Finance mgmt.

Question 1

The perpetuity formulas assume the first cash flow arrives 1 year from now, so if cashflows arrives in year 2, the present value of the perpetuity we get by applying formula is present value at year 1. this needs to be further discounted 1 year to get to PV of year 0.

Answer 1

Payout ratio=DPS/EPS

Question 2

Book value (start)=EPS/ROE

Answer 2

Book value (end)=Book value start + (EPS* Plowback ratio)

Question 3

ROE=EPS/Book value start

Answer 3

DPS=EPS* payout ratio

Question 4

g=ROE* plowback ratio

Answer 4

when ROE>r, the company should re-invest its profit into company’s growth.

Question 5

PV (perpetuity)= A / (r-g)

A: the constant amount of regular payment

r: rate of return
g: constant growth rate of the payment

Answer 5

Annuity: a constant cash flow fir T periods (starting in period 1)

PV(Annuity)= A* r^(-1)(1-(1+r)^(-T))
FV(Annuity)=PV (annuity)(1+r)^T

Question 6

NPV=C0 + C1/(1+r)

Answer 6

Cost of capital: the return foregone by not investing in financial markets

Question 7

a level stream of payments starting immediately is called an annuity due, which is worth (1+r) times the PV of an ordinary annuity.

Answer 7

quoted annual interest rate (APR: annual percentage rate by banks) and the effective annual rate CAN be different

Question 8

The perpetuity formulas assume the first cash flow arrives 1 year from now, so if cashflows arrives in year 2, the present value of the perpetuity we get by applying formula is present value at year 1. this needs to be further discounted 1 year to get to PV of year 0.

Answer 8

Payout ratio=DPS/EPS

Question 9

Book value (start)=EPS/ROE

Answer 9

Book value (end)=Book value start + (EPS* Plowback ratio)

Question 10

ROE=EPS/Book value start

Answer 10

DPS=EPS* payout ratio

Question 11

g=ROE* plowback ratio

Answer 11

when ROE>r, the company should re-invest its profit into company’s growth.

Question 12

PV (perpetuity)= A / (r-g)

A: the constant amount of regular payment

r: rate of return
g: constant growth rate of the payment

Answer 12

Annuity: a constant cash flow fir T periods (starting in period 1)

PV(Annuity)= A* r^(-1)(1-(1+r)^(-T))
FV(Annuity)=PV (annuity)(1+r)^T

Question 13

NPV=C0 + C1/(1+r)

Answer 13

Cost of capital: the return foregone by not investing in financial markets

Question 14

a level stream of payments starting immediately is called an annuity due, which is worth (1+r) times the PV of an ordinary annuity.

Answer 14

quoted annual interest rate (APR: annual percentage rate by banks) and the effective annual rate CAN be different

Question 15

CPI (consumer price index) is the weighted average of the changes in the prices of its components.

1+ real rate of return = (1+nominal rate of return) / (1+i)
when inflation (i) is low, approximation can be: real rate of return=nominal rate of return - i

Answer 15

for NPV, treat inflation consistently.

• discount nominal cash flow using nominal interest rate
• ….real cash flow using real interest rate

=> PV (real)=PV (nominal) / CPI of Y0

Question 16

Internal rate of return (IRR) is the discount rate that makes the project’s NPV equal zero.

it indicates that among multiple investment projects, the higher IRR, the better. the company should only consider the projects whose IRR is higher than its opp. cost of capital.

Answer 16

IRR leads to same decision as NPV if:
CF only occurred at Y0
Only one project is under consideration
Opp. cost of capital is the same for all periods
threshold rate is set equal to opp.cost of capital

Question 17

shortcoming of using IRR:

• sometimes IRR doesn’t exist (ni available solution to the equation
• multiple IRRs
• IRR doesn’t take into account size of projects
• IRR doesn’t take into account time patterns

Answer 17

payback period is the minimum length of time that sum of cash flows from a period is positive.

Question 18

payback period method ignores time value of money and cash flow after the minimum length of time.

Answer 18

NPV, IRR, payback period, profitability index, hurdle rate, sensitivity analysis … are all capital budgeting methoda

Question 19

working capital = inventory + accounts receivables - accounts payable

Answer 19

at NPV calculation, salvage value of a machine is fully taxable. so when company got the salvage value, only part of it will go to CF.

Question 20

at NPV calculation, working capital should be seen as a buffer needed at the start of the project and freed at the end.

Answer 20

Cash flow=(1-t)operating profit - capital expenditures + tdepreciation - change in working capital

Question 21

EBITDA=revenues - COGs - S&GA

EBIT=EBITDA - depreciation/amortization

Answer 21

CF= EBITDA (1-t) + tdepreciation&amortization - Capex - change of working capital

CF= EBIT *(1-t) + depreciation&amortization - Capex - change of working capital

Question 22

when evaluating a company,

• excludes CF from year 0 and before.
• use terminal value to summarize all CFs beyond a certain horizon
• only consider incremental CFs
• consider impact of project on costs and revenues of existing business i.e. cannibalization, synergy,

Answer 22

a firm’s stock price should be equal to PV of forecasted dividends that the firm will pay. the discounted rate should be the expected rate of return of securities of similar risk level (“opp. cost of capital).

Question 23

Value of assets=NPV of future CF + Cash not used for NPV

Value of equity=Asset - long-term Debt

Share price= value of equity/no. of shares outstanding

Answer 23

Fixed income securities: financial claims with promised cash flows of a fixed amount paid at fixed dates.

i.e, treasury bills/notes/bonds

Question 24

Maturity of bond: when is the bond’s final payout

Principle: face value of the bond, excl. interest

Coupon: periodic interest payment

Answer 24

at a bond’s maturity date, you get your last coupon payment along with a principle payment.

Question 25

Yield-to-maturity: the constant interest rate replacing different spot rate to get final total price of a bond till its maturity

Answer 25

the long-term interest rate is a geometric average of current and expected future short-term interest rates.

Question 26

the set of spot interest rates for different maturities is known as the term structure of interest rates.

Answer 26

EBIT interest coverage = EBIT/ interest expenses

we can conjecture interest rate by benchmarking if its est. EBIT coverage ration is consistent with the ones set up for different rated bonds

Question 27

Assume a company’s earnings, E, grow at rate g and are distributed as dividend, then an approximate value for price p is P=E/(r -g). then use different r and g, you can get the dividend per share (P).

Answer 27

PV (bond)

=PV(annuity of coupon payments)+PV(final payment of principal)

Question 28

premium bond: the bonds sold at a price higher than its face value. its yield to maturity is lower than current yields.

Answer 28

discount bond: the bonds sold at a lower price than its face value. i.e. zero coupon bond is one type of discount bond. investors will get a capital gain over the life of the bond.

Question 29

Can you buy treasury bonds at stock exchange?

Answer 29

No. they are traded by a network of bond dealers.

Question 30

Bond prices and interest rates must move in opposite direction.
i.e. the higher interest rates result in lower bond prices.

Answer 30

coupon rate is different from yield to maturity.

when annual yield is equal to the bond’s annual coupon rates, the bond sells for exactly its face value.

Question 31

Bonds’s rate of return= (coupon income +price change)/investment

Answer 31

for bonds whose cash payments more occurs near maturity, it’s a longer-term bonds than bonds whose cash payment over proportionally take place at early days. for long term bonds, they are more sensitive to fluctuations of interest rates.

Question 32

Duration of a bond=sum of (year * yearly PV fraction of total PV)

Modified duration = volatility%=duration/(1+yield)

volatility measures the % change in bond price for a 1 percentage point in yield.

Answer 32

the law of one price: the same commodity must sell at the same price in a well-functioning market. the cash payment delivered at the same day have to be discounted at the same spot rate.

Question 33

Book value = cumulative retained earnings

Answer 33

ROA(Return on Assets)=total earnings/ Book value

Question 34

EPS=(book value / issued shares) * %Return on equity = book value per share * ROE

Answer 34

Growth rate of book value = plowback ratio * ROE

Question 35

Company’s organic growth process=>

1. when company issues new shares, ROE will result in a total earnings. company can either use the earnings to pay dividend to investors or plowback it to reinvest on its own biz expansion.

Answer 35

Since share price=PV of future dividends (perpetuity), dividend per share = EPS * payout ratio, growth rate of book value = plowback ration * ROE, there is a tension between how much to take from EPS to reinvest in business growth and how much to pay to investors as dividends. the more dividends, the lower reinvestment therefore the lower growth rate of biz. but the lower dividend, the lower share price.

Question 36

By common stock valuation model (“Gordon growth model”),
stock price = dividend /(cost of capital - growth rate of BV), so when r=g, there is no stock price increase when a company expands its biz. only when g or ROA > r, stock price will go up.

growth rate of BV=ROA

Answer 36

a stock may not be a growth stock when it has

• growing EPSs
• growing dividend
• growing assets

a stock may be a growth on

• with EPS growing slower than cost of capital
• with DPS …..(as above)

Question 37

from yahoo finance, if you can find out dividend yield (=Dividend of Y0/Stock price Y0) and g( growth rate of earnings), it’s feasible to get implied cost of capital of a company.

Answer 37

when a company has no growth opp., its stock price of Y0 =EPS of Y1/ cost of capital (“r”)

when a company has growth opp., stock price of Y0 = dividend of Y1/(cost of capital - ROA) = EPS of Y1/r + PVGO (“ PV of growth opp.”)

Question 38

earnings yield = EPS of Y1/ Stock price of Y0

Price-earnings PE ratio: P of Y0 / EPS of Y1

Answer 38

sales of shares to raise new capital are said to occur in the primary market. stock exchanges are really markets for second shares, so they call themselves secondary market.

Question 39

NYSE is an auction market with an auctioneer being a computer.

Nasdaq is a dealer market. it is common for other financial instruments i.e. most bonds are traded in dealer markets.

Answer 39

Book value of a company usually excludes intangible assets such as trademark and patents.

Question 40

Book value can be a good cue for liquidation value (how much investors can get when a company is shut down and its assets are sold off). but it can miss including value of intangible assets.

Answer 40

Current stock price= (expected dividend of Y1+ expected stock price of Y1)/(1+r)

here r is called market capitalization rate or cost of equity capital, it’s essential opp. cost of capital

same as above
Stock price of Y1=(DIV2+ P2)/(1+r)

Question 41

For fast growing companies, they have yet paid dividends since they have been investing in projects which generate higher returns that opp. cost of capital. therefore their investors are willing to forgo immediate dividends and receive deferred dividends.

Answer 41

Cost of equity=dividend yield ratio (dividend/stock price)+ constant growth rate of dividend

but for companies which see multistage growth, it can use multiple stage DCY valuation model.

Question 42

Ways that a company can finance its projects:

1. internal funding (cash generated by operations)
2. equity (issuing new stocks: private equity or IPO)
3. debt (borrow bank loads, or issuing bonds)
4. others (convertibles, options, other securities)

Answer 42

How to finance the projects is one of the major decisions that CFO has to make.

Question 43

when a company maintains a constant leverage ratio in its project, we need to discount its tax shields with WACC.

if it maintains a fixed amount of debt, we discount tax shields with cost of debt, instead of WACC.

Answer 43

when a project is financed by debt, we say it’s a levered project.

Question 44

The value of a levered project = all equity value of the project + PV of interest tax shields (“ITS”)

Answer 44

when a company buys back their equity, they “retire” the equity.

when bonds reach maturity date, these bonds are “retired”.

Question 45

Dividend for Y1= earning per share * payout ratio

Answer 45

A firm’s mix of debt and equity financing is called capital structure.

Question 46

when a new project is of average risk and debt ratio with the rest of company, company’s WACC is applicable, otherwise it should be adjusted. when risks and debt ratios changed, WACC should be adjusted too. if debt ratio only temporarily changed, also okay to use company-wide WACC.

Answer 46

when a company’s future prospects are good, its stock can be traded above book value, for which its market value (share price * shares of outstanding) is higher than its book value. since WACC should reflect a view towards current value and expectations for future, WACC should be based on its market value.

Question 47

when a company takes a loan to finance a project, its after-tax interest going to debt investors = return of debt * (1- tax rate)* debt

so, when its expected equity income going to equity investors = after-tax cash flow - after-tax interest

Answer 47

when a project NPV=0, its expected equity return = cost of equity.

Question 48

when a new project will be financed by a higher debt ratio within a company, this project should be able to generate higher expected return of equity too to match its higher risk. igs borrowing rate of debt will certainly go up too.

Answer 48

a mutual fund is a company that pools money from many investors and invests the money in securities such as stocks, bonds, and short-term debt. the combined holdings of the mutual fund are known as its portfolio.

Question 49

Free CF is different from income.

• FCF is calculated before interest
• FCF is before deduction of depreciation
• WC and Capex should be considered for FCF

Free CF can be negative for fast growing company even the company is profit (income is positive). when growth slows down and prior investments start to roll in, FCF turns positive.

Answer 49

free cash flow= after-tax profit + depreciation- new investment in fixed assets - new investment in working capital

Question 50

when a company’s debt ratio is is constant, on top of FCF by WACC, we can also use flow-to-equity method.

Answer 50

usually companies only consider long-term debt in WACC calculation.

Question 51

when a project is financed more than debt and equity, WACC’s formula can be adjusted to include other funding sources such as preferred stock outstanding.

Answer 51

net working capital= current assets - current liabilities

Question 52

total assets = net working capital + properties, plant, equipment + growth opportunities

Answer 52

total capitalization = long-term debt + preferred stocks + equity

Question 53

Beta of assets =
Beta of debt * D/A

+ Beta of equity * E/A

Answer 53

if the risk is completely diversifiable, then the appropriate cost of capital for the company is the risk-free rate.

Question 54

Excess return (also called risk premium) = r- rf

here is rf is risk-free rate
r is return

Answer 54

there are 2 types of risks: diversifiable and non-diversifiable risks.

non-diversifiable risks is systematic/market risks. such as business cycle, inflation, volatility, credit, liquidity

Question 55

Beta measures the systematic risk in the CAPM.

Answer 55

we are inky rewarded only for systematic risks, not by idiosyncratic ones.

Question 56

when two stocks are positively correlated with each other and move in exact lockstep, there would be no gains at all from diversification. when they are perfectly negatively correlated at -1, the combination of these two stocks that would have no risk

Answer 56

we can use linear programming known as quadratic programming to solve portfolio problems.

Question 57

in a competitive market, you are unlikely to have a monopoly of good ideas. in that case, there is no reason to hold a different portfolio of common stocks from anybody else. this is why many professionals invest in market-index portfolio and most others hold well-diversified portfolios.

Answer 57

when a security has zero risk, unaffected by market at all, its beta is. 0. when its risk as average as the market portfolio, its beta is 1.

Question 58

CAPM (capital asset pricing model) says, in a competitive market, the expected risk premium varies in proportion to beta. expected risk premium on stock = beta * expected risk premium on market

E[rate of return for a stock]=risk free rate + Beta of asset * (market portfolio return - risk free return)

for companies in the same industry, Beta of asset should be similar despite their debt ratio.

Answer 58

Beta indicates a stock’s sensitivity to changes in the value of the market portfolio. it measures the marginal contribution of a stock to the risk of the market portfolio.

when a security has zero risk, unaffected by market at all, its beta is. 0. when its risk as average as the market portfolio, its beta is 1.

Question 59

Equity beta = covariance (returns of selected comparable, return of market portfolio)/Variance (market portfolio)

Answer 59

asset beta = E/(D+E) * equity beta + D/(D+E)*Debt Beta

usually Debt beta is 0 since the investment grade dent is barely impacted by markets.

here D and E are the market values of debt and equity, not book value.
E= number of shares*share price
D, can use proxy of book value of debt since it’s hard to get.

Question 60

Asset beta measures the systematic risk of the expected cash flows of the project or firm. in other words, the project is an asset, thus the project’s beta is an asset beta.

Answer 60

when calculating beta of a project, we need to identify comparable firms/projects. obtain equity beta for each pure play. compute asset beta of these firms as a weighted average of their respective equity and debt betas. then compute the project beta aa the arithmetic average of the asset betas.