Cost of Capital

Section 1Introduction to Cost of Capital

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Overall Cost of Capital of the Firm

Cost of Capital is the required rate of return on the various types of financing. The overall cost of capital is a weighted average of the individual required rates of return (costs);

In other word, it’s the opportunity cost of capital for suppliers of capital;

The Sources of Cost of Capital

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Should We Concern About Short Term Obligations?

No!!! Only non seasonal debts with explicit interest costs

should be considered;

Payables, accruals and other obligations with similar nature are excluded;

In addition maturity hedging approach requires to achieve a match between duration of investment and the debt;

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Should We Consider Historical Costs

No!!!

Finance focuses on future cash flows;

The cost of each element in WACC is calculated based on their current market prices;

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Weighted Average Cost of Capital

Weighted average cost of capital is the average after-tax cost of a company’s various capital sources, including common stock, preferred stock, bonds and any other long-term debt;

Therefore, WACC in it’s more general terms is WACC=wdrd(1-t)+wprp+were

wherewd-proportion of debt

rd-=cost of debt

t-tax ratewp-proportion of preferred stock

rp-cost of preferred stock

we-proportion of equity

re-cost of equity 7

WACC ExampleAssume that ABC corporation has following capital structure;30% debt,10% preferred stock,60% equity.It’s before tax debt cost is 8%,preferred stock cost is 10% and equity cost is 15%.If tax rate is 40% calculate company’s WACC.SolutionWACC=(0.3)(0.08)(1-0.4)+(0.1)(0.1)+(0.6)(0.15)= 11.44%

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Breaking Down of WACC FormulaTax Rate

In many country’s jurisdictions interest rates are tax- deductible;

Taking this fact into account pre-tax cost of debts should be adjusted for this tax shield;

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ExampleSuppose that company pays $1million on $10million of debt.If company pays 40% of tax then this $1million will only cost for $0.6million because the interest reduces company’s tax bill by $0.4million.Therefore,despite the fact that before tax interest rate is 10%,after-tax cost of debt is 6%

Breaking Down of WACC FormulaEstimating The Proportions of Capital

ExampleThe following information is available for Gewitch GmBh;

Market Value of Debt $ 50 millionMarket Value of Equity $60 million

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Capital Structure

wd=50/110=0.45

we=60/110=0.55

Applying of WACC in Capital Budgeting

WACC reflects the overall capital cost of company, but it’s frequently used for evaluation of individual projects as well;

For an average-risk project the discount rate will be equal to company’s WACC;

In systematic risk differs from the company’s current project portfolio then downward or upward adjustments should be made to WACC;

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WACC and NPV Calculations In capital budgeting WACC which corresponds with the average risk of company is used as discount rate to find NPV; However, if we use WACC as discount rate we are assuming that;

a. the project has the same risk as the average-risk project of the company;a. capital structure is not subject to any changes during the project’s life;

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Flotation Costs Flotation Costs are the costs associated with issuing securities such as underwriting, legal, listing, and printing fees.

a. Adjustment to Initial Outlayb. Adjustment to Discount Rate

Another Limitation of WACCFlotation Costs

Add Flotation Costs (FC) to the Initial Cash Outlay (ICO).

Impact: ReducesReduces the NPV

Adjustment to Initial Outlay (AIO)

NPV = n

t=1

CFt

(1 + k)t

- ( ICO + FC )

Subtract Flotation Costs from the proceeds (price) of the security and recalculate yield figures.

Re=D/P(1-F)+g

Impact: IncreasesIncreases the cost for any capital component with flotation costs.

Result: Increases the WACC, which decreasesdecreases the NPV.

Adjustment to Discount Rate (ADR)

Example of Flotation CostsLet’s consider a project that has $60 000 initial cash outlay and is expected to produce $10 000 cash inflow for each of next 10 years. Assume that company’s tax rate is 40% and before-tax debt cost is 5%.Furthermore suppose that dividend of next period is $1,the current market price of stock is $20 and the expected growth rate is 5%.Please consider the following information on capital structure. Flotation costs are 5% of new capital raised Source of Capital Amount Raised Proportion Debt 24 000 0.40 Equity 36 000 0.60RequiredCompare NPV figures by employing the both methods

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Example of Flotation CostsCost of equity=(1/20)+0.05=10%After tax cost of debt=5(1-0.4)=3%WACC=(0.40)(0.03)+(0.60)(0.1)=7.2%Standard NPV=69591-60 000=$9591a.AIO NPV=9591- 1800=$7791b.ADR NPV=69089-60000=$9089(WACC 7.3%)

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Which Approach is Better?

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ADR approach is misleading because it affects the PV of all future cash flows;

In this respect AIO is more logical as it only affects the initial cash outflow;

However, it might be quite a hard task to find project specific flotation costs;

As a result some textbooks offers to use ADR despite of it’s flaws;

Section 2Cost of Different Sources of

Capital

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Type of Financing Mrkt Val WeightLong-Term Debt $ 35M 35%Preferred Stock $ 15M 15%Common Stock Equity $ 50M 50%

Market Value of Long-Term Financing

Cost of Debt Cost of Debt Cost of Debt is the cost of debt financing when company issues bond or apply for long-term bank loan;

YTM(yield to maturity) approach will be employed if the market price of bond is known;

Otherwise, debt rating approach should be employed;

Yield To Maturity YTM is annual return that investor will make if he YTM is annual return that investor will make if he

purchases bond today and keeps it until maturity;purchases bond today and keeps it until maturity;

Bond Price=Cash FlowBond Price=Cash Flow11/(1+Yield)/(1+Yield)11+Cash Flow 2/(1+Yield)+Cash Flow 2/(1+Yield)22……+(Par ……+(Par Value)/(1+Yield)Value)/(1+Yield)nn

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Example;Valence Industries issues a new 10 year bond to finance a project.Coupon rate is 5% semi-annual.Upon issue the bond sell for $ 1025.If tax rate is 35% find after tax cost of debt.Coupon payment=(%5*1000)=$50-----Semiannual payment=$25$1025=25/(1+i)1+25/(1+i)2+….+1000/(1+i)20=2.3After tax rate=2.3*2(1-0.35)=4.6(0.65)=3%

Cost of Preferred Stock Cost of Preferred Stock is the required rate of return on investment of the preferred shareholders of the company.

rP = DP / Pp

Cost of Preferred Stock

where,dp-dividend per share

pp-price per share

Assume that Basket Wonders (BW) has preferred stock outstanding with par value of $100, dividend per share of $6.30, and a

current market value of $70 per share.

rP = $6.30 / $70

rrPP = 9%9%

Determination of the Cost of Preferred Stock

Cost of Common Equity Cost of equity is desired rate of return by shareholders in exchange of their investment in company; Estimating the cost of common equity is the most challenging because of uncertainty that surrounds timing and amount of returns;

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Capital-Asset Pricing ModelCapital-Asset Pricing Model

Dividend Discount ModelDividend Discount Model

Cost of Equity Approaches

Capital Asset Pricing

Model

Assumes that expected rate of return on stock is the sum of risk free-rate and the premium for bearing the

stock’s market risk.

ke = Rj = Rf + (Rm - Rf)j

Rf is a risk-free rate

Rm is market return rate

j is sensitivity of stock return to market returns

Assume that Basket Wonders (BW) has a company beta of 1.25. Research by Julie Miller suggests that the risk-free rate is 4% and the expected return on the market is

11.2% ke = Rf + (Rm - Rf)j

= 4% + (11.2% - 4%)1.25 kkee = 4% + 9% = 13%13%

Determination of the Cost of Equity (CAPM)

Dividend Discount Model

The cost of equity capitalcost of equity capital, ke, is the discount rate that equates the

present value of all expected future dividends with the current market

price of the stock. D1 D2 D

(1+ke)1 (1+ke)2 (1+ke)+ . . . ++P0 =

Constant Growth Model

The constant dividend growth constant dividend growth assumptionassumption reduces the model to:

ke = ( D1 / P0 ) + g

Assumes that dividends will grow at the constant rate “g” forever.

Assume that Basket Wonders (BW) has common stock outstanding with a current market value of $64.80 per share, current dividend of $3 per share, and a dividend growth rate of 8% forever

ke = ( D1 / P0 ) + g

ke = ($3(1.08) / $64.80) + .08

kkee = .05 + .08 = .13.13 or 13%13%

Determination of the Cost of Equity Capital

SECTION 3 Project Specific Risk

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CAPM in Risk Calculations

When the business risk of an investment project differs from the business risk of the investing company,it means that it is not appropriate to use the investing company’s existing cost of capital as the discount rate for the investment project;

Instead, the CAPM can be used to calculate a project-specific discount rate that reflects the business risk of the investment project;

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SUMMARY OF STEPS IN THE CALCULATION

The steps in calculating a project-specific discount rate for privately held company using the CAPM can be summarized, as follows:a. Locate suitable proxy companies. b. Determine the equity betas of the proxy companies, their gearings and tax rates. c. Unlever the proxy equity betas to obtain asset betas(exclude financial risk).d. Calculate an average asset beta.e. Adjust this unlevered beta based on company’s financial risk.f. Use the CAPM to calculate a project-specific cost of equity. 34

Project Specific RiskEXAMPLE

A company is planning to invest in a new project that is significantly different from its existing business operations. This companyis financed 30% by debt and 70% by equity. It has located three companies with business operations similar to the proposed investment, and details of these companies are as follows: Company A has an equity beta of 0.81 and is financed 25% by debt and 75% by equity.Company B has an equity beta of 0.98 and is financed 40% by debt and 60% by equity.Company C has an equity beta of 1.16 and is financed 50% by debt and 50% by equity. Assume that the risk-free rate of return is 4% per year, and that the equity risk premiumis 6% per year. Assume also that all the companies pay tax at a rate of 30% per year. Calculate a project-specific discount rate for the proposed investment.

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Project Specific RiskEXAMPLE

Unlevering the proxy equity betas:Asset beta for Company A= 0.81/((1+(1 - 0.30)*25/75)) = 0.657 Asset beta for Company B= 0.98/((1+(1 - 0.30)*40/60)) = 0.668 Asset beta for Company C= 1.16/((1+(1 - 0.30)*50/50)) = 0.682

Averaging the asset betas: (0.657 + 0.668 + 0.682)/3 = 2.007/3 = 0.669

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Project Specific RiskEXAMPLE

Regearing the average asset beta: 0.669 = βe/ ((1+ (1 - 0.3)30/70)) = Hence βe = 0.870Calculating the project-specific discount rate: E(ri) = Rf + βi(E(rm) - Rf) = 4 + (0.870 x 6) = 4 + 5.22 = 9.2%

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Thank You