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changes in macro economic variables. Figure 9.3 provides the firm value, debt value, and
equity value over time for the firm.

Figure 9.3: Firm Value over time with Long Term Debtt

Firm Value

Debt Value

Firm is bankrupt

Time (t)

Note that there are periods when the firm value drops below the debt value, which would
suggest that the firm is technically bankrupt in those periods. Firms that weigh this
possibility into their financing decision will therefore borrow less.
Now consider a firm which finances the assets described in Figure 9.2 with debt
that matches the assets exactly, in terms of cash flows, and also in terms of the sensitivity
of debt value to changes in macro economic variables. Figure 9.4 provides the firm value,
debt value and equity value for this firm.

Figure 9.4: Firm Value over time with Long Term Debtt

Firm Value
Value of Equity
Debt Value

Time (t)
Since debt value and firm value move together, the possibility of default is significantly
reduced. This, in turn, will allow the firm to carry much more debt, and the added debt


should provide tax benefits that make the firm more valuable. Thus, matching liability
cash flows to asset cash flows allows firms to have higher optimal debt ratios.

9.7. ˜: The Rationale for Asset and Liability Matching
In chapter 4, we argued that firms should focus on only market risk, since firm-
specific risk can be diversified away. By the same token, it should not matter if firms use
short term debt to finance long term assets, since investors in these firms can diversify
away this risk anyway.
a. True
b. False

Matching Liabilities to Assets
The first step every firm should take towards making the right financing choices
is to understand how cash flows on its assets vary over time. In this section, we consider
five aspects of financing choices, and how they are guided by the nature of the cash flows
generated by assets. We begin by looking at the question of financing maturity, i.e, the
choice between long term, medium term and short term debt, and argue that this choice
will be determined by how long term asset cash flows are. Next, we examine the choice
between fixed and floating rate debt, and how this choice will be affected by the way
inflation affects the cash flows on the assets financed by the debt. Third, we look at the
currency of in which the debt is to be denominated and link it to the currency in which
asset cash flows are generated. Fourth, we evaluate when firms should use convertible
debt instead of straight rate debt, and how this determination should be linked to how
much growth there is in asset cash flows. Finally, we analyze other features that can be
attached to debt, and how these options can be used to insulate a firm against specific
factors that affect cash flows on assets, either positively or negatively.

A. Financing Maturity
Firms can issue debt of varying maturities, ranging from very short term to very
long term. In making this choice, they should first be guided by how long term the cash
flows on their assets are. For instance, firms should not finance assets that generate cash
flows over the short term (say 2 to 3 years) using 20-year debt. In this section, we begin


by examining how best to assess the life of assets and liabilities, and then we consider
alternative strategies to matching financing with asset cash flows.
Measuring the Cashflow Lives of Liabilities and Assets
When we talk about projects as having a 10-year life or a bond as having a 30-
year maturity, we are referring to the time when the project ends or the bond comes due.
The cash flows on the project, however, occur over the 10-year period, and there are
usually interest payments on the bond every six months until maturity. The duration of
an asset or liability is a weighted maturity of all the cash flows on that asset or liability,
where the weights are based upon both the timing and the magnitude of the cash flows. In
general, larger and earlier cash flows are weighted more than are smaller and later cash
flows. The duration of a 30-year bond, with coupons every six months, will be lower than
30 years, and the duration of a 10-year project, with cash flows each year, will generally
be lower than 10 years.
A simple measure11 of duration for a bond, for instance, can be computed as
"t =N t *Coupon %
t + N * Face Value
$ '
(1+ r) N
$ t =1 (1+ r) '
dP/dr # &
Duration of Bond = =
(1 + r) t=N
" Coupon t Face Value %
$ t+ '
(1 + r) N &
# t =1 (1 + r)
$ '

where N is the maturity of the bond, and t is when each coupon comes due. Holding other
factors constant, the duration of a bond will increase with the maturity of the bond and
decrease with the coupon rate on the bond. For example, the duration of a 7%, 30-year
coupon bond, when interest rates are 8% and coupons are paid each year, can be written
as follows:
"t= 3 0 t * $ 70 30 * $1000 %
! +
$ '
(1.08)3 0 '
$ t =1 (1.08)
dP/dr # &
Duration of 30 - year Bond = = = 12.41
(1 + r) t=30
" $1000 %
$ 70
$ t+ '
(1.08) N '
$ t=1 (1.08)
# &

11 This measure of duration estimated above is called Macaulay duration, and it does make same strong
assumptions about the yield curve; specifically, the yield curve is assumed to be flat and move in parallel
shifts. Other duration measures change these assumptions. For purposes of our analysis, however, a rough
measure of duration will suffice.


What does the duration tell us? First, it provides a measure of when, on average,
the cash flows on this bond come due, factoring in both the magnitude of the cash flows
and the present value effects. This 30-year bond, for instance, has cash flows that come
due in about 12.41 years, after considering both the coupons and the face value. Second,
it is an approximate measure of how much the bond price will change for small changes
in interest rates. For instance, this 30-year bond will drop in value by approximately
12.41% for a 1% increase in interest rates. Note that the duration is lower than the
maturity. This will generally be true for coupon-bearing bonds, though special features in
the bond may sometimes increase duration.12 For zero-coupon bonds, the duration is
equal to the maturity.
This measure of duration can be extended to any asset with expected cash flows.
Thus, the duration of a project or asset can be estimated in terms of its pre-debt operating
cash flows:
" t = N t *CFt N * Terminal Value %
$ ! (1+ r)t + '
(1 + r) N
# t=1 &
Duration of Project/Asset = dPV/dr =
" t= N CFt Terminal Value%
! (1 + r)t + (1 + r)N '
$ t =1
# &
where CFt is the after-tax cash flow on the project in year t, the terminal value is a
measure of how much the project is worth at the end of its lifetime of N years. The
duration of an asset measures both when, on average, the cash flows on that asset come
due, and how much the value of the asset changes for a 1% change in interest rates.
One limitation of this analysis of duration is that it keeps cash flows fixed, while
interest rates change. On real projects, however, the cash flows will be adversely affected
by the increases in interest rates, and the degree of the effect will vary from business to
business - more for cyclical firms (automobiles, housing) and less for non-cyclical firms
(food processing). Thus the actual duration of most projects will be higher than the
estimates obtained by keeping cash flows constant. One way of estimating duration
without depending upon the traditional bond duration measures is to use historical data. If

12 For instance, making the coupon rate floating, rather than fixed, will reduce the duration of a bond.
Similarly, adding a call feature to a bond will decrease duration, while making bonds extendible will
increase duration.


the duration is, in fact, a measure of how sensitive asset values are to interest rate
changes, and a time series of data of asset value and interest rate changes is available, a
regression of the former on the latter should yield a measure of duration:
” Asset Valuet = a + b ” Interest Ratet
In this regression, the coefficient ˜b™ on interest rate changes should be a measure of the
duration of the assets. For firms with publicly traded stocks and bonds, the asset value is
the sum of the market values of the two. For a private company or for a public company
with a short history, the regression can be run, using changes in operating income as the
dependent variable “
” Operating Incomet = a + b ” Interest Ratet
Here again, the coefficient “b” is a measure of the duration of the assets.

Illustration 9.5: Calculating Duration for Disney Theme Park
In this application, we will calculate duration using the traditional measures for
the Disney Bangkok Theme Park that we analyzed in chapter 5. The cash flows for the
project are summarized in Table 9.10, together with the present value estimates,
calculated using the cost of capital for this project of 10.66%.
Table 9.10: Calculating a Project™s Duration: Disney Theme Park
Year Annual Cashflow Terminal Value Present Value Present value *t
0 -$2,000 -$2,000 $0
1 -$1,000 -$904 -$904
2 -$833 -$680 -$1,361
3 -$224 -$165 -$496
4 $417 $278 $1,112
5 $559 $337 $1,684
6 $614 $334 $2,006
7 $658 $324 $2,265
8 $726 $323 $2,582
9 $802 $322 $2,899
10 $837 $9,857 $3,882 $38,821
$2,050 $48,609

Duration of the Project = 48,609/2,050 = 23.71 years


This would suggest that the cash flows on this project come due, on average, in 23.71
years. The duration is longer than the life of the project because the cash flows in the first
few years are negative.

9.8. ˜: Project Life and Duration
In investment analyses, analysts often cut off project lives at an arbitrary point
and estimate a salvage or a terminal value. If these cash flows are used to estimate project
duration, we will tend to
a. understate duration
b. overstate duration
c. not affect the duration estimate
Duration Matching Strategies
In the last section, we considered ways of estimating the duration of assets and
liabilities. The basic idea is to match the duration of a firm™s assets to the duration of its
liabilities. This can be accomplished in two ways: by matching individual assets and
liabilities, or by matching the assets of the firm with its collective liabilities. In the first
approach, the Disney Theme Park project would be financed with bonds with duration of
approximately 24 years. While this approach provides a precise matching of each asset™s
characteristics to those of the financing used for it, it has several limitations. First, it is
expensive to arrange separate financing for each project, given the issuance costs
associated with raising funds. Second, this approach ignores interactions and correlations
between projects which might make project-specific financing sub-optimal for the firm.
Consequently, this approach works only for companies that have very large, independent
It is far more straightforward, and often cheaper, to match the duration of a firm™s
collective assets to the duration of its collective liabilities. If there is a significant


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