Pensions and the Cost of Capital  463
products companies, including Kellogg. The data include pension plans and 
other retiree benefits, such as health care. Each company’s plan is well funded, 
with pension shortfalls at or below 10 percent of projected benefit obligations.
There are two ways to incorporate pensions into the unlevering process. 
In the first method, we assume the pension fund manager has successfully 
matched the beta risk of plan assets to the beta risk of projected benefits. In 
this case, the funded portion will net out, and only the unfunded portion 
will affect the equity beta. In the second method, we relax the assumption of 
matched beta. While the second method is more flexible than the first, it re-
quires an estimate of the beta risk for plan assets. Since the estimate requires 
data found only in the notes (versus a professional data provider), as well as 
a few assumptions regarding asset composition, its use should be limited to 
situations where pensions play a critical role in company valuation.
In the first method, we assume that only the unfunded pension liability 
affects the equity beta. Since the unfunded pension liability mirrors debt, we 
can use the equation for unlevering beta presented in Chapter 15:
 
b
D
V b
E
V b
u
d
e
=
+

(1)
where bu equals the unlevered beta, bd equals the beta of debt, be equals the 
beta of equity, and E equals the market value of equity. The unfunded pen-
sion liability is a debt equivalent. Therefore, D equals traditional debt plus 
unfunded pension liabilities less excess cash.
In Exhibit 23.5, we estimate the unlevered beta for Kellogg and two other 
companies. We present the results with and without pensions for the purpose 
of comparison. In the analysis, we assume a debt beta of 0.17. Many assume 
that the debt beta equals zero, but we use a positive beta to assess the various 
methodologies in a consistent manner. The beta of equity for Kellogg, mea-
sured using five years of monthly stock returns, equals 0.64. The debt-to-value 
EXHIBIT 23.5  Unlevered Betas for Three Consumer Products Companies
Kellogg
General Mills
Mondele–z
Beta of debt
0.17
0.17
0.17
Beta of equity1
0.64
0.75
0.83
Beta of plan assets2
0.66
0.75
0.42
Debt-to-value, excluding pensions, %
31.8
39.3
25.4
Debt-to-value, including pensions, %
32.6
40.0
26.5
Unlevered beta
Average
Unlevered beta, unadjusted for pensions
0.49
0.52
0.66
0.59
Method 1: Treat unfunded pension as debt equivalent
0.48
0.52
0.66
0.59
Method 2: Allow plan asset beta to differ from obligations beta
0.39
0.42
0.63
0.52
1 Beta of equity from ThomsonOne, July 2019. 
2 Assumes the beta of debt investments equals 0.17 and the beta of all remaining investments equals 1.0.

464  Retirement Obligations
ratio equals 31.8 percent without unfunded pensions and 32.6 percent with un-
funded pensions. The resulting unlevered betas with and without unfunded 
pensions are nearly identical because Kellogg’s unfunded pension of $369 mil-
lion is quite small compared with its debt of $9.2 billion. Not surprisingly, the 
equity beta is higher than the unlevered beta, because leverage increases risk.
To unlever beta when the risk is mismatched, we separate plan assets from 
pension liabilities and apply the teachings of economists Franco Modigliani 
and Merton Miller (see Chapter 10) to solve for the risk of operating assets. In 
Appendix C, we step through the algebraic derivation, leading to the follow-
ing formula for unlevered beta:
 
b
D
V
V
b
E
V b
V
V b
u
pbo
d
e
pa
pa
=
+
+
−

(2)
where bu represents unlevered beta, bd represents the beta of debt, be represents 
the equity beta, bpa represents the beta of plan assets, D equals the value of 
traditional debt net cash, Vpbo equals the projected benefit obligations, E equals 
the market value of equity, Vpa equals the market value of plan assets, and V 
equals enterprise value, as measured by the sum of debt, unfunded pension 
liabilities, and the market value of equity.
To measure the beta of plan assets, we use the target allocation reported 
in the pension footnote. Following the research of Jin, Merton, and Bodie, we 
assume debt securities have a beta of 0.17 and other investments have a beta of 
1.0.6 Using the data from Exhibit 23.4 and Exhibit 23.5, we solve for unlevered 
beta. For Kellogg, the resulting unlevered beta equals 0.39. Because the beta 
of plan assets exceeds that of projected benefits, the resulting estimate of unle-
vered beta is lower than we obtained using earlier methods. Had the betas for 
plan assets and plan liabilities been the same, the two methods would yield 
the same results.
While each method has its benefits, we believe Equation 1 inclusive of 
unfunded pension liabilities is the easiest and most reliable method for un-
levering beta. An estimate of unfunded pension liabilities is already required 
for equity valuation, and the method does not require an extensive analysis 
of plan assets—a daunting task when there are many companies to analyze 
within an industry.
Relevering Beta to Estimate the Cost of Equity
Once you have estimated the unlevered industry beta, relever the industry 
beta to the company’s target capital structure and compute the company’s 
cost of capital. To relever the industry beta, do not incorporate pensions. While 
6 L. Jin, R. Merton, and Z. Bodie, “Do a Firm’s Equity Returns Reflect the Risk of Its Pension Plan?” 
Journal of Financial Economics 81, no. 1 (2006): 1–26.