0. Ross, Westerfield and Jordan 7e
Week 9 Lecture 9
Ross, Westerfield and Jordan 7e
Chapter 15
Cost of Capital

1. Last Week.. Expected Returns and Variances
Single asset & Portfolios
Using probabilities & Historical returns
Principle of Diversification
Systematic and Unsystematic Risk
Beta
CAPM
SML
Reward to Risk Ratio

2. Chapter 15 Outline Cost of Capital: Introduction Cost of Equity
Costs of Debt
Cost of Preferred Stock
Weighted Average Cost of Capital
Divisional and Project Costs of Capital
Flotation Costs

3. Why Cost of Capital Is Important
The return to an investor is the same as the cost to the company
Our cost of capital provides us with an indication of how the market views the risk of our assets
Knowing our cost of capital can also help us determine our required return for capital budgeting projects

4. Required Return = Cost of Capital
The Required Rate of Return = Discount Rate = Hurdle Rate = Cost of Capital
Need to know the required return for an investment so we can compute the NPV and decide whether or not to take the investment
Need to earn at least the required return to compensate investors for their financing
Required return – from the investor’s point of view
Cost of capital – from the firm’s point of view

5. Cost of Capital The firm is financed by a mixture of equity and debt
Cost of Capital is a mix of Cost of Equity and Cost of Debt
These costs are determined by the market
The firm determines the mix, Debt/Equity (D/E) reflecting it’s target capital structure.
To calculate cost of capital:
Calculate cost of equity
Calculate cost of debt
Combine them

6. Cost of Equity
The cost of equity is the return required by equity investors, the shareholders on their investment in the firm
Since this cost is not directly observable, it must be estimated
There are two main methods for determining the cost of equity:
Dividend Growth Model
CAPM

7. Cost of Equity - DGM Approach
Start with the dividend growth model formula where g is constant:
Where: RE is the required return for shareholders, P0 is the current price, D0 is the current/last dividend, D1 is the next dividend
and rearrange to solve for RE:
Where D1/P0 is the dividend yield, and g is the growth rate of dividends

8. DGM - Example 1
Bentex Ltd. recently paid a dividend of 40 cents per share. This dividend is expected to grow at 6% per year indefinitely. If the current market price of Bentex shares is $6 per share, estimate its cost of equity.
D0 = $0.40, g = 6%, P0 = $6, RE = ?
D1 = D0(1 + g) = $0.40(1.06) = $0.424
RE = (D1 / P0) + g = (0.424/6.00)
= , and thus the cost of equity is 13.07%.

9. DGM – Example 2
Suppose ABC company is expected to pay a dividend of $1.50 per share next year. There has been a steady growth in dividends of 5.1% per year. The current price is $25. What is the cost of equity?
D1 = $1.50, g = 5.1%, P0 = $25, RE = ?

10. Example - Estimating the Dividend Growth Rate ‘g’
One method for estimating the growth rate is to use the historical average
Year Dividend Change Return%
(1.30 – 1.23) / 1.23 = 5.7%
(1.36 – 1.30) / 1.30 = 4.6%
(1.43 – 1.36) / 1.36 = 5.1%
(1.50 – 1.43) / 1.43 = 4.9%
Average = ( ) / 4 = 5.1%
Another way is use analysts’ forecast

11. Advantages and Disadvantages of Dividend Growth Model
easy to understand and use
Disadvantages
Only applicable to companies currently paying dividends
Assumes dividend growth is constant
Cost of equity is sensitive to growth estimate
Does not explicitly consider risk

12. Cost of Equity - CAPM or SML Approach
Recall CAPM for any asset i is:
The CAPM cost of equity is:
Use the following information to compute our cost of equity
RE = Required return for shareholders
Rf = Risk-free rate
E(RM) – Rf = Market risk premium
E = Systematic risk of firm’s equity relative to the market

13. CAPM - Example
Suppose our ABC company has an equity beta of 0.58 and the current risk-free rate is 6.1%. If the expected market risk premium is 8.6%, what is the cost of equity capital?
βE = 0.58, Rf = 6.1%, E(RM) – Rf = 8.6%
RE = (0.086) = 11.1%
What if the expected market return is 8.6%?
RE = (0.086 – 0.061) = 7.55%

14. Advantages and Disadvantages of CAPM
Explicitly adjusts for risk
Applicable to all companies
Disadvantages
Have to estimate the expected market risk premium, which does vary over time
Have to estimate beta, which also varies over time
We are using the past to predict the future, which is not always reliable

15. Example – Cost of Equity
Suppose our company has a beta of 1.5. The market risk premium is expected to be 9% and the current risk-free rate is 6%. The market believes our dividends will grow at 6% per year and our last dividend was $2. The stock is currently selling for $ What is the cost of equity?
Using CAPM: RE = 6% + 1.5(9%) = 19.5%
Using DGM: RE = [2(1.06) / 15.65] = 19.55%

16. Cost of Preferred Stock
Reminders
Preferred stock pays a constant dividend
Dividends are expected to be paid forever
Preferred stock return = Perpetuity RP
P0 = D/Rp RP = D / P0
Example:
Your company has preferred stock that has an annual dividend of $3. If the current price is $25, what is the cost of preferred stock?
25 = 3/Rp therefore RP = 3 / 25 = 12%

17. Cost of Debt
The cost of debt is the required return on our company’s debt
We usually focus on the cost of long-term debt or bonds
The required return is best estimated by computing the yield-to-maturity or YTM
The cost of debt is NOT the coupon rate
For publicly listed debt use YTM
If the firm has no publicly traded debt, use YTM on similar debt that is traded.

18. YTM of Bond In general: Where Need to solve for RD
C is coupon interest payment,
RD is required market return or YTM,
T is the number of periods left until repayment,
F is face value.
Need to solve for RD

19. Example – Cost of Debt
Gloss Ltd issued a 20-year, 12% bond 10 years ago. The bond is currently priced at $860, and pays interest annually. What is its cost of debt?
Excel solution gives RD = , meaning that Gloss’s cost of debt is 14.76%.

20. Example - Cost of Debt
Suppose a firm has a bond issue currently outstanding that has 25 years left to maturity and pays coupons semiannually. The coupon rate is 9% per year. The bond’s current price is $ per $1000 bond. What is the cost of debt?
t = 25 years x 2 = 50; C = $90/2 = 45;
F = $1000; Bond Price or P = $908.75;
RD or YTM = ?
By trial and error semiannual yield = 5%
YTM = RD = 5% x 2 = 10%

21. Weighted Average Cost of Capital
We can use the individual costs of capital that we have computed to get our “average” cost of capital for the firm.
WACC is the required return on our assets, based on the market’s perception of the risk of those assets
The weights are determined by how much of each type of financing we use
WACC = wE*RE + wP*RP + wD*RD

22. Capital Structure Weights
Notation
E = market value of equity = nr. of outstanding shares times price per share
P = market value of preference shares = nr. of outstanding preference shares times price per share
D = market value of debt = nr. of outstanding bonds times bond price
V = market value of the firm = E + P + D
Weights
wE = E/V = percent financed with equity
wP = P/V = percent financed with preference stock
wD = D/V = percent financed with debt
wE + wP + wD = 1

23. Example – Weights & WACC
Cost of debt = 5.7 %, Cost of equity = 14.0 %
Cost of preference shares = 9.0 %
Source of Capital M.Value Weight
Long term debt $40 m %
Pref. shares $10 m %
Equity $ 50 m %
Total m %
WACC = (E/V)*RE + (P/V)*RP + (D/V)*RD
= (0.5)* (0.1)* (0.4)*0.057 =
WACC = 10.18% (Unadjusted)

24. WACC – Adjusted
The company gets a tax deduction for interest on debt, reducing the effective cost of debt.
If TC is the corporate tax rate then the after tax cost of debt is RD*(1  TC), and the WACC adjusted for taxation effects is given by:
WACC = wE*RE + wP*RPS + wD*RD*(1  TC) or
WACC = (E/V)*RE + (P/V)*RPS +(D/V)*RD*(1  TC)
Previous example: If tax rate is 30%, then
WACC = (0.5)* (0.1)* (0.4)*0.057(0.7)
= or 9.5%.

25. WACC - Extended Example (1)
Equity Information
50 million shares
$80 per share
Beta = 1.15
Market risk premium = 9%
Risk-free rate = 5%
Debt Information
$1 billion in outstanding debt (face value)
Current quote = 110%
Coupon rate = 9%, semiannual coupons
15 years to maturity
Tax rate = 40%
Step 1: Calculate cost of equity and cost of debt
Step 2: Calculate the market value of each source of
financing and the weights
Step 3: Calculate the WACC adjusting for tax.

26. WACC - Extended Example (2)
What is the cost of equity?
βE = 1.5, Rf = 5%, RM – Rf = 9%, RE = ?
RE = 5% (9%) = 15.35%
What is the cost of debt?
t = 15y x 2=30; Price = $1100; C = $90/2 = 45; F = $1000; by trial & error semi yield =
RD = 3.927% x 2 = 7.854%
What is the after-tax cost of debt?
RD(1-TC) = 7.854(1-0.4) = 4.712%

27. WACC - Extended Example (3)
What are the capital structure weights?
E = 50 million x $80 = $4 billion
D = $1 b x 110% = $1.1 billion Or
$1 b/1000 = 1 million bonds issued
1 m bonds x $1100 = $1.1 billion
V = = 5.1 billion
wE = E/V = 4 / 5.1 =
wD = D/V = 1.1 / 5.1 =
What is the WACC?
WACC = wE*RE + wD*RD*(1  TC)
WACC = (15.35%) (4.712%) = 13.06%

28. Finding the Weights from D/E
Suppose Belo Corp has a target D/E ratio of Cost of Debt is 10% and cost of equity is 20%. If tax is 34%, what is WACC?
First calculate WE and WD.
If D/E = what is E = ? D = ?
Assign any value to equity. E = 1
D/1= 0.33 then D = 0.33 and V = 1.33
E/V = 1/1.33 = and
D/V = 0.33/1.33 =
WACC = wE*RE + wD*RD*(1  TC)
WACC = 0.75 x x 0.10 x (1-0.34) = 16.65%

29. Finding D/E
If BHP has a WACC of 21.67% and the cost of equity is 29.2%, cost of debt is 10%, what is it’s target D/E ratio? Assume tax is 34%.
We know that E + D = V or WE + WD = 1
We express one in terms of another:
WE = 1 - WD
And insert in WACC equation:
= WE x WD x 0.10 x (1-0.34)
= (1-WD) x WD x 0.10 x (1-0.34)

30. Finding D/E (cont.) 0.2167 = (1-WD) x 0.292 + WD x 0.10 x (1-0.34)
Solve for WD the only unknown variable:
= – WD x WD x 0.066
– = – WD x WD x 0.066
= -WD x ( )
= WD x 0.226
WD = / = 0.333
Therefore WE = 1 – WD, WE = = 0.667
D/E = 0.333/0.667 = 0.5

31. Table 15.1 Cost of Equity & Debt

32. Table 15.1 WACC

33. Useful Websites Yahoo Finance www.nasdbondinfo.com www.sec.gov
Share price
Beta
Book value per share
Analysts estimates
T-Bill rate
Bond information
Company filings

34. Divisional and Project Costs of Capital
Using the WACC as our discount rate is only appropriate for projects that have the same risk as the firm’s current operations
If we are looking at a project that does NOT have the same risk as the firm, then we need to determine the appropriate discount rate for that project
Divisions also often require separate discount rates

35. Using WACC for All Projects - Example
Project Req. Ret. IRR WACC
A % reject 17% accept 15%
B % accept 18% accept 15%
C % accept 12% reject 15%
Assume the WACC = 15%
If we use the WACC for all projects regardless of risk
Accept A and B, reject C
If correct required return based on specific risk is used
Accept B and C, reject A

36. Divisional and Project costs of capital
WACC is the appropriate discount rate only when the project is about the same risk as the firm.
Other approaches to estimating a discount rate:
divisional cost of capital—used if a company has more than one division with different levels of risk;
pure play approach—a discount rate that is unique to a particular project is used;
subjective approach—projects are allocated to specific risk classes which, in turn, have specified discount rates.

37. Other Approaches Pure Play Approach: Subjective Approach:
Look at companies in the same line of business as the new project
Calculate an average WACC for all the companies and use this rate as the discount rate of the new project
Subjective Approach:
Consider the project’s risk relative to the firm overall risk
If the project risk > firm risk,
use a discount rate > WACC
If the project risk < firm risk,
use a discount rate < WACC

38. Flotation Costs
The required return depends on the risk, not how the money is raised
However, the cost of issuing new securities should not just be ignored either
Basic Approach
Compute the weighted average flotation cost
Use the target weights because the firm will issue securities in these percentages over the long term
fA = (E/V)*fE + (D/V)* fD
where fA is the weighted average flotation cost, fE is the equity flotation cost proportion, and fD is debt flotation cost proportion.
True cost of project = Cost/(1-fA)

39. Flotation Cost Example
A firm has a target structure that is 80% equity and 20% debt. The costs for raising equity are 20% and the cost of raising debt are 6%. If the firm needs $65 million for a new facility, what is the true cost after accounting for flotation costs?
fA = (E/V)*fE + (D/V)* fD
= 0.8* * fA = or 17.2%
If the flotation cost is 17.2%, and we need to raise $65 million net, the true cost of the facility would be:
$65/(1 - fA) = 65/ = $78.50 million
The firm needs to raise $78.5 million to account for flotation costs and to have $65 million left to invest.
Since 78.5/65 = , this suggests that for every dollar required by the project, the firm must raise $ to finance its projects.

40. Quick Quiz
What are the two approaches for computing the cost of equity?
What is the cost of debt?
How do you compute the after-tax cost of debt?
How do you compute the capital structure weights required for the WACC?
When is appropriate to use WACC as the discount rate for projects?
What is the proportion of E and D if we have a D/E ratio of 1.2

41. End Chapter 15