Anna Goodman
Finance 300 – Final Paper
December 12th, 2015
"How do Firms Value Assets?"
Understanding how to value assets is important for firms and investors when considering
buying or selling assets. Assets play a critical role in any firms’ success: they have the
potential to create utility and profit. There are three basic forms of asset valuation that
ultimately influence decisions made in the market: book value, market value, and
production value.
Although each have unique elements, they have connective tissue, meaning that one can’t
be talked about talking about the others. This begs the real question: how to buyers and
sellers of assets come up with their settlement price? The price is obviously influenced by
market, book, and production value – but the price paid on the day of the transaction
ultimately embodies all three. Somehow, the two parties came to an agreement with all
three valuations in mind. How did they come to that number, and how do each of the
valuations play a part in determining that number?
To understand how the assets were valued and how the sale price came to be, it is essential
to discuss the basic definitions of book value, market value, and production value and
understand how each plays a role in asset valuation.
Book Value
Book value is the assets’ accounting identity; it denotes the cost of the asset. The balance
sheet is a good place to start when determining book value because it represents a point in
time, rather than a flow of assets and liabilities over time. Generally, the total assets minus
the total liabilities of a firm represent book value. This value can be skewed by a firm’s
subjective representation of their own assets and liabilities published on their balance
sheet, therefore using market value and production value to further assess the asset is
important.
Market Value
Market value is known as “the true vale of any asset, i.e. the amount of cash we could
actually get if we sold it.”1 It’s the amount that buyers hope to get for it. The market value
can’t be determined merely from looking at the balance sheet because takes into account
stocks, bonds, and real estate, management. Economic goodwill, which captures a value of
reputation, employees, brand name, etc. is also an aspect in measuring market value.
There are many ways to measure market value: earning per share, EBITDA ratio, enterprise
value, price to earnings ratio, and price to sales ratio. Some theories, including the Miller
and Modigliani Irrelevance theory stat that capital structure has no effect on value,
whereby market value is determined by earning power and risk of investment. This is
where determining the value of equity becomes interesting, but it must also be taken with
1
(Ross)
precaution as the market value can be very skewed based on supply and demand, and
expectations in that market.
Production Value
Production value tries to capture the value of a company that reflects it’s future potential:
opportunity cost, time, future values, earnings, operating cash flow, and dividend
payments– all bundled together. Production value basically asks the question “how much
income will this asset generate?” This is the question that any investor will ask themselves
before investing, because why invest in something that will create losses!? This is probably
the most interesting valuation, and often takes different market or book values into
account for valuation equations. There are many ways to determine production value. This
paper will explore different valuation options including discounted cash flow, the internal
rate of return, the dividend growth model, the weighted average cost of capital, the key
value driver and the many different ways of interpreting r – which can all help connect
book, market, and production value to the sale cost.
Discounted Cash Flow Model
The discounted cash flow model this takes all future cash flows (CF) and discounts them
back to the present value rate. This can help determine whether the investment creates
value for it’s owners and if the investment can be worth more than it costs. This also links
book value with production value, as the first initial cash flow is essentially the book value
𝐶𝐹
paid. Where 𝑃𝑉 = (1+𝑟)𝑡 , and 𝐹𝑉 = (𝐶𝐹)(1 + 𝑟)𝑡 , r is the rate based on the conditions and
the market, and t is time. If buyers and sellers can’t agree on a price, either the cash flow
expectations need to be relaxed, or the r needs to be relaxed. Cash flows can also be used to
determine the internal rate of return – another measurement of value.
Internal Rate of Return
The internal rate of return is can also be determined using the discounted cash flow model
when net present value equals zero. This rate can be used to know if an investment is
worthwhile: when IRR>R, it is acceptable.
Dividend Growth Model
Another way to determine production value is through the dividend growth model. The
dividend growth model determines the present value of a share based on future dividend
payments (div), the discount rate (r ), and the growth rate (g). This essentially links book
value to production value! The dividend growth model rate in perpetuity is explained by
𝐷𝑖𝑣
the equation:𝑃0 = 𝑟−𝑔 . This is equation is used to determine the dividend at time one but
can be used to determine the present value of the discounted cash flow during for an
explicit period( by summing all values). In order to find the value in perpetuity, the present
𝐷𝑖𝑣
value of the continuing value must be determined (PVCV): where CV = 𝑟−𝑔 is divided by
(1 + 𝑟)𝑡 . Adding the summation of DCF and the PVCV gives the net present value! Net
present value of an explicit period plus the value in perpetuity is a great valuation of
production!
This model is great as long as the growth rate does not exceed the discount rate because it
can account for capital gains and losses. This model falters when the growth rate exceeds
the discount rate, because the stock price is “illegally” infinitely large and completely
inaccurate. If the growth rate exceeds the discount rate, the KVD model can offer a more
accurate valuation or the weighted average cost of capital can be used as r.
Weighted Average Cost of Capital
The weighted average cost of capital is a rate based on a firms’ objective input, calculated
based on available values that reflect the companies cost structure of capital, i.e. “what does
their capital cost.” WACC uses the three sources of capital: preferred stock, common stock,
and bonds/debt to determine the rate. The tricky part is determining the cost of each
source of capital.
Cost of Equity
For cost of equity (Re) the CAPM model can be used: 𝑅𝐸 = 𝑅𝐹 + 𝛽(𝑅𝑚 − 𝑅𝐹 ) Where 𝑅𝐹 is
the risk free rate, 𝑅𝑀 is the market rate and 𝛽 is the rate of risk for the company in
question. It boils down to show how risky is the investment. CAPM is the best way to
determine the cost of equity and can also be used to find the cost of preferred stock and
debt, but there are better ways.
Cost of Preferred Stock
The cost of preferred stock can be determined by dividing the dividend price by its book
value (once again linking production value to book value…). The bond book value equation
1
is: BV=C(
1−(1+𝑌𝑇𝑀)𝑛
𝑌𝑇𝑀
)+
𝐹𝑎𝑐𝑒 𝑉𝑎𝑙𝑢𝑒
(1+𝑌𝑇𝑀)𝑛
.
Cost of Debt
And finally, the cost of debt can be calculated by dividing Interest over the book value. Once
these are calculated, they can then be weighted to find the weighted average cost of capital:
𝐸
𝑃
𝐷
(𝑅𝑒) ( ) + (𝑅𝑝) ( ) + (𝑅𝑑) ( ) (1 − 𝑇). For WACC, the tax rate is also needed. So, when
𝑉
𝑉
𝑉
WACC increases, so does the firm’s value and the firm’s risk. WACC is also the firms cost of
financing and it’s overall required return. So from their perspective, it can be a great
indicator of r.
Another amazing way WACC can be used as a tool for valuation is to compare it with
Return on Invested Capital (ROIC). Basically, comparing the cost versus the benefit of
invested capital. If the cost of capital is greater than the return, this indicates that growth
actually destroys value. Whereas if the cost of capital is less that the return, this indicates
that growth will create value. This would be an important metric to use when evaluating
production value!
To reiterate the point of finding WACC, the problem of trying to determine a valuation
when growth exceeds required return needed to be solved. WACC can be used in the key
value driver model(KVD), a model that can be used in the place of the dividend growth
model with g>r.
Key Value Driver Model
The key value driver(KVD) is another good valuation tool for production value because it
1−
𝑔
𝑅𝑂𝐼𝐶
links cash flow to growth and return on invested capital (ROIC). To find the KVD: (𝑊𝐴𝐶𝐶−𝑔)
Since the KVD model uses ROIC, it solves the problem that g>r created in the dividend
growth model. If, when determining the present value, g>r, it’s likely that the continuing
value model had issues (such as not enough time) – therefore using the KVD model would
be the best for this situation.
Issues in Determining R
Book value, market value, and production value all converge at the time of sale. The
valuation of assets can be determined very differently and through many models. Book
value is the basic assets minus liabilities. Basic book values are often needed in calculating
both market and production values. Market value is the amount of cash a firm could get for
the entirety of their assets, and is sometimes based on EPS, EBITDA or enterprise value. But
production value has more intrinsic values because it accounts for the value of production,
including future values – “what profits will this asset create.” When these three values
converge, it means the buyer and seller have essentially agreed on r – the required return
and WACC. Although short term WACC and r are different, it’s at this point that they
essentially converge. From an investors standpoint, r would be based on what they hope
the investment will give them whereas the firm would likely use WACC as r. So, in many
cases, r for the firm will be different than r of the investor. For the values to converge the
firm either needs to relax their r or the buyer needs to relax the cash flow expectations
(based on the DCF model).
Another interpretation of r, according to Ross, Westerfield, and Jordan, can be found when
𝐷𝑖𝑣
𝐷
you rearrange the dividend growth model 𝑃0 = 𝑟−𝑔 to solve for r  R = 𝑃1 + g. Therefore,
0
the required return has two components: the dividend yield and the capital gains yield. The
𝐷
dividend yield is the dividend over the price: 𝑃1 where the stocks’ expected cash dividend is
0
divided by the current price.2 The capital gains yield (g) is the rate at which the value of the
investment grows.3 Adding the two together results in the required return.
Using the DCF can become complicated when trying to determine r. As mentioned earlier,
for the dividend growth model, R can be found by adding the dividend yield and the capital
gains yield. But with the net present value calculation DCF+PVCV it’s tough to pinpoint or
solve for r. How to define r? R is essentially the opportunity cost /expectation. In the
dividend growth model, r can sometimes be used as WACC – the weighted average cost of
𝐸
𝑃
𝐷
capital: 𝑊𝐴𝐶𝐶 = (𝑅𝑒) (𝑉) + (𝑅𝑝) (𝑉) + (𝑅𝑑) (𝑉 ) (1 − 𝑇).
2
3
(Ross)
(Ross)
This is especially true from the standpoint of the firm because WACC reflects the firm’s
required return. But, from an investors standpoint, r would be based on what they hope the
investment will give them! So, in many cases, (and as mentioned earlier) r for the firm will
be different than r of the investor. This is the main issue!
Valuation Consensus
Basically, firm valuation is dictated by both parties agreeing to a combination of book,
market, and production values – and it all seems to boil down to the EXPECTATIONS of
both parties, particularity their interpretations of r or WACC. One way to change ones r or
WACC could be through leveraging or deleveraging. This involves an interesting link
between market value and production value when analyzing the exception of the Miller and
Modigliani Theorem. This exception combines Market Values with production values and
shows that earnings per share can actually change the value/market capitalization of an
asset. In order to reconcile, the cost of equity must be greater than the cost of debt. A higher
debt-to-equity ratio leads to a higher required return on equity, because of the higher risk
involved for equity-holders in a company with debt – and vice versa.4 Therefore by
leveraging or deleveraging, firms could influence their WACC in order to appeal more or
less to a buyer’s r value.
Another way to “fix” this could be by changing the time expectation for the DCF-PVCV
model or by changing the expected cash flows. Using different capital structures could
change a bad investment into a potentially amazing investment – but it’s all about knowing
why and when to do this. If both parties can find a way to agree on the combination of
book (assets minus liabilities), market (“how much can I get for this”), and production
value (“how much profit can this generate for me”) through adjusting r, cash flows,
expectations, and time – there can be overall gains. All three asset valuations are closely
connected and imperative in the asset valuation – it’s all a matter of perspective,
consideration, and consensus when buying or selling.
4
(Wiki)