1. CHAPTER 10
The Cost of Capital

2. Topics Cost of Capital Components WACC Debt Preferred Common Equity
Composite
Risk Adjustments
WACC with Flotation Costs

3. Sources of Long-term Capital
Long-Term Debt
Preferred Stock
Common Stock
Retained Earnings
New Common Stock rs rd
rps
rce re
10-3 3

4. WACC Weighted Average Cost of Capital
WACC = wdrd(1-T) + wpsrps + wcers
(10.10)
Where:
wd = % of debt in capital structure
wps = % of preferred stock in capital structure
wce = % of common equity in capital structure
rd = firm’s cost of debt
rps= firm’s cost of preferred stock
rs = firm’s cost of equity
T = firm’s corporate tax rate
Weights
Component costs

5. 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

6. 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

7. NCC’s Cost of Debt (rd)
Calculator Solution , S. /
%- = 5.50%
A 22-year, 9% semiannual coupon bond sells for $835.42
Bond pays a semiannual coupon:
rd = 5.5% x 2 = 11%

8. 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%( ) = 6.6%
Use nominal rate

9. 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

10. Adjusting the Cost of Debt for Flotation Costs
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

11. NCC’s Cost of Debt (rd) with Flotation Costs
Calculator Solution , S. /
%- = 3.34%
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
Nominal after-tax cost of debt with flotation costs = 6.68%

12. 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

13. NCC’s Cost of preferred stock: PP = $100 $10 Dividend F = 2.5%
Where:
Dps = Preferred dividend
PPS = Preferred stock price
F = Flotation cost %

14. 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

15. Funding with New Common Equity
Mature firms rarely issue new equity
High flotation costs
Negative signal to the market
Downward pressure on stock price

16. 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

17. 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

18. 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

19. 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

20. CAPM Cost of Equity - Steps
Estimate risk-free rate (rRF)
Estimate market risk premium (RPM) or expected return on the market (RM)
Estimate beta (β)
Substitute into CAPM

21. 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

22. 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:
Historical or analysts’ estimates
Value Line or Reuters

23. RPM Estimate – #1 RPM = 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% % = 11.73%
Problems:
Past = future?
Growth rates sensitive to period measured

24. 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% % = 17.79%
Problems:
Earnings growth ≠ dividend growth
1-year growth rate ≠ long-term growth
Analysts’ accuracy
Differing analysts’ opinions

25. Estimating RPM (or RM) RPM = Equity risk premium RM RPM=RM- rRF
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]

26. 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

27. NCC’s CAPM Cost of Equity
rRF = 8% RPM = 6% β= 1.1
rs = rRF + (RM - rRF )β
= 8.0% + (6.0%)1.1
= 14.6%

28. 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

29. DCF Approach: Inputs Current stock price (P0) Current dividend (D0)
Growth rate (g)

30. 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

31. 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 = 7%

32. Earnings Retention Assumptions
Retention rate is constant
ROE on new investments is constant
No new common stock will be issued
The risk of future projects is very close to the risk of the overall firm

33. 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%

34. NCC’s DCF Cost of Equity, rs
D1 = $ P0 = $ g = 7%
rs = D1 P0
+ g =
D0(1+g)
+ g =
$2.40
$32
+ 0.07
= %

35. 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

36. 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

37. Final Estimate of rs Method Estimate Used by CAPM 14.6% 74% - 85% DCF
14.5%
16%
rd + RP
14.7%
Non-public
Average

38. Flotation Costs for Equity re = Cost of New Equity
NCC: D1 = $ P0 = $ F = 12.5%

39. Topics Cost of Capital Components WACC Debt Preferred Common Equity
Composite
Risk Adjusted
WACC with Flotation Costs

40. WACC Weighted Average Cost of Capital
WACC = wdrd(1-T) + wpsrps + wcers
(10.10)
Where:
wd = % of debt in capital structure
wps= % of preferred stock in capital structure
wce= % of common equity in capital structure
rd = firm’s cost of debt
rps= firm’s cost of preferred stock
rs= firm’s cost of equity
T = firm’s corporate tax rate
Weights
Component costs

41. 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

42. NCC’s WACC Weighted Average Cost of Capital
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
WACC =0.3(11%)(1-.40)+0.1(10.3%)+0.6(14.6%)
WACC = 11.77%

43. 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

44. 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

45. Estimating Weights Given: The stock price is $50
There are 3 million shares of stock
$25 million of preferred stock
$75 million of debt

46. Estimating Weights Vce = $50 x (3 million) = $150 million
Vps = $25 million
Vd = $75 million
Total value = $150 + $25 + $75 = $250 million

47. Estimating Weights

48. WACC

49. 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

50. Topics Cost of Capital Components WACC Debt Preferred Common Equity
Composite
Risk Adjusted
WACC with Flotation Costs

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

52. Divisional Risk and the Cost of Capital
Rate of Return
(%)
Acceptance Region
WACC
WACC H
Acceptance Region
Rejection Region
WACC F
Rejection Region
WACC L
Risk
Risk
Risk L H

53. Using WACC for All Projects - Example
What would happen if we use the WACC for all projects regardless of risk?
Assume the WACC = 15%
Ask students which projects would be accepted if they used the WACC for the discount rate? Compare 15% to IRR and accept projects A and B.
Now ask students which projects should be accepted if you use the required return based on the risk of the project? Accept B and C.
So, what happened when we used the WACC? We accepted a risky project that we shouldn’t have and rejected a less risky project that we should have accepted. What will happen to the overall risk of the firm if the company does this on a consistent basis? Most students will see that the firm will become riskier.

54. 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

55. 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

56. Huron Steel Example

57. 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

58. Subjective Approach - Example
Risk Level
Discount Rate
Very Low Risk
WACC – 8% %
Low Risk
WACC – 3% %
Same Risk as Firm
WACC %
High Risk
WACC + 5% %
Very High Risk
WACC + 10% %

59. Topics Cost of Capital Components WACC Debt Preferred Common Equity
Composite
Risk Adjusted
WACC with Flotation Costs

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

61. NCC’s WACC With New Debt
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%
WACC = wdrATd + wpsrps + wcre
WACC = 0.3(6.68%)+0.1(10.3%) +0.6(14.6%)
WACC = 2.004% % % = %

62. NCC’s WACC With New Debt & New Equity
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%
WACC = wdrATd + wpsrps + wcre
WACC = 0.3(6.68%)+0.1(10.3%) +0.6(15.6%)
WACC = 2.004% % % = %

63. NCC’s WACC WACC Description WACC No New Issues 11.770% With New Debt
11.794%
With New Debt & New Equity
12.394%

64. 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

65. Increasing Marginal Cost of Capital% 16 15 14
WACC2 = % 13
WACC1 = 11.77% 12
External debt & equity 10
No external funds 9 8
500
700
Capital Required 61 48

66. 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

67. CHAPTER 10
The Cost of Capital