1 chapter 10 the cost of capital. 2 topics cost of capital components debt preferred common equity...

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CHAPTER 10

The Cost of Capital

2

Topics

Cost of Capital Components Debt Preferred Common Equity

WACC Composite Risk Adjustments WACC with Flotation Costs

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Sources of Long-term Capital

10-3

rd

rsrps

rce re

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WACCWeighted Average Cost of Capital

Where:

wd = % of debt in capital structurewps = % of preferred stock in capital structurewce = % of common equity in capital structure

rd = firm’s cost of debtrps= firm’s cost of preferred stockrs = firm’s cost of equity

T = firm’s corporate tax rate

Weights

Component costs

WACC = wdrd(1-T) + wpsrps + wcers (10.10)

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Capital Components Capital components = sources of

funding from investors Accounts payable, accruals, and

deferred taxes ≠ sources of funding from investors Not included in calculation of the

cost of capital Adjustments made when calculating

project cash flows

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Cost of Debt Method 1: Ask an investment

banker what the coupon rate would be on new debt

Method 2: Find the bond rating for the company and use the yield on other bonds with a similar rating

Method 3: Find the yield on the company’s outstanding debt

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NCC’s Cost of Debt (rd)

A 22-year, 9% semiannual coupon bond sells for $835.42

Bond pays a semiannual coupon:rd = 5.5% x 2 = 11%

Calculator Solution 44 835.42

45 1000

= 5.50%

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Component Cost of Debt

Interest is tax deductible, so the after tax (AT) cost of debt is: rd AT = rd BT(1 - T) rd AT = 11%(1 - 0.40) =

6.6% Use nominal rate

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Flotation Costs on New Debt Flotation costs on debt usually low Frequently ignored

“Project Financing” Adjusts project’s cash flows for

flotation costs of debt Debt has specific claim on the

project’s cash flows

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Adjusting the Cost of Debt for Flotation Costs

N

1tN

dt

d )]T1(r1[

M

)]T1(r1[

)T1(INT)F1(M 2)-(10

Where:

M = Bond’s par value (face value)

F = Flotation cost as a %

N = Number of coupon payments

T = Corporate tax rate

INT = Dollars of interest per period

rd(1-T) = after tax cost of debt adjusted for inflation

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NCC’s Cost of Debt (rd) with Flotation Costs

NCC can issue 30-year bonds

N = 60 11% annual coupon rate

Coupons paid semiannually PMT = [(.11 x 1000)/2]*(1-.40) PMT = $33

Flotation cost = 1% PV = -1000(1-.01) = -990

Face value = M = 1000

Calculator Solution 60 990

33 1000

= 3.34%

Nominal after-tax cost of debt with flotation costs = 6.68%

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Preferred Stock

Flotation costs for preferred are significant Use net price

Preferred dividends are not deductible No tax adjustment Use rps

Nominal rps is used

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NCC’s Cost of preferred stock: PP = $100 $10 Dividend F =

2.5%

3)-(10 )F1(P

Dr

ps

psps

Where:

Dps = Preferred dividend

PPS = Preferred stock priceF = Flotation cost %

10.3%

)025.1(100$

10$rps

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Cost of Common Equity

Two Ways to raise equity financing: Directly

Issue new shares of common stock Indirectly

Reinvesting earnings not paid out as dividends

Use retained earnings

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Funding with New Common Equity

Mature firms rarely issue new equity High flotation costs Negative signal to the market Downward pressure on stock

price

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Cost of Retained Earnings

Earnings can be reinvested or paid out as dividends

Investors could buy other securities, earn a return

Thus, there is an opportunity cost if earnings are reinvested

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Cost for Reinvested Earnings

Opportunity cost: The return stockholders could earn on alternative investments of equal risk They could buy similar stocks and earn

rs, or company could repurchase its own stock and earn rs

rs = the cost of reinvested earnings = the cost of equity

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Three ways to determine the cost of equity, rs:

1. CAPM: rs = rRF + (RM - rRF)β

= rRF + (RPM)β

2. DCF: rs = D1/P0 + g

3. Own-Bond-Yield-Plus-Risk Premium:

rs = rd + Bond RP

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= rRF + (RPM)β

2. DCF: rs = D1/P0 + g


rs = rd + Bond RP

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1. Estimate risk-free rate (rRF)

2. Estimate market risk premium (RPM) or expected return on the market (RM)

3. Estimate beta (β)4. Substitute into CAPM

CAPM Cost of Equity - Steps

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Estimating rRF

Common stock = long-term security

T-Bills more volatile than T-Bonds Most analysts use the rate on a

long-term (10 to 30 years) government bond as an estimate of rRF

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Estimating RPM or RM

Historical - Ibbotson & Associates 1926-most recent year 6.5% arithmetic mean - if constant risk

aversion 4.9 % geometric mean – best future

estimate Ex Ante = Forward-Looking

If market in equilibrium: Return Required Return Expected MMRF0

1M RRPrg

P

Dr̂

Historical or analysts’ estimates

Value Line or Reuters

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RPM Estimate – #1RPM = 11.73%

rM Estimate (Reuters, Spring 2008) Dividend yield on S&P500 = 2.61% Dividend growth rate = 13.20% rM=[0.0261(1+.132)]+0.132=16.15%

Forward-looking RPM: Long-term T-Bond rate = 4.42% 16.15% - 4.42% = 11.73%

Problems: Past = future? Growth rates sensitive to period

measured

gP

)g1(Dr̂

0

0M

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RPM Estimate – #2 RPM = 17.79%

rM Estimate (Spring 2008) Reuters S&P500 dividend yield = 2.61% Yahoo Earnings growth rate = 19.1% rM=[0.0261(1+.191)]+0.191=22.21%

Forward-looking RPM: 22.21% - 4.42% = 17.79%

Problems: Earnings growth ≠ dividend growth 1-year growth rate ≠ long-term growth Analysts’ accuracy Differing analysts’ opinions

gP

)g1(Dr̂

0

0M

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Estimating RPM (or RM)

RPM = Equity risk premium Most analysts use a rate of 5% to

6.5% for the market risk premium RM

S&P500 index return =proxy for the market return

RPM=RM- rRF

Brigham-Daves →RPM = [3.5, 6.5]

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Estimating Beta - β Beta estimates vary Beta estimates are “noisy”

Wide confidence interval Historical Beta

4-5 years/monthly or 1-2 years/weekly

Adjusted Beta Fundamental Beta

Multinational issues

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NCC’s CAPM Cost of Equity

rs = rRF + (RM - rRF )β

= 8.0% + (6.0%)1.1

= 14.6%

rRF = 8% RPM = 6% β= 1.1

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= rRF + (RPM)β

2. DCF: rs = D1/P0 + g


rs = rd + Bond RP

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DCF Approach: Inputs

1. Current stock price (P0)

2. Current dividend (D0)

3. Growth rate (g)

g expected

5)-(10

o

1ss

s

10

P

Dr̂r

gr

DP̂

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Estimating the Growth Rate

The historical growth rate If you believe future = past

The earnings retention model Analysts’ estimates:

Value Line, Zack’s, Yahoo.Finance

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Earnings Retention Model NCC Data:

ROE = 14.5% Dividend payout ratio = 52%

Retention ratio = 100% - dividend payout Retention rate = 100% - 52% = 48%

Retention growth rate: g = ROE x (Retention rate) g = (14.5%) x 0.48 = 7%

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Earnings Retention Assumptions

1. Retention rate is constant2. ROE on new investments is

constant3. No new common stock will be

issued4. The risk of future projects is very

close to the risk of the overall firm

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Using Analysts’ Forecasts Analysts’ estimate earnings growth

= proxy for dividend growth Sometimes involve non-constant growth

Develop a proxy constant rate

Analysts’ Estimates for NCC: 10.4% annual growth for 5 years 6.5% growth after 5 years

Analysts’ estimates usually best source

g = 6.9%

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NCC’s DCF Cost of Equity, rs

rs = D1

P0

+ g =D0(1+g)

P0

+ g

= $2.40

$32+ 0.07

= 0.075 + 0.07

= 14.5%

D1 = $2.40 P0 = $32 g = 7%

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= rRF + (RPM)β

2. DCF: rs = D1/P0 + g


rs = rd + Bond RP

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The Own-Bond-Yield-Plus-Risk-Premium Method: rd = 11%, RP = 3.7%

rs = rd + RP rs = 11.0% + 3.7% = 14.7%

This RP CAPM RPM

Produces ballpark estimate of rs Useful check

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Final Estimate of rs

Method Estimate

Used by

CAPM 14.6% 74% - 85%

DCF 14.5% 16%

rd + RP 14.7% Non-public

Average 14.6%

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Flotation Costs for Equityre = Cost of New Equity

9)-(10 g)F1(P

Dr̂r

0

1ee

NCC: D1 = $2.40 P0 = $32 F = 12.5%

15.6%

07.)125.1(32$

40.2$r̂r ee

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Topics


WACC Composite Risk Adjusted WACC with Flotation Costs

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WACCWeighted Average Cost of Capital

Where:

wd = % of debt in capital structurewps= % of preferred stock in capital structurewce= % of common equity in capital structure

rd = firm’s cost of debtrps= firm’s cost of preferred stockrs= firm’s cost of equity

T = firm’s corporate tax rate

Weights

Component costs

WACC = wdrd(1-T) + wpsrps + wcers (10.10)

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WACC Weights

Weights =percentages of the firm that will be financed by each component

If possible, always use the target weights for the percentages of the firm that will be financed with the various types of capital NCC: 30% debt, 10% Preferred, 60% Equity

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NCC’s WACCWeighted Average Cost of Capital

WACC =0.3(11%)(1-.40)+0.1(10.3%)+0.6(14.6%)

WACC = 11.77%

Component w r

Debt (before tax)

0.30 11.0%

Preferred Stock 0.10 10.3%

Common equity 0.60 14.6%WACC = wDrD (1- T)+ wPsrPs + wcrs

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Cost of Capital Issues Before-tax vs. After-tax Capital

Costs Long- and short-term debt affected

Historical Costs vs. Marginal Costs Target Weights vs. Annual Financing

Choices Target Weights vs. Book Values

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Estimating Weights for the Capital Structure

Estimate the weights using current market values rather than current book values

If market value of debt is not known: Usually reasonable to use the book

values of debt, especially if the debt is short-term

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Estimating Weights

Given: The stock price is $50 There are 3 million shares of

stock $25 million of preferred stock $75 million of debt

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Estimating Weights

Vce = $50 x (3 million) = $150 million

Vps = $25 million Vd = $75 million Total value = $150 + $25 + $75 =

$250 million

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Estimating Weights

Value WeightStock price $50Share O/S 3,000,000

Preferred Stock $25,000,000 $25,000,000 10%

Debt $75,000,000 $75,000,000 30%

$250,000,000 100%

$150,000,000 60%

Total Firm

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WACC

Tax Rate = 40% Cost of Capital

Stock price $50Share O/S 3,000,000

Preferred Stock $25,000,000 $25,000,000 10% 10.30% 1.03%

Debt $75,000,000 $75,000,000 30% 11.00% 60% 1.98%

$250,000,000 100% 11.77%

WACC

8.76%

Tax Effect

14.60%

Total Firm

Value Weight

$150,000,000 60%

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Factors that influence a company’s WACC Market conditions

Interest rates The market risk premium Tax rates

Firm’s capital structure Firm’s dividend policy Firm’s investment policy

Firms with riskier projects generally have a higher WACC

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Topics



51

Risk-Adjusted WACC The composite WACC reflects the

risk of an average project undertaken by the firm

Different divisions/projects may have different risks

The division’s or project’s WACC should be adjusted to reflect the appropriate risk and capital structure

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Divisional Risk and the Cost of Capital

Rate of Return (%)

WACC

Rejection Region

Acceptance Region

Risk

WACC H

WACC L

WACC F

0 Risk L Risk H

Acceptance Region

Rejection Region

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Using WACC for All Projects - Example

What would happen if we use the WACC for all projects regardless of risk?

Assume the WACC = 15%Required

Project Return IRR If 15% Risk AdjA 20% 17% Accept RejectB 15% 18% Accept AcceptC 10% 12% Reject Accept

Decision

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The Risk-Adjusted Divisional Cost of Capital

Estimate the cost of capital that the division would have if it were a stand-alone firm

Requires estimating the division’s beta, cost of debt, and capital structure CAPM frequently used

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Pure Play Method for Estimating Beta for a Division or a Project

Find several publicly traded companies exclusively in project’s business

Use average of their betas as proxy for project’s beta

Hard to find such companies

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Huron Steel Example

Riskfree rate = 7%Market risk premium = 6%

Division Beta COC % BusSteel 1.1 13.60% 70%Barge 1.5 16.00% 20%Distrib 0.5 10.00% 10%Overall 1.12 13.72%

Huron Steel Company

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Subjective Approach Consider the project’s risk

relative to the firm overall If project risk > firm risk

Project discount rate > WACC If project risk < firm risk

Project discount rate < WACC

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Subjective Approach - Example

Risk Level Discount Rate

Very Low Risk WACC – 8% 7%

Low Risk WACC – 3% 12%

Same Risk as Firm WACC 15%

High Risk WACC + 5% 20%

Very High Risk WACC + 10% 25%

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Topics



60

Flotation Costs Flotation costs depend on the risk

of the firm and the type of capital being raised

Flotation costs: Highest for common equity Most firms issue equity infrequently

Flotation costs frequently ignored when calculating WACC

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NCC’s WACC With New Debt

WACC = wdrATd + wpsrps + wcre

WACC = 0.3(6.68%)+0.1(10.3%) +0.6(14.6%)WACC = 2.004% + 1.03% + 9.36% = 11.794%

Component w r

New Debt (after-tax)

d 0.30 6.68%

Preferred Stock ps 0.10 10.3%

New Common equity

c 0.60 14.6%

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NCC’s WACC With New Debt & New Equity

WACC = wdrATd + wpsrps + wcre

WACC = 0.3(6.68%)+0.1(10.3%) +0.6(15.6%)WACC = 2.004% + 1.03% + 9.36% = 12.394%

Component w r

New Debt (after-tax)

d 0.30 6.68%

Preferred Stock ps 0.10 10.3%

New Common equity

c 0.60 15.6%

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NCC’s WACC

WACC Description WACC

No New Issues 11.770%

With New Debt 11.794%

With New Debt & New Equity

12.394%

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Increasing Marginal Cost of Capital Externally raised capital flotation costs

Increases the cost of capital Investors often perceive large capital

budgets as being risky Drives up the cost of capital

If external funds will be raised, then the NPV of all projects should be estimated using this higher marginal cost of capital

500 700

%

Capital Required

WACC1 = 11.77%

WACC2 = 12.394%

8

9

10

12

13

14

15

16

Increasing Marginal Cost of Capital

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No external funds

External debt & equity

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Four Mistakes to Avoid Current (YTM) vs. historical (Coupon rate) cost

of debt Mixing current and historical measures to

estimate the market risk premium Book weights vs. Market Weights

Use Target weights Use market value of equity Book value of debt is a reasonable proxy for market

value Incorrect cost of capital components

Only investor provided funding

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CHAPTER 10

The Cost of Capital

1 chapter 10 the cost of capital. 2 topics cost of capital components debt preferred common equity...

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