Chapter 7

Question 1

what does the law of one price imply

Answer 1

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

Question 2

what are the 2 potential source of cash flows from owning a stock

Answer 2

dividends and selling the stock at a future date

Question 3

how do we discount risky cash flows

Answer 3

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.

Question 4

define equity cost of capital

Answer 4

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.

Question 5

how do we find the stock price using equity cost of capital

Answer 5

P0 = (Div + P1)/(1 + re)

Question 6

why does a stock in a a competitive market must be a zero-NPV investment opportunity

Answer 6

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.

Question 7

what formula to total return with equity cost of capital for 1 year of investing

Answer 7

re = [(Div + P1)/P0] - 1

re = (Div/P0) + [(P1-P0)/P0]

re = dividend yield + capital gain rate

Question 8

define capital gain

Answer 8

the amount by which the sale price of an asset exceeds its initial purchase price

(P1-P0)

Question 9

define capital gain rate

Answer 9

dividing the capital gain by the current stock price to express the capital gain as a percentage return

Question 10

define the total return of the stock

Answer 10

the sum of the dividend yield and capital gain rate

Question 11

what should the expected total return of the stock and why

Answer 11

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.

Question 12

what’s the equation for equity cost of capital for multiple years (2 years)

Answer 12

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.

Question 13

does a 1 year investor care abut the dividend and stock price in year 2?

Answer 13

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

Question 14

define the dividend-discount model

Answer 14

model for stock valuation based on determining the present value of all expected future dividends

Question 15

what’s the dividend-discount model

Answer 15

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.

Question 16

what does the price of the stock equal to in a dividend discount model

Answer 16

the price of the stock is equal to the present value of the expected future dividends it will pay.

Question 17

how can we assume the future dividends the firm will pay

Answer 17

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

Question 18

what’s the constant dividend growth model

Answer 18

p0 = div1/(re-g)

a model for valuing a stock by viewing its dividends as a constant growth perpetuity

Question 19

what does the value of the firm depend on

Answer 19

the value of the firm depends on the current dividend level divided by the equity cost of capital adjusted by the growth rate.

Question 20

what’s another formula for equity cost of capital using expected capital gain rate

Answer 20

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.

Question 21

what’s the tradeoff that a firm faces when wanting to increase expected growth rate and current dividends level to maximize its share price

Answer 21

the firm faces a tradeoff: Increasing growth may require investment, but money spent on investment cannot be used to pay dividends.

Question 22

what’s the dividend payout rate

Answer 22

the fraction of a firm’s earnings that the firm pays as dividend each year

Question 23

what’s the formula to finding the rate of growth of a firm’s dividends

Answer 23

divt = (earnings/share outstanding) * dividend pay out rate

Question 24

how can a firm increase its dividend

Answer 24

It can increase its earnings (net income). It can increase its dividend payout rate. It can decrease its shares outstanding.

Question 25

what can a firm do with its earning assuming that the firm doesn’t issue new share or buy back existing shares

Answer 25

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.

Question 26

what’s the formula for change in earnings if all increases in future earnings result exclusively from new investment made with retained earnings, then

Answer 26

change in earnings = new investment x return on new investment

Question 27

define the retention rate

Answer 27

the fraction of a firm’s current earnings that the firm retains

Question 28

wat’s the formula for new investment? and earnings growth rate

Answer 28

new investment = earnings x retention rate

earnings growth rate = change in earnings/earnings = retention rate x return on new investment

Question 29

how can the growth of dividends = growth of earnings

Answer 29

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

Question 30

define the firm’s sustainable growth rate

Answer 30

the rate at which a firm can grow using only retained earnings

Question 31

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?

Answer 31

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.

Question 32

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

Answer 32

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

Question 33

what’s the dividend discount model with constant long term growth

Answer 33

p0 = DIv1/(1+re) + DIv2/([1+ re]^2) + …+ DIvn/[(1+re)^n] + 1/[(1+re)^n] * [DIvn+1/(re-g)]

Question 34

why is it difficult to forecast dividends

Answer 34

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

Question 35

what are the two alternative approaches to valuing the firm’s shares that avoid some of the difficulties of the dividend-discount model

Answer 35

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.

Question 36

define share repurchase

Answer 36

the firm uses excess cash to buy back its own stock

Question 37

what are the 2 consequences share repurchases have on the dividend-discount model

Answer 37

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.

Question 38

what’s unique about the dividend-discount model

Answer 38

we valued a share from the perspective of a single shareholder, discounting the dividends the shareholder will receive:

P0 = PV(future dividends per share)

Question 39

define total payout model

Answer 39

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

Question 40

dividend discount model vs total payout method

Answer 40

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.

Question 41

what’s the discounted free cash flow model

Answer 41

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.

Question 42

what’s the enterprise value

Answer 42

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.

Question 43

how can we estimate a firm’s enterprise value

Answer 43

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

Question 44

explain this formula: free cash flow = [EBIT x (1-tc)] + depreciation - capital expenditures - change in net working capital

Answer 44

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.

Question 45

what’s a firm’s net investment

Answer 45

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.

Question 46

what’s the formula for free cash flow with net investment

Answer 46

free cash flow = [EBIT x (1-tc)] - net investment - change in net working capital

Question 47

what’s free cash flow

Answer 47

measures the cash generated by the firm before any payments to debt or equity holders are considered

Question 48

how can we estimate a firm’s current enterprise value with firm’s free cash flow

Answer 48

compute the present value of the firm’s free cash flow

v0 = pv(future free cash flow of firm)

Question 49

how can we solve for the share price given the enterprise value

Answer 49

p0 = (v0 + cash0 - debt0)/share outstanding0

Question 50

discounted free cash flow model vs dividend discount model

Answer 50

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

Question 51

discounted free cash flow vs earlier models

Answer 51

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

Question 52

define Weighted average cost of capital

Answer 52

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

Question 53

Rwacc vs Re

Answer 53

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.

Question 54

how to forecast firm’s terminal value of the enterprise

Answer 54

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

Question 55

what is the long run growth rate gfcf typically based on

Answer 55

the expected long run growth rate of the firm’s revenues

Question 56

what’s an important connection between the discounted free cash flow model for the firm and the NPV rule for capital budgeting

Answer 56

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.

Question 57

why are many forecasts and estimates necessary to estimate the free cash flows of a project/firm

Answer 57

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

Question 58

why is it important to conduct a sensitivity analysis

Answer 58

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.

Question 59

what are the 2 sensitivity analyses

Answer 59

how the valuation changes with a change in revenue growth, and how the valuation changes with a change in EBIT margin

Question 60

what are the different valuation methods thus far discussed

Answer 60

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.

Question 61

define the method of comparables

Answer 61

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

Question 62

what’s the caveat of the law of one price in methods of comparable

Answer 62

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.

Question 63

define valuation multiple

Answer 63

a ratio of a firm’s value to some measure of the firm’s scale or cash flow

Question 64

why do we use the price-earnings ratio as a valuation multiple for a firm’s stock

Answer 64

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.

Question 65

what’s the firm’s P/E ratio

Answer 65

P/E ratio = share price/earnings per share

Question 66

how to interpret the P/E multiple using the stock price formula

Answer 66

estimate the value of a firm’s share by multiplying its current earning per share by the average P/E ratio of comparable firms

Question 67

what’s a firm’s forward P/E

Answer 67

a firm’s price-earnings (P/E) ratio calculated using the earnings over the next 12 months

Question 68

what’s a firm’s trailing P/E

Answer 68

the firm’s price-earnings ratio calculated using the earnings over the prior 12 months

Question 69

which do we prefer in valuations? forward or trailing P/E?

Answer 69

forward P/E is generally preferred as we are most concerned with future earnings

Question 70

what are the limitations of a firm’s multiples

Answer 70

usefulness of a valuation multiple will depend son the nature of the differences between firms and the sensitivity of the multiples to these differences

Question 71

where do differences in these multiples arise from?

Answer 71

most likely due to differences in expected future growth rates, profitability, risk, costs of capital

Question 72

what’s a limitation of comparable analysis

Answer 72

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

Question 73

what’s an advantage of the DCF

Answer 73

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.

Question 74

what’s important to note when valuing companies?

Answer 74

the valuations are only good at the time we do them, market prices and stock prices are constantly changing with new information available

Question 75

what’s the valuation triad

Answer 75

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.