Chapter 7 Flashcards
what does the law of one price imply
to value any security we must determine the expected cash flows an investor will receive from owning it. we value a stock with the dividend-discount model
what are the 2 potential source of cash flows from owning a stock
dividends and selling the stock at a future date
how do we discount risky cash flows
we do not use risk-free interest rate, we discount based on the equity cost of capital re for the stock which is the expected return of other investments available in the market with equivalent risk to the firm’s shares.
define equity cost of capital
the appropriate rate used to discount expected cash flows that will be received by holding a firm’s shares. it’s the expected rate of return of securities trade in the market that have equivalent risk the firm’s shares.
how do we find the stock price using equity cost of capital
P0 = (Div + P1)/(1 + re)
why does a stock in a a competitive market must be a zero-NPV investment opportunity
If the current stock price were less than this amount, it would be a positive-NPV investment opportunity. We would therefore expect investors to rush in and buy it, driving up the stock’s price. If the stock price exceeded this amount, selling it would have a positive NPV and the stock price would quickly fall.
what formula to total return with equity cost of capital for 1 year of investing
re = [(Div + P1)/P0] - 1
re = (Div/P0) + [(P1-P0)/P0]
re = dividend yield + capital gain rate
define capital gain
the amount by which the sale price of an asset exceeds its initial purchase price
(P1-P0)
define capital gain rate
dividing the capital gain by the current stock price to express the capital gain as a percentage return
define the total return of the stock
the sum of the dividend yield and capital gain rate
what should the expected total return of the stock and why
it should equal the expected return of other investments available in the market with equivalent risk
The firm must pay its shareholders a return commensurate with the return they can earn elsewhere while taking the same risk. If the stock offered a higher return than other securities with the same risk, investors would sell those other investments and buy the stock instead. This activity would drive up the stock’s current price, lowering its dividend yield and capital gain rate until equity cost of capital equation holds true. If the stock offered a lower expected return, investors would sell the stock and drive down its price until equation equity cost of capital was again satisfied.
what’s the equation for equity cost of capital for multiple years (2 years)
p0 = [div1/(1+ re)] + [(div2 + P2)/(1 + re)]
Thus, the formula for the stock price for a two-year investor is the same as the one for a sequence of two one-year investors.
does a 1 year investor care abut the dividend and stock price in year 2?
While a one-year investor does not care about the dividend and stock price in year 2 directly, she will care about them indirectly because they will affect the price for which she can sell the stock at the end of year 1
define the dividend-discount model
model for stock valuation based on determining the present value of all expected future dividends
what’s the dividend-discount model
p0 = div1/(1+re) + div2/(1+re)^2 +..+ Divn/(1+re)^n + Pn/(1+re)^n
applies to a single n-year investor, who will collect dividends for n years and then sell the stock, or to a series of investors who hold the stock for shorter periods and then resell it. Note that this equation holds for any horizon n. Thus, all investors (with the same beliefs) will attach the same value to the stock, independent of their investment horizons. How long they intend to hold the stock and whether they collect their return in the form of dividends or capital gains is irrelevant.
what does the price of the stock equal to in a dividend discount model
the price of the stock is equal to the present value of the expected future dividends it will pay.
how can we assume the future dividends the firm will pay
A common approximation is to assume that in the long run, dividends will grow at a constant rate to estimate these future dividends the firm will pay
what’s the constant dividend growth model
p0 = div1/(re-g)
a model for valuing a stock by viewing its dividends as a constant growth perpetuity
what does the value of the firm depend on
the value of the firm depends on the current dividend level divided by the equity cost of capital adjusted by the growth rate.
what’s another formula for equity cost of capital using expected capital gain rate
re = (Div1/P0) + g
we see that g equals the expected capital gain rate. In other words, with constant expected dividend growth, the expected growth rate of the share price matches the growth rate of dividends.
what’s the tradeoff that a firm faces when wanting to increase expected growth rate and current dividends level to maximize its share price
the firm faces a tradeoff: Increasing growth may require investment, but money spent on investment cannot be used to pay dividends.
what’s the dividend payout rate
the fraction of a firm’s earnings that the firm pays as dividend each year
what’s the formula to finding the rate of growth of a firm’s dividends
divt = (earnings/share outstanding) * dividend pay out rate
how can a firm increase its dividend
It can increase its earnings (net income). It can increase its dividend payout rate. It can decrease its shares outstanding.
what can a firm do with its earning assuming that the firm doesn’t issue new share or buy back existing shares
A firm can do one of two things with its earnings: It can pay them out to investors, or it can retain and reinvest them. By investing more cash today, a firm can increase its future earnings and dividends. For simplicity, let’s assume that if no investment is made, the firm does not grow, so the current level of earnings generated by the firm remains constant.
what’s the formula for change in earnings if all increases in future earnings result exclusively from new investment made with retained earnings, then
change in earnings = new investment x return on new investment
define the retention rate
the fraction of a firm’s current earnings that the firm retains
wat’s the formula for new investment? and earnings growth rate
new investment = earnings x retention rate
earnings growth rate = change in earnings/earnings = retention rate x return on new investment
how can the growth of dividends = growth of earnings
If the firm chooses to keep its dividend payout rate constant
g = retention rate x return on new investment
also known as the firm’s sustainable growth rate
define the firm’s sustainable growth rate
the rate at which a firm can grow using only retained earnings
If a firm wants to increase its share price, should it cut its dividend and invest more, or should it cut investment and increase its dividend?
Not surprisingly, the answer will depend on the profitability of the firm’s investments.
the effect of cutting the firm’s dividend to grow crucially depends on the return on new investment.
cutting the firm’s dividend to increase investment will raise the stock price if, and only if, the new investments have a positive NPV.
why can we not use a constant dividend growth model to value the stock of the whole life of a firm? how can we value the stock
First, these firms often pay no dividends when they are young. Second, their growth rate continues to change over time until they mature. However, we can use the general form of the dividend-discount model to value such a firm by applying the constant growth model to calculate the future share price of the stock once the firm matures and its expected growth rate stabilizes. Specifically, if the firm is expected to grow at a long-term rate g after year , then from the constant dividend growth model:
Pn = DIVn+1/(re - g)
and then get the dividend discount model with constant long term growth
what’s the dividend discount model with constant long term growth
p0 = DIv1/(1+re) + DIv2/([1+ re]^2) + …+ DIvn/[(1+re)^n] + 1/[(1+re)^n] * [DIvn+1/(re-g)]
why is it difficult to forecast dividends
Forecasting dividends requires forecasting the firm’s earnings, dividend payout rate, and future share count. But future earnings will depend on interest expenses (which in turn depend on how much the firm borrows), and its share count and dividend payout rate will depend on whether the firm uses a portion of its earnings to repurchase shares. Because borrowing and repurchase decisions are at management’s discretion, they can be more difficult to forecast reliably than other, more fundamental aspects of the firm’s cash flows
what are the two alternative approaches to valuing the firm’s shares that avoid some of the difficulties of the dividend-discount model
First, we consider the total payout model, which allows us to ignore the firm’s choice between dividends and share repurchases. Then, we consider the discounted free cash flow model, which focuses on the cash flows to all of the firm’s investors, both debt and equity holders, and allows us to avoid estimating the impact of the firm’s borrowing decisions on earnings.
define share repurchase
the firm uses excess cash to buy back its own stock
what are the 2 consequences share repurchases have on the dividend-discount model
First, the more cash the firm uses to repurchase shares, the less it has available to pay dividends. Second, by repurchasing shares, the firm decreases its share count, which increases its earning and dividends on a per-share basis.
what’s unique about the dividend-discount model
we valued a share from the perspective of a single shareholder, discounting the dividends the shareholder will receive:
P0 = PV(future dividends per share)
define total payout model
a firm’s total payouts to equity holders are discounted and then divided by the current number of share outstanding to determine the share price - which values all of the firm’s equity, rather than a single share.
p0 = pv(future total dividends and repurchases)/shares outstanding
dividend discount model vs total payout method
The only change is that we discount total dividends and share repurchases and use the growth rate of total earnings (rather than earnings per share) when forecasting the growth of the firm’s total payouts. This method can be more reliable and easier to apply when the firm uses share repurchases.
what’s the discounted free cash flow model
a method for estimating a firm’s enterprise value by discounting its future free cash flow
The advantage of the discounted free cash flow model is that it allows us to value a firm without explicitly forecasting its dividends, share repurchases, or use of debt.
what’s the enterprise value
enterprise value = market value of equity + debt - cash
The enterprise value is the value of the firm’s underlying business, unencumbered by debt and separate from any cash or marketable securities. We can interpret the enterprise value as the net cost of acquiring the firm’s equity, taking its cash, paying off all debt, and thus owning the unlevered business.
how can we estimate a firm’s enterprise value
we computed the present value of the firm’s total payouts to equity holders. Likewise, to estimate a firm’s enterprise value, we compute the present value of the free cash flow (FCF) that the firm, as a whole, has available to pay all investors, both debt and equity holders. Each year, the free cash flow for the entire firm can be determined as follows:
free cash flow = [EBIT x (1-tc)] + depreciation - capital expenditures - change in net working capital
where tc = firm’s corporate tax rate
explain this formula: free cash flow = [EBIT x (1-tc)] + depreciation - capital expenditures - change in net working capital
The firm’s corporate tax rate is represented by . If, for tax purposes, capital cost allowance (CCA) replaces depreciation, then CCA would be used in the calculation of EBIT and would also replace depreciation in Eq. 7.18. Depreciation (or CCA) is added back as it was a non-cash deduction when calculating EBIT. Capital expenditures are subtracted as they consume cash but are not reflected in EBIT. We subtract Change in Net Working Capital to undo non-cash accruals that may impact EBIT and to include other changes in balance sheet current accounts that may not be reflected in EBIT.
what’s a firm’s net investment
net investment = capital expenditures - depreciation
We can loosely interpret net investment as investment intended to support the firm’s growth, above and beyond the level needed to maintain the firm’s existing capital.
what’s the formula for free cash flow with net investment
free cash flow = [EBIT x (1-tc)] - net investment - change in net working capital
what’s free cash flow
measures the cash generated by the firm before any payments to debt or equity holders are considered
how can we estimate a firm’s current enterprise value with firm’s free cash flow
compute the present value of the firm’s free cash flow
v0 = pv(future free cash flow of firm)
how can we solve for the share price given the enterprise value
p0 = (v0 + cash0 - debt0)/share outstanding0
discounted free cash flow model vs dividend discount model
in the dividend-discount model, the firm’s cash and debt are included indirectly through the effect of interest income and expenses on earnings. In the discounted free cash flow model, we ignore interest income and expenses because free cash flow is based on EBIT, but then adjust for cash and debt directly
discounted free cash flow vs earlier models
s the discount rate. In previous calculations, we used the firm’s equity cost of capital, , because we were discounting the cash flows to equity holders. Here, we are discounting the free cash flow that will be paid to both debt and equity holders. Thus, we should use the firm’s weighted average cost of capital (WACC), denoted by Rwacc
define Weighted average cost of capital
the average of a firm’s equity and after tax cost of capital, weighted by the fraction of the firm’s enterprise value that corresponds to equity and debt, discount free cash flows using the WACC computes their value include the interest tax shield
Rwacc vs Re
Rwacc= cost of capital the firm must pay to all of its investors, both debt and equity holders. If the firm has no debt, then Rwacc = Re. But when a firm has debt, Rwacc is an average of the firm’s debt and equity cost of capital. In that case, because debt is generally less risky than equity, Rwacc is generally less than Re. We can also interpret the WACC as reflecting the average risk of all of the firm’s investments.
how to forecast firm’s terminal value of the enterprise
Given the firm’s weighted average cost of capital, we implement the discounted free cash flow model in much the same way as we did the dividend-discount model. That is, we forecast the firm’s free cash flow up to some horizon, together with a terminal (continuation) value of the enterprise:
v0 = FCF1/(1+rwacc) + FCF2/(1+ rwacc)^2 + …+ FCFn/(1+rwacc)^n + Vn/(1+rwacc)^n
Often, the terminal value is estimated by assuming a constant long-run growth rate for free cash flows beyond year n, so that: Vn = FCFn+1/(rwacc - gfcf) = [(1+ gfcf)/(rwacc - gfcf)] x FCFn
what is the long run growth rate gfcf typically based on
the expected long run growth rate of the firm’s revenues
what’s an important connection between the discounted free cash flow model for the firm and the NPV rule for capital budgeting
Because the firm’s free cash flow is equal to the sum of the free cash flows from the firm’s current and future investments, we can interpret the firm’s enterprise value as the total NPV that the firm will earn from continuing its existing projects and initiating new ones. Hence, the NPV of any individual project represents its contribution to the firm’s enterprise value. To maximize the firm’s share price, we should abide by the NPV decision rule of accepting projects that have a positive NPV.
why are many forecasts and estimates necessary to estimate the free cash flows of a project/firm
We must forecast future sales, operating expenses, taxes, capital requirements, and other factors. On the one hand, estimating free cash flow in this way gives us flexibility to incorporate many specific details about the future prospects of the firm. On the other hand, some uncertainty inevitably surrounds each assumption
why is it important to conduct a sensitivity analysis
translate this uncertainty into a range of potential values for the stock. A sensitivity analysis shows how our final calculated value changes with respect to changes in one of the input variables in our model.
what are the 2 sensitivity analyses
how the valuation changes with a change in revenue growth, and how the valuation changes with a change in EBIT margin
what are the different valuation methods thus far discussed
The value of the stock is determined by the present value of its future dividends. We can estimate the total market capitalization of the firm’s equity (value) from the present value of the firm’s total payouts, which includes dividends and share repurchases. Finally, the present value of the firm’s free cash flow, which is the cash the firm has available to make payments to equity or debt holders, determines the firm’s enterprise value.
define the method of comparables
an estimation of the value of a firm based on the value of other, comparable firms or other investments that are expected to generate very similar cash flows in the future
what’s the caveat of the law of one price in methods of comparable
identical companies do not exist. Even two firms in the same industry selling the same types of products, while similar in many respects, are likely to be of a different size or scale.
define valuation multiple
a ratio of a firm’s value to some measure of the firm’s scale or cash flow
why do we use the price-earnings ratio as a valuation multiple for a firm’s stock
we can estimate the value of a firm’s share by multiplying its current earnings per share by the average ratio of comparable firms.
Because differences in the scale of firms’ earnings are likely to persist, you should be willing to pay proportionally more for a stock with higher current earnings.
The intuition behind its use is that when you buy a stock, you are in a sense buying the rights to the firm’s future earnings.
what’s the firm’s P/E ratio
P/E ratio = share price/earnings per share
how to interpret the P/E multiple using the stock price formula
estimate the value of a firm’s share by multiplying its current earning per share by the average P/E ratio of comparable firms
what’s a firm’s forward P/E
a firm’s price-earnings (P/E) ratio calculated using the earnings over the next 12 months
what’s a firm’s trailing P/E
the firm’s price-earnings ratio calculated using the earnings over the prior 12 months
which do we prefer in valuations? forward or trailing P/E?
forward P/E is generally preferred as we are most concerned with future earnings
what are the limitations of a firm’s multiples
usefulness of a valuation multiple will depend son the nature of the differences between firms and the sensitivity of the multiples to these differences
where do differences in these multiples arise from?
most likely due to differences in expected future growth rates, profitability, risk, costs of capital
what’s a limitation of comparable analysis
it doesn’t take into account the important differences among firms - such differences of management teams are ignored when applying a valuation multiple
they provide only info regarding the value of a firm relative to other firms in the comparison set -using multiples will not help us determine if an entire industry is overvalued
what’s an advantage of the DCF
they allow us to incorporate specific information about the firm’s cost of capital or future growth. Thus, because the true driver of value for any firm is its ability to generate cash flows for its investors, the DCF methods have the potential to be more accurate than the use of a valuation multiple. In addition, DCF methods make explicit the future performance the firm must achieve in order to justify its current value.
what’s important to note when valuing companies?
the valuations are only good at the time we do them, market prices and stock prices are constantly changing with new information available
what’s the valuation triad
a valuation model includes share value, future cash flows, cost of capital
Valuation models determine the relationship among the firm’s future cash flows, its cost of capital, and the value of its shares. The stock’s expected cash flows and cost of capital can be used to assess its market price. Conversely, the market price can be used to assess the firm’s future cash flows or cost of capital.
