Discussion paper series iteration or circularity in wacc calculation

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Discussion Paper Series: Iteration or
Circularity in WACC Calculation
Email exchange in 2012 between Sukarnen with Prof. Michael C. Ehrhardt (The Paul and
Beverly Castagna Professor of Investments, The University of Tennessee Finance
Department, USA)
Karnen to Prof. Ehrhardt:
Dear Mr. Michael C. Ehrhardt,
I am a big fan for your books, one of my favorites is the Search for Value: Measuring the
Company’s Cost of Capital (quite old, published in 1994, yet it is pretty enlightening for me,
still keep it handy with me). At the moment, I am reading your book Corporate Valuation: A
Guide for Managers and Investors. Pretty much finished, yet there is something that a bit
bothering me. It is about the equity value resulting from the DCF (chapter 13 , page 280)
compared to the value of operations (or company value), its ratio is 97.63%, which is not the
same with the target weight in the WACC calculation (Chapter 11, page 235) which you use
78%.
Sukarnen
DILARANG MENG-COPY, MENYALIN,
ATAU MENDISTRIBUSIKAN
SEBAGIAN ATAU SELURUH TULISAN
INI TANPA PERSETUJUAN TERTULIS
DARI PENULIS
Untuk pertanyaan atau komentar bisa
diposting melalui website
www.futurumcorfinan.com

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I know from Damodaran’s book (Investment Valuation, page 613), he said that:
As in all firm valuation, there is an element of circular reasoning involved in this valuation.
The footnote no. 2 (on the same page) said that the circular reasoning comes in because we
use the current market value of equity and debt to compute the cost of capital. We then use
the cost of capital to estimate the value of equity and debt. If this is unacceptable, the
process can be iterated, with the cost of capital being recomputed using the estimated
values of debt and equity, and continued until there is convergence.
May I know how you see this circular reasoning, will it still be ok to have target weights for
debt (to Debt+Equity market value) and equity (to Debt+Equity market value) used in WACC
computation be different with the resulted equity value (to total company value) obtained
from DCF?
Damodaran just said above, “….If this is unacceptable, the process can be iterated….”, yet
he is not quite clear as to when it is acceptable and when it is not acceptable.
Can I see the issue above as you mentioned in the footnote no. 5 (page 55), where you said:
Be careful in interpreting our meaning when we speak of the required rate of return. We are
not saying that the investor really expects to earn 12% each and every year, but rather that
the investor knows the return will fluctuate from year to year, and that it will fluctuate
somewhat more than the market return (its beta is greater than 1), but that its return should
average 12% over a multiyear holding period.
If this is the case, then basically, in the company valuation, I don’t have to do the iteration
process (as suggested by Damodaran) to make sure that resulted equity value will have the
same ratio to the company value as the one I use in the WACC computation? Is this safe to
say this? However, at the same time, seems something is not quite reasonable. Using
WACC as a discount rate to value the free cash flows of a company, somehow, the
underlying assumption is that we assume the company’s debt-to-total-value ratio remains
constant over the life of the company’s free cash flows (including the terminal free cash
flows), to make sure that WACC (and levered cost of equity). Or the company will need to
adjust its leverage continuously to maintain a constant debt-equity ratio in terms of market
values. Yet, we know for sure, that debt-to-total-value ratio mostly will vary from year to year,
making both levered cost of equity and WACC vary from year to year as well.

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Can we say on safe side when performing the company valuation using WACC as its
discount rate, that since the financing is a time-consuming task, the ratio cannot be adjusted
on a day-to-day (month-to-month or year-to-year) basis, rather, the adjustment can be
expected to occur over the long run? If the answer is yes, then we do not have to worry too
much on what Damodaran said about doing reiteration process (since the value obtained
from reiteration value does not necessarily give us the “correct”/”same” value)?
Prof. Ehrhardt to Karnen:
Dear Karnen,
I think there are two issues, both involving the weights used in estimating the WACC and
the actual debt in the company’s capital structure.
First, the weights used in the WACC are targets, so we should not expect the actual weights
(based on the market values of debt and equity) to exactly equal the targets for either the
current date or the projected future dates. However, we should expect the actual weights in
the projected statements to be close to the target weights used to calculate the WACC. If
this is not the case, then it is inappropriate to use the WACC based on the targets. In fact,
when projecting future financial statements, it is possible to “set” the debt each year so that
the ratio of debt/ (value of operations) do equal the target debt ratio. If the choice of dividend
policy (i.e., high dividends) causes the firm to need “extra” debt to keep the balance sheets
balanced, then management needs to reconsider the target capital structure and/or the
dividend policy.
In this first situation, management can choose the actual dollar values of debt in the future
so that the ratio of debt/operations is constant. In the second situation, suppose a privately
held company is satisfied with the amount of debt it is holding. In order to estimate the value
of equity, you need the target WACC. But you can’t estimate the target WACC without
knowing the value of debt and equity. Hence, there is circularity. There are two approaches.
First, management could pick a target WACC and then project the financial statements such
that level of debt/ (value of operations) each year gives the target weight. Notice that this
might imply that the current value of debt must change substantially in the projections.
Second, if you don’t want the current value of debt to change (i.e., management feels this
level is appropriate), then you could pick a trial weight and use this to calculate the WACC.
Then calculate the value of operations and the value of equity. Then calculate the resulting
weight of debt/ (value of operations). If this isn’t equal to the original weight, then replace the

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original with this new value and repeat the process. The weight usually converges after
several repetitions.
Karnen to Prof. Ehrhardt:
From what I read on your email, seems to me at the start of the valuation process, then we
should set either:
 target debt to equity RATIO or
 target LEVEL of debt (which potentially results in having debt-to-equity ratio vary
from year to year in the forecast)
For the target debt-to-equity ratio (in which WACC is easier to apply), however, along the
making of forecast, we still need to check against the resulted equity value (as of valuation
date?) to ensure that what we put as a target ratio is not too far different, or at least we could
justify it (or accept it?).
It seems to me there is no point to make the debt-to-equity ratio exactly the same even
though this is possible to do using MS Excel formula.
From your Valuation book I read, it appears you picked up the approach not to do the
iteration process.
Having said that, I believe, bottom line is about "guessing" whether the risks of the cash
flows or any earnings metrics are constant throughout the forecast period and into the
perpetuity. This will be directly reflected in the discount rate(s) being used in the valuation.
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