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Chapter 13

The Cost of Capital

Learning Objectives

1. Explain what the weighted average cost of capital for a firm is and why it is often sed

as a discont rate to evalate projects.

!. Calclate the cost of debt for a firm.

3. Calclate the cost of common stoc" and the cost of preferred stoc" for a firm.

#. Calclate the weighted average cost of capital for a firm$ explain the limitations of sing

a firm%s weighted average cost of capital as the discont rate when evalating a project$

and discss the alternatives that are available.

&. Chapter Otline

13.1 The 'irm%s Overall Cost of Capital

Since unique riskcan be eliminated by holding a diversified portfolio, systematic riskis

the only risk that investors require compensation for bearing.

We concluded in Chapter 7 that we could rely on the CA! to arrive at the e"pected rate

of return for a particular investment.

#n this chapter, we address the practical concerns that can make that concept difficult

to implement.

$irms do not issue publicly traded shares for individual pro%ects.

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As a result, firms have no way to directly estimate the discount rate that

reflects the risk of the incremental cash flows from a particular pro%ect.

$inancial managers deal with this problem by estimating the cost of capital for

the firm as a whole and then requiring analysts within the firm to use this cost of

capital to discount the cash flows for all pro%ects.

o A problem with this approach is that it ignores the fact that a firm is

really a collection of pro%ects with varying levels of risk.

A. The Finance Balance Sheet

&he finance balance sheet is based on market values rather than book values.

&he total book value of the assets reported on an accounting balance sheet does

not necessarily reflect the total market value of those assets since the book

value is largely based on historical costs, while the total market value of the

assets equals the present value of the total cash flows that those assets are

e"pected to generate in the future.

&he left'hand side of the accounting balance sheet reports the book values of a firm(s

assets, while the right'hand side reports how those assets were financed.

&he value of the claims that investors hold must equal the value of the cash flows that they

have a right to receive.

&his is because the total market value of the debt and the equity at a firm equals the

present value of the cash flows that the debt holders and the stockholders have the

right to receive.

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o &he people who have lent money to a firm and the people who have

purchased the firm(s stock have the right to receive all of the cash flows

that the firm is e"pected to generate in the future.

!) of assets * !) of liabilities + !) of equity

B. How Firms Estimate Their Cost of Capital

#f analysts at a firm could estimate the betas for each of the firm(s individual

pro%ects, they could estimate the beta for the entire firm as a weighted average

of the betas for the individual pro%ects.

o nfortunately, because analysts are not typically able to estimate

betas for individual pro%ects, they generally cannot use this

approach.

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o #nstead, analysts must use their knowledge of the finance balance

sheet, along with the concept of market efficiency, to estimate the

cost of capital for the firm.

-ather than perform the calculations for the individual projectsrepresented on

the left'hand side of the finance balance sheet, analysts perform a similar set of

calculations for the different types of financingdebt and equity/ on the right'

hand side of the finance balance sheet.

o As long as they can estimate the cost of each type of financing by

observing that cost in the capital markets, they can compute the cost

of capital for the firm by using the following equation0

$irm 1 1 2 2 3 3

1

n

i i n n

i

k x k x k x k x k x k =

= = + + + + L

o #f we divide the costs of capital into debt and equity portions of the

firm, then we can use the above to arrive at the weighted average

cost of capital ()*CC+for the firm0 k$irm*

x4ebtk4ebt+x5quityk5quity

&he appropriate discount rate to use when evaluating a capital budgeting pro%ect depends largelyon the risk of the pro%ect. &he new pro%ect will have a positive 6) only if its return e"ceedswhat the financial markets offer on investments of similar risk. We called this minimum requiredreturn the cost of capitalassociated with the pro%ect. &he weighted average cost of capital

WACC/ is the cost of capital for the firm as a whole, and it can be interpreted as the requiredreturn on the overall firm. #n discussing the WACC, we will recognie the fact that a firm willnormally raise capital in a variety of forms and that these different forms of capital may havedifferent costs associated with them. &a"es are an important consideration in determining therequired return on an investment, because we are always interested in valuing the afterta" cash flowsfrom a pro%ect. We will therefore discuss how to incorporate ta"es e"plicitly into our estimates of thecost of capital.

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An accurate estimate of the cost of capital is important for various reasons0

good capital budgeting decisions 8 neither the 6) rule nor the #-- rule can beimplemented without knowledge of the appropriate discount rate.

financing decisions 8 the optimal9target capital structure minimies the cost of capital.

operating decisions 8 cost of capital is used by regulatory agencies in order to determinethe :fair; return in some regulated industries e.g. electric utilities/.

-equired -eturn versus Cost of Capital0 Cost of capital, required return, and

appropriate discount rate are different phrases that all refer to the opportunity cost ofusing capital in one way as opposed to alternative financial market investments of thesame systematic risk. ,e-ired retrnis from an investor(s point of view< cost ofcapitalis the same return from the firm(s point of view< appropriate discont rate

is the same return used in a ) calculation.

The cost of capital depends primarily on the se of the fnds$ not the sorce.

The investment decisions of the firm are separate from the financing decisions.

$inancial olicy and Cost of Capital0 &he particular mi"ture of debt and equity a firm

chooses to employ is referred to as its capital strctre< this is a managerial variable.$or now, we will take the firm=s financial policy as given. #n particular, we willassume that the firm has a fi"ed debt'equity ratio that it maintains. &his ratio reflects

the firm=s target or optimal capital structure. >iven that a firm uses both debt andequity capital, this overall cost of capital will be a mi"ture of the returns needed tocompensate its creditors and its stockholders. #n other words, a firm=s cost of capitalwill reflect both its cost of debt capital and its cost of equity capital.

13.! The Cost of ebt

Analysts often cannot directly observe the rate of return that investors require for a

particular type of financing and instead must rely on the security prices they can

observe in the financial markets to estimate that required rate.

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o #t makes sense to rely on security prices only if you believe that the financial

markets are reasonably efficient at incorporating new information into these

prices.

o #f the markets were not efficient, estimates of e"pected returns that were based

on market security prices would be unreliable.

A. Key Concepts for Estimating the Cost of Debt

With regard to the cost associated with each type of debt that a firm uses when

we estimate the cost of capital for a firm, we are particularly interested in the

cost of the firm(s long'term debt.

When we refer to debt we usually mean the debt that, when it was

borrowed, was set to mature in more than one year.

4ebt with a maturity of more than one year can typically be viewed as

permanent debt because firms often borrow the money to pay off this debt

when it matures.

&he cost of a firm(s long'term debt are estimated on the date on which the

analysis is done.

&his is important because the interest rate or historical interest rate

determined at the time of original debt issuance/ that the firm is paying

on its outstanding debt does not necessarily reflect its current cost of

debt.

&he current cost of long'term debt is the appropriate cost of debt for WACC

calculations.

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&his is the relevant cost because the WACC is the opportunity cost of

capital for the firm(s investors as of today.

B. Estimating the Current Cost of a Bon or an !utstaning "oan

&he current cost of debt for a publicly traded bond is the yield'to'maturity

calculation.

o &o estimate this cost, we first convert the bond data to reflect semiannual

compounding as well as account for the effective annual interest rate

5A-/ to account for the actual current annual cost of the debt.

We must also account for the cost of issuing the bond?issuance

costs using the net proceeds that the company receives for the bond

rather than the price that is paid by the investor.

$or the current cost of long'term bank or other private debt, the firm may simply

call its banker and ask what rate the bank would charge if it decided to refinance

the debt today.

C. Ta#es an the Cost of Debt

$irms can deduct interest payments for ta" purposes.

&he after'ta" cost of interest payments equals the preta" cost times 1 minus the ta"

rate0 k4ebt after'ta"* k4ebt preta"1 8 t/

D. Estimating the Cost of Debt for a Firm

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&o estimate the firm(s overall cost of debt when it has several debt issues

outstanding, we must first estimate the costs of the individual debt issues and then

calculate a weighted average of these costs.

nlike a firm=s cost of equity, its cost of debt can normally be observed either directly orindirectly, because the cost of debt is simply the interest rate the firm must pay on newborrowing, and we can observe interest rates in the financial markets. $or e"ample, if the firmalready has bonds outstanding, then the yield to maturity on those bonds is the market'requiredrate on the firm=s debt.

Alternatively, if we knew that the firm=s bonds were rated, say, AA, then we could simply findout what the interest rate on newly issued AA'rated bonds was. 5ither way, there is no need toactually estimate a beta for the debt since we can directly observe the rate we want to know.

&he coupon rate on the firm=s outstanding debt is irrelevant here. &hat %ust tells us roughly whatthe firm=s cost of debt was back when the bonds were issued, not what the cost of debt is today.&his is why we have to look at the yield on the debt in today=s marketplace.

5"ample0 @ou are analying the cost of debt for a firm. @ou know that the firm(s 1'year maturity,B. percent coupon bonds are selling at a price of DB23.B. &he bonds pay interest semiannually. #fthese bonds are the only debt outstanding for the firm, what is the after'ta" cost of debt for this firm ifthe firm is in the 3E percent marginal ta" rateF

6 * 1 " 2 * 2B

) * 'B23.B!& * .EB " D1,EEE/ 9 2 * 2.E$) * 1EEE

#9@- * GGG " 2 *

k4ebt after'ta"* k4ebt preta"" 1 8 t/ *

7.7H

+

+

=

3

rice/2Iond)aluear

!aturityto@ears

rice/Iond')aluearCoupon

@&!5stimated

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13.3 The Cost of E-ity

&he cost of equity for a firm is a weighted average of the costs of the different

types of stock that the firm has outstanding at a particular point in time.

A. Common Stoc$

o Just as information about market rates of return is used to estimate the cost of debt,

market information is also used to estimate the cost of equity.

&here are several ways to do this, and the most appropriate approach will

depend on what information is available and how reliable the analyst believes

it is.

o &he te"t discusses three alternative methods for estimating the cost of common stock.

o /ethod 10 sing the Capital *sset 2ricing /odel (C*2/+

sing the CA! equation, 5-i/ * -rf+ KiL5-m/ 8 -rfM, we find that the cost

of common stock equals the risk'free rate of return plus compensation for the

systematic risk associated with the common stock.

Some practical considerations must be considered when choosing the

appropriate risk'free rate, beta, and market risk premium for the above

calculation.

&he recommended risk'free rate to use is the risk'free rate on a long'

term &reasury security because the equity claim is a long'term claim on

the firm(s cash flows.

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o A long'term risk'free rate better reflects long'term inflation

e"pectations and the cost of getting investors to part with their

money for a long period of time than a short'term rate.

@ou can estimate the beta for that stock using a regression analysis.

o #dentifying the appropriate beta is much more complicated if

the common stock is not publicly traded.

o &his problem may be overcome by identifying a :comparable;

company with publicly traded stock that is in the same business

and that has a similar amount of debt.

o When a good comparable company cannot be identified, it is

sometimes possible to use an average of the betas for the public

firms in the same industry.

#t is not possible to directly observe the market risk premium since we

don(t know what rate of return investors e"pect for the market

portfolio.

o $or this reason, financial analysts generally use a measure of the

average risk premium investors have actually earned in the past

as an indication of the risk premium they might require today.

o $rom 1N2O through the end of 2EEO, actual returns on the .S.

stock market e"ceeded actual returns on long'term .S.

government bonds by an average of O.1 percent per year.

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#f a financial analyst believes that the market risk

premium in the past is a reasonable estimate of the risk

premium today, then he or she might use O.1 percent

or a value close to it/ as the market risk premium for

the future.

Ietas are widely available and &'bond or &'bill rates are often used for -f. &he e"pected marketrisk premium, 5-m/ 8 -f, is the more difficult number to come up with. Pne of the problems isthat we really do need an e"pectation, but we only have past information, and market riskpremiums do vary through time. 5arly in 2EEE, $ederal -eserve Chairman, Alan >reenspan,indicated that part of his concern with the current state of the .S. stock markets is the reductionin the market risk premium. Qe felt that investors were either becoming less risk averse, or they

did not truly understand the risk they were taking by investing in the stock. 6onetheless, thehistorical average is often used as an estimate for the e"pected market risk premium.

' &his approach e"plicitly ad%usts for risk in a fashion that is consistent with capital markethistory.' #t is applicable to virtually all publicly'traded stocks for which the value of K can bedetermined.' &he main disadvantage is that the past is not a perfect predictor of the future, and both beta andthe market risk premium vary through time.

o /ethod !0 sing the Constant4rowth ividend /odel

sing 5quation N.,1

E

4 *

- 'g, we can rearrange to solve for -?or kcsas we

now prefer to call it01

cs

E

4* +

k g

#n order to solve for the cost of common stock, we must estimate the dividend

that stockholders will receive ne"t period, 41, as well as the rate at which the

market e"pects dividends to grow over the long run,g.

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&his approach is useful for a firm that pays dividends that will grow at a

constant rate.

&his approach might be consistent for an electric utility but not for

a fast growing high'tech firm.

Pf the required data, only g is not directly observable L6ote0 4 1* 4E1 + g/M. &hedeficiencies of this approach are 1/ it assumes that dividends grow at a constant rate< 2/ thevalue of g must be estimated and forecasting errors impact the value of kcs< and 3/ risk is note"plicitly considered.

&o use the dividend growth model, we must come up with an estimate for g, the growth rate.&here are essentially two ways of doing this0 1/ use historical growth rates or 2/ use analysts=forecasts of future growth rates. Analysts= forecasts are available from a variety of sources.

5"ample from @ahooR $inance0 #I!< from ack(s0#I!/.

Alternatively, we might observe dividends for the previous, say, five years, calculate the year'to'year growth rates, and average them. $or e"ample, suppose we observe the following for somecompany0

@ear 4ividend D Change H Change

2EE

D.EE ' '

2EE

O

D.E D.E 1E.EEH

2EE7

D.7 D.3 7.NH

2EEB

D.2 D.E 1E.3H

2EEN

D.O D.E 7.O2H

Arithmetic average growth rate * 1E.EEH + 7.NH + 1E.3H + 7.O2H/ 9 * N.E2H

>eometric average growth rate * D.O 9 D.EE/19/ 8 1 * N.E1BH

5"ample0 Whitewall &ire Co. %ust paid a D1.OE dividend on its common shares. #f Whitewall ise"pected to increase its annual dividend by 2 percent per year into the foreseeable future and thecurrent price of Whitewall(s common shares is D11.OO, then what is the cost of common equity forWhitewallF
http://finance.yahoo.com/q/ae?s=IBMhttp://www.zacks.com/research/report.php?PHPSESSID=594ec652e9adb5efdeedd602a1fe57d9&t=ibm&type=estimateshttp://www.zacks.com/research/report.php?PHPSESSID=594ec652e9adb5efdeedd602a1fe57d9&t=ibm&type=estimateshttp://finance.yahoo.com/q/ae?s=IBMhttp://www.zacks.com/research/report.php?PHPSESSID=594ec652e9adb5efdeedd602a1fe57d9&t=ibm&type=estimates

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gk

DP

cs

cs

==1OO.11D

1OH

o /ethod 30 sing a /ltistage4rowth ividend /odel

&he multistage'growth dividend model allows for faster dividend growth rates

in the near term, followed by a constant long'term growth rate.

&he approach is based on the supernormal growth dividend model

discussed in Chapter N.

o &he comple"ity of this approach lies in choosing the correct

number of stages of forecasted growth as well as how long each

stage will last.

Iecause of the algebraic comple"ity in solving for the required rate of

return, the value is generally solved for using a trial'and'error method,

after forecasting the different stages of dividend growth.

o )hich /ethod 5hold )e se6

#n practice, most people use the CA! !ethod 1/ to estimate the cost of

equity if the result is going to be used in the discount rate for evaluating a

pro%ect.

5"ample0 @ou know that the return of !omentum Cyclicals( common shares reacts to

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macroeconomic information 1.O more times than the return of the market. #f the risk'free rate ofreturn is percent and the market risk premium is O percent, then what is !omentum Cyclicals(cost of common equity capitalF

]R)!"RR)!"R rfmrfcs +=

13.OH

B. %referre Stoc$

&he characteristics of preferred stock allow us to use the perpetuity model, 5quation

O.3, to estimate the cost of preferred equity. &he cost of preferred stock financing can

also be observed in the financial markets. A firm which e"pects to issue preferred

stock would compute the yield for either its own currently outstanding preferred stock

issue or for preferred stock issued by other firms with ratings similar to the proposed

offering.

o Just as with common stock, we can find the cost of preferred equity by

rearranging the pricing equation for preferred shares0ps

ps

ps

4*

k

o 6ote that the CA! can be used to estimate the cost of preferred equity, %ust

as it can be used to estimate the cost of common equity.

Si"th $ourth Iank has an issue of preferred stock with a DO stated dividend that %ust sold for DN per

share. What is the bank=s cost of preferred stockF

kps*

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O.3BH

1!.# sing the )*CC in 2ractice

&he after'ta" version of the formula for the weighted'average cost of capital is0

4ebt 4ebt preta" ps ps cs csWACC 1 /x k t x k x k= + + .

&he financial analyst should use market values rather than book values to calculate

WACC.

Example )*CC for a firm0&he #maginary roducts Co. currently has D3EE million of marketvalue debt outstanding. &he N percent coupon bonds semiannual pay/ have a maturity of 1 yearsand are currently priced at D1,E.E3 per bond. &he firm also has an issue of 2 million preferredshares outstanding with a market price of D12.EE. &he preferred shares offer an annual dividend ofD1.2E. #maginary also has 1 million shares of common stock outstanding with a price of D2E.EE pershare. &he firm is e"pected to pay a D2.2E common dividend one year from today, and that dividendis e"pected to increase by percent per year forever. #f #maginary is sub%ect to a E percent marginalta" rate, then what is the firm(s weighted average cost of capitalF

5oltion0

5tep 10 &otal amount of debt, common equity, and preferred equity04ebt * D3EE,EEE,EEE given/referred equity * D12 " 2,EEE,EEE * D2,EEE,EEECommon equity * D2E " 1,EEE,EEE * D2BE,EEE,EEE&otal capital * DOE,EEE,EEEx4ebt* 3EE9OE * E.NO7xps* 29OE * E.E3N7xcs* 2BE9OE * E.O3O

5tep !0Cost of capital components0Cost of debt0

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D1,E.E3 * D " )#$A3E, @&!92/ + D1,EEE " )#$3E, @&!92/Solving, we find that @&! * E.EB this is a preta" number/.

6 * 1 " 2 * 3E) * '1E.E3

!& * .EN " D1,EEE/ 9 2 * $) * 1EEE

#9@- * 2.2 " 2 * .B

Cost of preferred equity0

1E.EEE.12D

2E.1D===

ps

psP

Dk

Cost of common equity0

1O.EE.EEE.2ED

2E.2D1 =+=+= gP

Dk

cs

cs

5tep 30Combine using the WACC formula.

cscspspsde#tde#t kxkxtkx$%&& ++= /1 *

( ) ( ) ( )E.NO7 E.EB 1 E./ E.E3N7 E.1E E.O3O E.1O E.EN2O, or N.2OH$%&&= + + =

A. "imitations of &ACC as a Discount 'ate for E(aluating %ro)ects

$inancial theory tells us that the rate that should be used to discount these incremental

cash flows is the rate that reflects their systematic risk.

&his means that the WACC is going to be the appropriate discount rate for evaluating

a pro%ect only when the pro%ect has cash flows with systematic risks that are e"actly

the same as those for the firm as a whole.

o When a single rate, such as the WACC, is used to discount cash flows for

pro%ects with varying levels of risk, the discount rate will be too low in some

cases and too high in others.

o When the discount rate is too low, the firm runs the risk of accepting a

negative'6) pro%ect.

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&he estimated 6) will be positive even though the true 6) is

negative.

o When the discount rate is too high, the firm runs the risk of re%ecting a

positive'6) pro%ect.

&he estimated 6) will be negative even though the true 6) is

positive.

&he key point is that it is correct to use a firm(s WACC to discount the cash flows for

a pro%ect only if the following conditions hold.

o Condition 10A firm(s WACC should be used to evaluate the cash flows for a

new pro%ect only if the level of systematic risk for that pro%ect is the same as

that for the portfolio of pro%ects that currently comprise the firm.

o Condition !0A firm(s WACC should be used to evaluate a pro%ect only if that

pro%ect uses the same financing mi"?the same proportions of debt, preferred

shares, and common shares?used to finance the firm as a whole.

B. Alternati(es to *sing &ACC for E(aluating %ro)ects

#f the discount rate for a pro%ect cannot be estimated directly, a financial analyst might

try to find a public firm that is in a business that is similar to the pro%ect.

o &his public company would be what financial analysts call a preplay

comparablebecause it is e"actly like the pro%ect.

o &his approach is generally not feasible due to the difficulty of finding a public

firm that is only in the business represented by the pro%ect.

$inancial managers sometimes classify pro%ects into categories based on their

systematic risks.

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o &hey then specify a discount rate that is to be used to discount the cash flows

for all pro%ects within each category.

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Chapter 13 5ample 2roblems

/ltiple Choice

'dentify the choice that #est completes the statement or answers the question(

1. 7ow firms estimate their cost of capital0@ou are analying the cost of capital for a firm

that is financed with O percent equity and 3 percent debt. &he cost of debt capital is B

percent, while the cost of equity capital is 2E percent for the firm. What is the overall cost of

capital for the firmF

12.2H1.EH1.BH

2E.EH

2. The cost of debt0 Ieckham Corporation has bonds outstanding with 13 years to maturity and

are currently priced at D7O.1O. #f the bonds have a coupon rate of B. percent, then what is

the after'ta" cost of debt for Ieckham if its marginal ta" rate is 3HF Assume that your

calculation is made as on Wall Street.

O.2EHB.12H12.EEH

12.BNEH

3. The cost of e-ity0 Jacque 5wing 4rilling, #nc., has a beta of 1.3 and is trying to calculate its

cost of equity capital. #f the risk'free rate of return is B percent and the e"pected return on the

market is 12 percent, then what is the firm=s after'ta" cost of equity capital if the firm=s

marginal ta" rate is E percentF

7.N2H13.2EH1.7H

23.OEH

. The cost of e-ity0 >angland Water >uns, #nc., is e"pected to pay a dividend of D2.1E one

year from today. #f the firm=s growth in dividends is e"pected to remain at a flat 3 percent

forever, then what is the cost of equity capital for >angland if the price of its common shares

is currently D17.EF

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12.EEH1.OH1.EEH1.3OH

. The cost of preferred e-ity0 Iilly=s >oat Coats has a preferred share issue outstanding witha current price of D3B.BN. &he firm last paid a dividend on the issue of D3.E per share. What

is the firm=s cost of preferred equityF

7HBHNH1EH

O. sing the )*CC in practice0 -onnie=s Comics has found that its cost of common equity

capital is 1 percent and its cost of debt capital is 12 percent. #f the firm is financed withD2E,EEE,EEE of common shares market value/ and D7E,EEE,EEE of debt, then what is the

after'ta" weighted average cost of capital for -onnie=s if it is sub%ect to a 3 percent marginal

ta" rateF

O.EHN.OEHB.7H13.OH

7. sing the )*CC in practice0 4ro=s Qiking >ear, #nc., has found that its common equity

capital shares have a beta equal to 1. while the risk'free return is B percent and the e"pected

return on the market is 1 percent. #t has 7'year maturity bonds outstanding with a price of

D7O7.E3 that have a coupon rate of 7 percent.. #f the firm is financed with D12E,EEE,EEE of

common shares market value/ and DBE,EEE,EEE of debt, then what is the after'ta" weighted

average cost of capital for 4ro=s if it is sub%ect to a 3 percent marginal ta" rateF Calculate

the cost of debt as it would be done on Wall Street.

1E.2EH

11.7OH11.BBH13.32H

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Chapter 13 5ample 2roblems

*nswer 5ection

/LT&2LE C7O&CE

1. A6S0 CTearning Pb%ective0 TP

Tevel of 4ifficulty0 Qard

$eedback0 k$irm*x4ebtk4ebt+x5quityk5quity* E.3 " E.EB/ + E.O " E.2/ * E.1B

2. A6S0 I

Tearning Pb%ective0 TP 2

Tevel of 4ifficulty0 !edium

$eedback0 sing the formula for pricing bonds, we have

3. A6S0 I



$eedback0

repared by Jim Ueys

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. A6S0 C


Tevel of 4ifficulty0 !edium

$eedback0

. A6S0 C



$eedback0

O. A6S0 I

Tearning Pb%ective0 TP


$eedback0

6oting that the proportion of debt and equity is0

"4ebt* D7E,EEE9D7E,EEE + D2E,EEE/ * E.7

"cs* D2,EEE,EEE9D7E,EEE + D2E,EEE/ * E.2

&he formula for the WACC is0

WACC * "4ebtk4ebt preta" 1'&/ + "cskcs* LE.7 " .12 " 1 ' .3/M + LE.2 " E.1M * .EB + .E37 * .ENO * N.O

repared by Jim Ueys

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7. A6S0 4

Tearning Pb%ective0 TP


$eedback0

pk13 notes

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