , g = 5% , P0 = $50ke = ?

Solution:Using equation (4), Chapter 7, and including F, we have:

# Accounting vs. Financial/Economic Valuation

Alex Tajirian



kps 'Dividendps

Pps& F

'$10

$113.1&2.00'

$10$111.1

' 0.09 ' 9.0%

2.7 COST OF PREFERRED STOCK, kps

Given:Dividendps = $10 annually, perpetually paidprice (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:

Note. No tax adjustment is needed since preferred dividends arepaid from after-tax income.

Alex Tajirian



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 DebtGiven: Semiannual bond; coupon rate = 12%; years to maturity = 15;

price of a similar bond = $1,153.72; T = 40%kd(1-T) = ?

Alex Tajirian



coupon 'coupon interest × par value

2'

12% × $1,0002

' 60

PV ' SUM of discounted CFsY $1,153.75 ' 60(PVIFAk d

2

,30 ) % $1,000(PVIFk d2

,30)

Try k d2

' 6%

Y 60(PVIFA6,30) % 1,000(PVIF6,30)' 60(13.7648) % 1,000(.1741) ' 825.88 % 174.1 ' 999.98

< price ' $1,153.72You have to try a number < 6%, say k d

2

' 4%

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

Solution: Based on formula for PV of bondsStep 1: Calculate semi-annual couponStep 2: Use Trial & Error methodsTrial & Error Method:

If you try kd/2 = 5%, you will get it right.

ˆ̂ kd = 5% x 2 = 10% Y kd(1-T) = 10%(0.6) = 6%

Alex Tajirian



WACC ' wdkd(1&T) % wpskps % wsks % weke

' 0.3(10%)(0.6) % 0.1(9%) % 0.6(14%) % 0' 1.8% % 0.9% % 8.4%' 11.1%

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 thisexample,

? What is the amount raised of each component?

Alex Tajirian



? What is the maximum amount of financing that can be sustainedwithout issuing new equity?

Alex Tajirian



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?

Alex Tajirian



3 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 ofprojects = risk of company

L Remember: discount rate reflects risk of CFs.

If company has no debt, thenkproject = kRF + (km - kRF)$project

Alex Tajirian



USING COMPANY kVs. Project k

Project risk < firm’s Project risk > firm’s

Reject good projects Accept Bad Projects

Beta

k

firm’sk

risk-free

Alex Tajirian



3.1 Project Required Return (k project) and NPV.

if and

implication of usingNPVWACC

projectrisk

$ Companyrisk

Y(kproject - WACC) NPVproject NPVWACC

yes

yes

No

No

+

+

-

-

- + accepting bad projects

+ + no problem

+ - rejecting good projects

- - no problem

NPVproject = NPV using k project as the discount rate

NPVWACC = NPV using company WACC as the discount rate

L use k = kproject to appropriately incorporate project CF-risk

Alex Tajirian



3.2 PROJECT COST OF CAPITAL IN PRACTICE.

! To incorporate risk of CFS, companies have adopted a "crude" wayof calculating kproject. The "hurdle rate" is one such method. It reflectsboth 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 existingbusiness

15% 0

cost of improvement,known technology

10% -5%

Alex Tajirian



PROJECT COST OF CAPITAL

Does FirmHave Debt?

Is Project SameRisk As Firm?

Is Project SameRisk As Firm?

Use FirmK

Use k ReflectingProject Beta

Use “Hurdle Rate”

Use FirmWACC

No

NoNo

Yes

YesYes

Alex Tajirian



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

Unlike U.S. firms, Japanese firms have traditionally relied more on bankloans as a source of financing. This has enhanced firm monitoring bycreditors (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.

Alex Tajirian



T From P0 'Dividend

kY kps '

Dividendps

Pps

Including Floatation costs Y kps 'Dividendps

Pps&F

T From P0 'Dividend1

k&gY k '

Dividend1

P0

% g

including Floatation costs Y ke 'Dividend1

P0(1&F)% g

T WACC ' wdkd(1&T) % weke % wpskps % wsks

5 SUMMARY

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

Note. Only debt is tax deductible.

The weights are determined by the target capital structure. The target proportions are notbook values.

Alex Tajirian



6 QUESTIONS

I. Agree/Disagree-Explain

1 If a manager, with no finance background, uses the firm's WACC as the cost of projectfinance, 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 debtb. interest rates increasec. inflation increasesd. company undertakes risky projectse. tax rates are increased

Alex Tajirian



III. NUMERICAL.

1 WAK Inc. has a cost of equity of 15%, before-tax cost of debt of 10%, and a marginal taxrate 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.

Alex Tajirian



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 costof capital (k). Thus, they do impact capital budgeting decisions.

II. What Happens to kd(1-T) and WACC if:a. firm incurs more debtb. interest rates increasec. inflation increasesd. company undertakes risky projectse. tax rates are increased

Alex Tajirian



wd 'DebtAsset

'500

500%1,500' .25

ws ' 1&wd ' .75

Y WACC ' wdkd(1&T) % wsks

' .25(.10)(.6) % .75(.15) ' 12.75%

III. Problems.1. Step 1: Calculate weights: proportions of each source of capitalStep 2: substitute in WACC equation

Capital Sources Amount

Long-term debt 500

Equity 1,500

2,000

(b) What happens if stock is not trading at book value, i.e., book value is different frommarket 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 valueproportions.

Alex Tajirian

cost of capital

Documents

projects cost of capital

cost of capital important

cost of financing

financing cost

equity equity

cost componentscase

ke ks cost of new equity

equity debt debt