Financial Management
Dr. Andrea Rigamonti
andrea.rigamonti@econ.muni.cz
Lecture 5
Content:
• Weighted Average Cost of Capital
• Valuing stocks
Weighted Average Cost of capital
The Weighted Average Cost of Capital (WACC) is the
average return required by all of the firm’s investors.
It is determined by the firm’s capital structure (the firm’s
relative amounts of debt and equity), interest rates, the
firm’s risk, and the market’s attitude toward risk.
We can compute it as
𝑅 𝑤𝑎𝑐𝑐 =
𝐸
𝐸 + 𝐷
𝑅 𝐸 +
𝐷
𝐸 + 𝐷
𝑅 𝐷(1 − 𝑇)
where 𝐸 is the market value of the firm’s equity, 𝐷 is the
market value of the firm’s debt, 𝑅 𝐸 is the cost of equity,
𝑅 𝐷 is the cost of debt, and 𝑇 is the corporate tax rate.
Valuing stocks – Dividend-discount model
The first stock valuation model we consider is the
dividend-discount model.
The cash flows received by stock owners (dividends,
capital gain) are risky, and therefore they are discounted
by the equity cost of capital 𝑅 𝐸.
In a perfectly competitive market, buying or selling a
share must be a zero-NPV investment opportunity, and
the price P0 of the stock at time 0 has to be:
𝑃0 =
𝐷𝑖𝑣1 + 𝑃1
1 + 𝑅 𝐸
Valuing stocks – Dividend-discount model
If we multiply by 1 + 𝑅 𝐸, divide by 𝑃0, and subtract 1 from
both sides we get:
𝑅 𝐸 =
𝐷𝑖𝑣1 + 𝑃1
𝑃0
− 1 =
𝐷𝑖𝑣1
𝑃0
+
𝑃1 − 𝑃0
𝑃0
𝐷𝑖𝑣1
𝑃0
is the dividend yield
𝑃1−𝑃0
𝑃0
is the capital gain rate
The sum of the two is called the total return of the stock.
The equation states that the stock’s total return should
equal the equity cost of capital.
Valuing stocks – Dividend-discount model
In 𝑃0 =
𝐷𝑖𝑣1+𝑃1
1+𝑅 𝐸
we can replace the final stock price with
the value that the next holder of the stock, with any
investment horizon H, would be willing to pay, obtaining:
𝑃0 = ෍
𝑛=1
∞
𝐷𝑖𝑣 𝑛
(1 + 𝑅 𝐸) 𝑛
If investors have exactly the same beliefs about the future
cash flows, their valuation of the stock will not depend on
their investment horizon.
Valuing stocks – Dividend-discount model
Dividend-discount model: the stock price is equal to the
present value of the expected future dividends it will pay.
In practice, a certain dividend growth rate 𝑔 has to be
assumed to apply this model. In the simplest case where
𝒈 is constant, the price of stock can be computed as:
𝑃0 =
𝐷𝑖𝑣1
𝑅 𝐸 − 𝑔
The main limitation of the dividend-discount model is that
there is a tremendous amount of uncertainty associated
with any forecast of a firm’s future dividends.
Valuing stocks – Total payout model
Recently, an increasing number of firms have replaced
dividend payouts with share repurchases, that is, the
firm uses excess cash to buy back its own stock. Two
effects:
• the more cash the firm uses to repurchase shares,
the less it has available to pay dividends;
• by repurchasing shares, the firm decreases its share
count, which increases its per-share earnings and
dividends.
Valuing stocks – Total payout model
The total payout model values all of the firm’s equity,
rather than a single share. To do so, we discount the total
payouts that the firm makes to shareholders (dividends +
share repurchases). Then, we divide by the current number
of shares outstanding to determine the share price.
𝑃0 =
𝑃𝑉 𝐹𝑢𝑡𝑢𝑟𝑒 𝑇𝑜𝑡𝑎𝑙 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 𝑎𝑛𝑑 𝑅𝑒𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒𝑠
𝑆ℎ𝑎𝑟𝑒𝑠 𝑂𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔0
Forecasting the growth rate of total earnings (rather than
earnings per share) when forecasting the growth of the
firm’s total payouts can be more reliable and easier to
apply when the firm uses share repurchases.
Valuing stocks – Total payout model
To apply the total payout model, we still need to make
assumptions regarding the growth rate of future payouts.
We can again make a simple assumption of constant growth
rate 𝑔, in which case we have:
𝑃𝑉 𝐹𝑢𝑡𝑢𝑟𝑒 𝑇𝑜𝑡𝑎𝑙 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 𝑎𝑛𝑑 𝑅𝑒𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒𝑠
=
𝐷𝑖𝑣1 + 𝑅𝑒𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒𝑠1
𝑅 𝐸 − 𝑔
Valuing stocks – Discounted free cash flow model
The discounted free cash flow model begins by determining
the firm’s enterprise value, i.e. the total value of the firm to
all investors, both equity and debt holders:
𝐸𝑛𝑡𝑒𝑟𝑝𝑟𝑖𝑠𝑒 𝑉𝑎𝑙𝑢𝑒 = 𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦 + 𝐷𝑒𝑏𝑡 − 𝐶𝑎𝑠ℎ
The advantage is that we don’t have to explicitly forecast the
firm’s dividends, share repurchases, or its use of debt.
To estimate the enterprise value, we compute the present
value of the free cash flow (FCF) that the firm has available
to pay all investors, both debt and equity holders. The FCF is
the cash a company generates after accounting for cash
outflows to support operations and maintain its assets.
Valuing stocks – Discounted free cash flow model
The share price is than given by:
𝑃0 =
𝑃𝑉 𝐹𝑢𝑡𝑢𝑟𝑒 𝐹𝑟𝑒𝑒 𝐶𝑎𝑠ℎ 𝐹𝑙𝑜𝑤 𝑜𝑓 𝐹𝑖𝑟𝑚 + 𝐶𝑎𝑠ℎ0 − 𝐷𝑒𝑏𝑡0
𝑆ℎ𝑎𝑟𝑒𝑠 𝑂𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔0
In discounting the free cash flow that will be paid to both
debt and equity holders we should use the firm’s weighted
average cost of capital (WACC), 𝑅 𝑤𝑎𝑐𝑐, which is the average
cost of capital the firm must pay to all of its investors.
If the firm has no debt, 𝑅 𝑤𝑎𝑐𝑐= 𝑅 𝐸. But when a firm has
debt, 𝑅 𝑤𝑎𝑐𝑐 is an average of the firm’s debt and equity cost
of capital. In that case, because debt is generally less risky
than equity, 𝑅 𝑤𝑎𝑐𝑐 is generally less than 𝑅 𝐸.
Valuing stocks – Discounted free cash flow model
Given the firm’s weighted average cost of capital, the
current value of the enterprise 𝑉0 is:
𝑉0 = ෍
𝑡=1
∞
𝐹𝐶𝐹𝑡
1 + 𝑅 𝑤𝑎𝑐𝑐
𝑡
As there is an infinite sum, to implement the discounted
free cash flow model we need to make some assumptions.
The easiest case is if we assume that cash flows are
constant forever. In this case we have a perpetuity:
𝑉0 =
𝐹𝐶𝐹
𝑅 𝑤𝑎𝑐𝑐
Valuing stocks – Discounted free cash flow model
Alternatively, we can assume that the FCF grow at a
constant rate 𝑔 forever (from period 1). In this case we
have a growing perpetuity:
𝑉0 =
𝐹𝐶𝐹1
𝑅 𝑤𝑎𝑐𝑐 − 𝑔
Both these assumptions are unrealistic.
A more realistic assumption is that the free cash flows
currently grow at non-constant rates, but that long-term
growth will level off to a constant rate.
Valuing stocks – Discounted free cash flow model
In the last scenario, we forecast the firm’s free cash flow up
to some horizon, together with a terminal (continuation)
value of the enterprise 𝑉 𝑁:
𝑉0 =
𝐹𝐶𝐹1
1 + 𝑅 𝑤𝑎𝑐𝑐
+
𝐹𝐶𝐹2
1 + 𝑅 𝑤𝑎𝑐𝑐
2
+ ⋯ +
𝐹𝐶𝐹 𝑁 + 𝑉𝑁
1 + 𝑅 𝑤𝑎𝑐𝑐
𝑁
where
𝑉𝑁 =
𝐹𝐶𝐹 𝑁+1
𝑅 𝑤𝑎𝑐𝑐 − 𝑔
=
𝐹𝐶𝐹 𝑁 + 𝑔𝐹𝐶𝐹 𝑁
𝑅 𝑤𝑎𝑐𝑐 − 𝑔
The long-run growth rate g is typically based on the
expected long-run growth rate of the firm’s revenues.
Valuing stocks
No single technique provides a final answer regarding a
stock’s true value.
All approaches require forecasts that are too uncertain
to provide a definitive assessment of the firm’s value.
Most real-world practitioners use a combination of
these approaches and gain confidence if the results are
consistent across a variety of methods.