324  Estimating the Cost of Capital 
rate plus the cumulative sum of its exposure to each factor times the factor’s 
risk premium (λ):24
E R
r
t
f
k k
(
) =
+
+
+
+
β λ
β λ
β λ
1
2
...
Otherwise, arbitrage (positive return with zero risk) is possible.
On paper, the theory is extremely powerful. Any deviations from the 
model result in unlimited returns with no risk. In practice, implementation of 
the model has been tricky, as there is little agreement about how many factors 
there are, what they represent, and how to measure them. For this reason, use 
of the APT resides primarily in the classroom.
Estimating the After-Tax Cost of Debt
The weighted average cost of capital blends the cost of equity with the after-
tax cost of debt. To estimate the cost of debt for investment-grade companies, 
use the yield to maturity of the company’s long-term, option-free bonds. Mul-
tiply your estimate of the cost of debt by 1 minus the marginal tax rate to 
determine the cost of debt on an after-tax basis.
Technically speaking, yield to maturity is only a proxy for expected re-
turn, because the yield is a promised rate of return on a company’s debt; it as-
sumes all coupon payments are made on time and the debt is paid in full. An 
enterprise valuation based on the yield to maturity is therefore theoretically 
inconsistent, as expected free cash flows should be discounted by an expected 
return, not a promised yield. For companies with investment-grade debt (debt 
rated at BBB or better), the probability of default is so low that we believe this 
inconsistency is immaterial, especially when compared with the estimation 
error surrounding the cost of equity. Thus, for estimating the cost of debt for 
a company with investment-grade debt, yield to maturity is a suitable proxy.
For companies with below-investment-grade debt, we recommend one of 
two methods. If the debt-to-value ratio is uncharacteristically high, estimate 
the cost of debt using a target capital structure that better reflects the long-
term dynamics of the industry. If the company’s strategy includes substantial 
leverage, value the company using adjusted present value (APV) discounted 
at the unlevered cost of equity, rather than the WACC.
Yield to Maturity as a Proxy
To solve for yield to maturity (YTM), reverse engineer the discount rate required 
to set the present value of the bond’s promised cash flows equal to its price:
Price
Coupon
YTM
Coupon
YTM
Face
Coupon
YTM
=
+
(
)
+
+
+
+
+
+
1
1
1
2
(
)
...
(
)N
24 For a thorough discussion of the arbitrage pricing theory, see M. Grinblatt and S. Titman, Financial 
Markets and Corporate Strategy, 2nd ed. (New York: McGraw-Hill, 2001).

Estimating the After-Tax Cost of Debt  325
Ideally, yield to maturity should be calculated on liquid, option-free, long-
term debt. As discussed earlier in this chapter, short-term bonds do not match 
the duration of the company’s free cash flow. If the bond is rarely traded, the 
bond price will be outdated, or “stale.” Using stale prices will lead to an out-
dated yield to maturity. Yield to maturity can also be distorted when corpo-
rate bonds have attached options, such as callability or convertibility at a fixed 
price, as their value will affect the bond’s price but not its promised cash flows.
In the United States, you can download the yield to maturity for corporate 
debt free of charge by using the TRACE pricing database.25 Exhibit 15.9 dis-
plays TRACE data for Costco’s 3 percent bonds due in May 2027 (the longest 
duration bond in Costco’s capital structure). TRACE reports four data items: 
when the trade occurred, the size of the trade, the bond price, and the implied 
yield to maturity. When measuring the yield to maturity, use the largest trades 
available, as smaller trades are unreliable. The largest trade for Costco’s 2027 
bond on August 30, 2019, was consummated at 2.01 percent (0.6 percent above 
the yield for a seven-year U.S. Treasury bond).
For companies with only short-term bonds or bonds that rarely trade, do 
not use market prices. Instead, use credit ratings to determine yield to ma-
turity. First, determine the company’s credit rating on unsecured long-term 
debt. Next, examine the average yield to maturity on a portfolio of long-term 
bonds with the same credit rating. Use this yield as a proxy for the company’s 
implied yield on long-term debt.
25 The Financial Industry Regulatory Authority (FINRA) introduced TRACE (Trade Reporting and 
Compliance Engine) in July 2002. The system captures and disseminates transactions in investment-
grade, high-yield, and convertible corporate debt, representing all over-the-counter market activity in 
these bonds.
EXHIBIT 15.9  Costco: Trading Data on Corporate Debt, August 2019
Bond: 3% due May 15, 2027
Trade
Trade 
date
Trade 
time
Trade volume, 
thousands
Bond 
price, $
Yield, %
1
8/30/19
15:48
250.0
106.8
2.01
2
8/30/19
15:48
250.0
106.8
2.01
3
8/30/19
15:35
26.0
107.0
1.98
4
8/30/19
15:35
26.0
107.0
1.98
5
8/30/19
15:35
26.0
107.0
1.98
6
8/30/19
15:17
5.0
106.7
2.03
7
8/30/19
15:17
5.0
106.7
2.03
8
8/30/19
14:40
200.0
106.9
2.00
9
8/30/19
14:40
200.0
106.9
2.00
10
8/30/19
10:39
14.0
106.7
2.03
Costco bond yield
2.0
7-year U.S. Treasury yield
(1.4)
Costco default premium
0.6
Source: Financial Industry Regulatory Authority’s Trade Reporting and Compliance Engine (TRACE).