Cost of Capital

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Announcements & Reminders

Student End-of-Term Evaluations (SETE)

• Your opinions are very important and greatly appreciated.

• Evaluations are anonymous.

• Your evaluations will provide feedback to improve course content and delivery for future semesters.

• Please do your evaluation before 6:00 am on Monday, December 8.

Next Week

• Final Exam, Room 226Wednesday, December 10, 5:30-7:30 pm

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• Determine initial cost of project• Estimate project’s future net cash flows by

year over its expected life (cash inflows minus cash outflows)

• Determine appropriate cost of capital based on riskiness of project

• Compute values for project evaluation– NPV– IRR– MIRR– Payback period– Discounted payback period– Profitability index

• Make decision based on applicable decision rules

• Post-audit and ongoing reviews

Capital Budgeting Process Overview

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CapitalBudgetingTechnique

s(Parrino 9)

Cost ofCapital(Parrino

11)

CapitalBudgetingCash Flows

(Parrino 10)

1. What are the three major categories (sections) of cash flows to consider in capital budgeting?

2. What cash flows are considered in both the initial investment and the terminal cash flow?

3. Why is depreciation added back when calculating the incremental after-tax project cash flows?

4. Why do we consider cash flows, and why after-tax cash flows?

5. How is after-tax salvage value of an asset calculated?

Cash Flows for Capital Budgeting

Chapter 10 Review Questions

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1. Explain weighted-average cost of capital for a firm– Explain why it is often used as a discount rate to

evaluate projects

2. Calculate cost of debt for a firm

3. Calculate cost of preferred stock for a firm

4. Calculate cost of common stock for a firm

5. Calculate weighted-average cost of capital for a firm– Explain limitations of using a firm’s weighted-average

cost of capital as a discount rate when evaluatinga project

– Discuss alternatives to firm’s weighted-average cost of capital

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Learning Objectives

Cost of Capital – Chapter 11

• Firm’s cost of financing (use of investor funds)– Average return required by firm’s investors– What must be paid to attract funds

• Base rate of return that a project must earn to increase firm value

• WACC = weighted-average cost of capital– Weighted-average cost of types of financing– Weights are percentages of capital structure

• Capital structure– Most firms attempt to maintain optimal mix of debt and

equity financing

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Cost of Capital

• Types of capital used by firms to raise money:

– kdebt pretax = EAY = before tax cost of debt

– kdebt after-tax = EAY(1-T) = after-tax cost of debt

– kps = cost of preferred stock

– kcs = cost of common stock

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Capital Components of WACC

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The Finance Balance Sheet

MV of assets = MV of liabilities + MV of equity (11.1)

• Cost of debt is weighted-average cost of all of the firm’s debt combined– Consider bonds outstanding and all loans outstanding at

market value

• Current cost of debt for a publicly traded bond = yield to maturity (YTM) adjusted for effective annual interest rate (EAR or EAY)– Account for float (issue) costs

• Current cost of long-term bank or other private debt– Call the banker and ask what rate the bank would charge

if they decided to refinance the debt today

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Estimating Cost of Debt

• Net proceeds – Funds actually received by the firm– Used to find pretax cost of debt

• Issuance costs– Underwriting – investment bankers– Administrative – legal, accounting, etc.

• After-tax compounded cost of debt (true cost)– EAY (YTM adjusted for compounding)

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Cost of Bonds (Long-Term Debt)

• Company wants to issue $1,000 par value, 9% coupon, 20-year bonds with semi-annual interest payments

• Similar risk bonds are being issued at coupon rates > 9%so the company has to sell bonds for $980 each

• In addition, the company must pay issuance costs of $30 per bond

• Net proceeds to the company: $950 each• Calculate pretax cost of debt (annual YTM and EAY)

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Calculating Pretax Cost of Bonds

Calculation Example

See YTM/EAY handout

• Interest payments are tax deductible – Interest expense reduces firm’s taxable income– This leads to smaller tax liability

• This makes debt the cheapest form of financing

• After-tax cost of debt– kdebt pretax (or EAY) = pretax cost of debt– T is the firm’s tax rate

kdebt after-tax = EAY(1 – T)

• If the firm’s tax rate is 40% and the pretax cost of debt is 9.79%, what is the after-tax cost?

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After-Tax Cost of Bonds

Cost of Preferred Stock

• Rate of return investors require on firm’s preferred stock

• Preferred dividend divided by net issuing price

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kps = Dps (11.6)Pps

Where:kps = cost of preferred stockDps = constant (fixed) dividendPps = per-share net proceeds firm receives from issue or sale after deducting issue costs

• Student Investment Co. wants to issue a preferred stock with the following features:– $77 par value (which is what it will sell for)– 10% dividend ($7.70/share)– Issue (flotation) costs/share = $3

• What are the net proceeds per share?• What is the company’s cost of preferred stock?

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Cost of Preferred Stock

Calculation Example

kps = Dps (11.6)Pps

Where:Dps = constant (fixed) dividendPps = per-share net proceeds firm receives from issue or sale after deducting issue costs

Cost of Common Equity

• Return required from common equity investors

• Based on market values of common stock

• Three alternative methods for estimating cost of common stock– Most appropriate method to use depends on what

information is available and how reliable the analyst believes it is

– Method 1: Using Capital Asset Pricing Model (CAPM)– Method 2: Using Constant-Growth Dividend Model– Method 3: Using Multistage-Growth Dividend Model

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kcs = Rrf + (βcs × market risk premium)

Where:kcs = cost of common equityRrf = risk-free rate of returnβcs = beta coefficient for common stockMarket risk premium = expected market return - risk-free rate

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The CAPM Approach

Calculating Cost of Common Stock

• Price and expected rate of return on a share of common stock depends on the dividends expected on the stock.

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Calculating Cost of Common Stock

Discounted Cash Flow (DCF) Approach*

kcs = D1 + g (11.5)

P0

Where:kcs = cost of common stockg = constant growth rate**D1 = next period’s expected dividendP0 = current stock price

formulaassumes

constant dividendgrowth rate

• * Expected rate of return• ** “g” may need to be calculated

• Assumptions– Current risk-free rate is 2%– Annual market return is 8%– Company’s beta is 1.8

• What is the cost of common stock?

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CAPM Method – Calculation Example

Calculating Cost of Common Stock

kcs = Rrf + (βcs × market risk premium)

• Assumptions– Dividend in year 1 = $3.50– Current market price = $33.63– Dividends are growing at 2%/yr

• What is the cost of common stock?

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Calculating Cost of Common Stock

Constant Growth Method – Calculation Example

kcs = D1 + g (11.5)

P0

• Calculated the same as existing common stock

• Difference is in market price– Price will be lower due to flotation/issuance costs– May have to underprice shares to sell

• Cost is higher than existing common stock

• Usually most expensive type of financing for a company

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Costs of New Common Stock Issues

Capital Structure and WACC

• Optimal Capital Structure– % debt, % preferred stock and % common equity in firm’s

capital structure that will maximize the price of the firm’s stock

• WACC (weighted-average cost of capital)– Weighted average of the component costs of debt,

preferred stock and common equity– Based on market values for each type of capital

• Why use a weighted average?– Use of debt impacts the ability to use equity, and vice versa– Weighted-average cost must be used to evaluate projects

• Regardless of specific financing used to fund a particular project

– Required return on the mix of investments (from investors’ perspective)

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WACC = xDebt kDebt pretax (1-t) + xps kps + xcs kcs (11.7)

Where:t = tax ratexDebt = proportion of debt in firm’s capital structurexps = proportion of preferred stock in firm’s capital structurexcs = proportion of common stock in firm’s capital structurekDebt pretax = before-tax cost of debtkps = cost of preferred stockkcs = cost of common stock

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Weighted-Average Cost of Capital (WACC)

Two important points should be noted for the WACC calculation:

1. Best to convert the weights into decimal form and leave the individual costs in percentage terms.

2. The weights must be non-negative and sum to 1.0 or 1.00.

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Calculating WACC – Important Points

• We found the costs of the types of capital for Student Investment Co. to be as follows:– Cost of debt, kdebt after-tax = 5.87%– Cost of preferred stock, kps = 10.41%– Cost of new common stock, kcs = 12.80%

• The company has the following market values for capital. Use these to determine the weights used in calculating its WACC.– Long-term debt (amount owed) = $399,923– Preferred stock (based on market price)

= 1,300 shares outstanding at $77/share– Common stock equity (market price)

= 14,867 shares outstanding at $33.63/share

• Calculate the WACC based on the above information.

• What is the WACC used for?

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Calculating WACC

Student Investment Co. Calculation Example

WACC = xDebt kDebt pretax (1-t) + xps kps + xcs kcs

Market Cost WeightedValue Weight (given) Cost

Debt after-tax $ 399,923 [a] 0.40 [d] 5.87% 2.35% [h]Preferred stock 100,100 [b] 0.10 [e] 10.41% 1.04% [i]Common stock 499,977 [c] 0.50 [f] 12.80% 6.40% [j]Total $ 1,000,000 1.00 [g] 9.79% WACC

[a] given[b] 1,300 shares at $77 per share = $100,100[c] 14,867 shares at $33.63 per share = $499,977[d] 399,923/1,000,000 = 0.40[e] 100,100/1,000,000 = 0.10[f] 499,977/1,000,00 = 0.50[g] Make sure weights add to 1.0 or 1.00[h] 0.40 x 5.87% = 2.35%[i] 0.10 x 10.41% = 1.04%[j] 0.50 x 12.80% = 6.4%

Formula: WACC = (0.40)(5.87%) + (0.10)(10.41%) + (0.50)(12.80%) = 9.79%

Calculating WACC

Student Investment Co. Calculation Example - Solution

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Potential Errors When Using WACC

Two types of problems can arise when a firm’s WACC is used to evaluate individual projects:• A project with a

positive NVP may be rejected (green area)

• A project with a negative NVP may be accepted (pink area)

Alternatives to Using WACC

• If the discount rate for a project cannot be estimated directly, a financial analyst might try to find a public firm that is in a business that is similar to the project.– “Pure-play” comparable because it is exactly like project

• This approach is generally not feasible due to the difficulty of finding a public firm that is only in the business represented by the project.

• Financial managers sometimes classify projects into categories based on their systematic risks.– They then specify a discount rate that is to be used to

discount the cash flows for all projects within each category.

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Project or Category Discount Rates

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Potential Errors When Using Multiple Discount Rates

Final ExamPrep Suggestions

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• Wednesday, December 10– 5:30-7:30 pm: Final Exam, Room 226

• Covers following information:– Parrino Chapters 9-11– WSJ Book Chapters 6-7– Cumulative topics (listed later in slides)

• What should you bring?– Financial calculator– Pencils– Erasers– Brain

Final Exam Information

(continued)

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• Material that is fair game:– Homework and worksheets – Chapter information from both textbooks– Lecture content, slides and discussion

• Format– Multiple choice – Problems (like homework, assignments and worksheets)– Short essay– Formulas will be provided on separate page of exam

Exam Information (cont’d)

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• Do the Practice Exam prepared by the SI’s• Re-work and check against solutions on BbLearn

– All homework and worksheet problems– Pre-Exam “In-Class” Assignment– SI Practice Exam

• Review lecture slides and class notes• Review Parrino chapter summaries and re-read sections

which are still unclear• Review WSJ book chapters• Practice using your financial calculator for TVM, NVP, IRR

and regular math– Texas Instruments guides for BAII-Plus and graphing

calculators are on BbLearn under “FIN 311 Content”

How Should You Study?

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• Exam review session (including practice exam) with SI’s– Sunday, December 7, 5:00-7:00 pm, Gardner Auditorium

• Ask SI’s if you need help (no later than December 7)

• Work Parrino “Self-Study” Problems, if you need more practice (solutions in textbook)

More Study Tools

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Exam Strategies

• Answer the questions you are confident that you know first.

• Spend more time on the portions of the exam that have higher point values.

• If you do skip questions and intend to go back to them later, MAKE SURE YOU GO BACK AND COMPLETE THEM.

• If you have time, double-check your answers.

• Show your work and calculator inputs with your answers.

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• TVM problems and techniques– What is it you are trying to determine?

(i.e., PV, FV, Payment, Interest rate, etc.)– What do you know – what information has been given?

• Use this information as your inputs– Growth rates (solving for I)– Show your calculator inputs on your exam

• Main goal for a firm and a firm’s management

Cumulative Topics

Exam Content

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• WACC (weighted-average cost of capital)– Investor’s required return for each type of capital;

determined by market prices for capital– Cost of debt (after-tax)– Cost of preferred stock– Cost of new common stock– Least expensive vs. most expensive financing– Capital structure

Capital Budgeting – WACC

Exam Content

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• Capital Budgeting process (steps)

• Capital Budgeting cash flows– Determining relevant cash flows

• Initial investment, incremental after-tax operating cash flows, terminal cash flows

• Net working capital calculation• Include opportunity costs• Ignore sunk costs

• Capital Budgeting techniques and decision rules– NPV (use relevant cash flows and WACC)– IRR and MIRR (compare to WACC)– Payback period

Capital Budgeting (cont’d)

Exam Content

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• Taxes– Calculation of withholding taxes and take-home pay– Pretax 401(k) contributions and their effect on the marginal

tax rate

• Insurance– General policy components

• Coverage• Premiums• Deductibles• Claims

– Effect of changes in components on cost of insurance (premiums)

Taxes and Insurance

Exam Content

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Coming Events

Homework, Assignment & Practice Exam• Due no later than 12 noon Friday, December 5

– Parrino Questions & Problems – Chapter 11– Online through WileyPLUS via BbLearn

• Due no later than 2:00 pm Friday, December 5– Pre-Exam “In-Class” Assignment #3 (50 points possible)– Individual assignment – not in groups– Via Support Services with label and date-time stamp– Solutions to be posted on BbLearn shortly after deadline

• SI Practice Exam and Solutions – expected to be posted by Friday, Dec. 5

Next Week• Sunday, December 7

– 5:00-7:00 pm, Exam Review Session with SI’s (including practice exam) Gardner Auditorium

• Wednesday, December 10– 5:30-7:30 pm, Final Exam, Room 226

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Appendix

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Bond Valuation

• Semiannual market yield = 8%/2 = 4%• Semiannual coupon payment = par x coupon/2

= $1,000 x 5%/2 = $25• Notice the N: 3 years convert to 6 because semiannual• Remember when calculating semiannual i/2 and n x 2

Enter

Answer

N i PMTPV FV

6 4 25 1,000

-921.37

Semiannual Compounding Calculation Example

What is the market value of a three-year, 5% coupon bond with a market yield of 8% and semiannual coupon payments?

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Bond Yields

• What is it?– Rate that makes present value of bond’s cash flows equal

price of bond– Rate a bondholder earns if bond is held to maturity and

all coupon and principal payments are made as promised• Changes daily as interest rates change

• When using a financial calculator, we are solving for i

Yield-To-Maturity (YTM)

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• What is it?– In bond trading, the effective annual interest rate (EAR)

is called the effective annual yield (EAY).– Method to annualize a bond yield

• Formula

EAY = (1 + Quoted Interest Rate/m)m -1Where:Quoted Interest Rate = simple annual yield (i.e., semiannual yield x 2)m = number of compounding periods per year

• Simple annual yield is yield per period multiplied by the number of compounding periods– For bonds with semiannual compounding,

simple annual yield = semiannual yield 2

Bond Yields

Effective Annual Yield

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Yield-to-Maturity and Effective Annual Yield Example

An investor buys a 30-year bond with a $1,000 face value for $800. The bond’s coupon rate is 8% and interest payments are made semiannually. What are the bond’s yield-to-maturity and effective annual yield?

Enter

Answer

N i PMTPV FV

60

5.07

40 1,000-800

Calculation Example

• Step 1: Calculate semiannual yield

(continued)44

• Step 2: Calculate Yield-to-Maturity (YTM)

• Step 3: Calculate Effective Annual Yield (EAY)

Enter

Answer

x =

.0507 2

.1014

Enter

Answer

x2 1

1.0507 -

.1040

=

Yield-to-Maturity and Effective Annual Yield

Calculation Example (cont’d)

10.14%

10.40%

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Interest Rates

Anna is charged 1% interest when she borrows $2000 for one week. What is the annual percentage interest rate (APR) on the loan?

52% or 0.52 52 x (0.01) APR

Annual Percentage Rate (APR) Example with Equation

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Interest Rates

• EAR accounts for number of compounding periods and adjusts annualized interest rate for time value of money

• EAR is more accurate measure of rates involved in lending and investing

Calculating Effective Annual Interest Rate (EAR)

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Interest Rates

Anna is charged 1% interest when she borrows $2000 for one week. What is the effective annual interest rate (EAR)?

67.77% or 0.6777

1 - 1.6777

1 - 0.01) (1 EAR 52

Effective Interest Annual Rate (EAR) Example with Equation

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Interest Rates

Your credit card has an APR of 12 % (1% per month). What is the EAR?

12.68% or 0.1268

1 - 1.1268

1- 0.01) (1

1 - 0.12/12) (1 EAR

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Effective Interest Annual Rate (EAR) Example with Equation

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