finance test 3

molina corp's sales last year were $280,000, and its net income was $23,000. what was its profit margin?

8.21%

operating margin

EBIT/sales

solving for PV:calculator

INPUTS: N=3 I/YR=4 PMT=0 FV=100 OUTPUT: PV=-88.90

the dupont equation

ROE = profit margin x total assets turnover x equity multiplier ROE = (NI/sales) x (sales/TA) x (TA/equity)

nominal rate (INOM)

also called the quoted or stated rate - an annual rate that ignores compounding effects - INOM is stated in contracts - e.g. 4% quarterly or 4% daily interest

liquidity

can we make required payments? - liquid asset: an asset that can be converted to cash quickly without having to reduce the asset's price very much - liquidity ratios: show the relationship of a firm's cash and other current assets to its current liabilities

current ratio

current assets/current liabilities

DRP

default risk premium - the difference between the interest rate on a US treasury bond and a corporate bond of equal maturity and marketability - avg default risk premiums vary over time - tend to get larger when the economy is weaker and borrowers are more likely to have a hard time paying off their debts

solving for N

if sales grow at 10% per year, how long before sales double? INPUTS: I/YR=10 PV=-1 PMT=0 FV=2 OUTPUT: N=7.3

profit margin

net income/sales

ratio analysis involves analyzing financial statements to help appraise a firm's financial position and strength

true

the current and quick ratios both help us measure a firm's liquidity. the current ration measures the relationship of the firm's current assets to its current liabilities, while the quick ratio measures the firm's ability to pay off short-term obligations without relying on the sale of inventories.

true

solving for interest

what annual interest rate would cause $100 to grow to $119.10 in 3 years? INPUTS: N=3 PV=-100 PMT=0 FV=119.10 OUTPUT: I/YR=6

last year marocco corp's sales were $505 million. if sales grow at 8% per year, how large (in millions) will they be 7 years later?

$865.48 solve for FV

quick ratio

( current assets-inventories)/current liabilities

one-year forward rate

(1.062)2=(1.060)(1+x) 1.12784/1.060=(1+x) 6.4004%=x - the pure expectations theory says that one-year securities will yield 6.4004%, one year from now - notice, if an arithmetic average is used, the answer is still very close. solve: 6.2%=(6.0%+x)/2, and the result will be 6.4%

three-year security, two years from now

(1.065)5=(1.062)2(1+x)3 1.37009/1.12784=(1+x)3 6.7006%=x - the pure expectations theory says that three-year securities will yield 6.7005%, two years from now

the quick ratio is defined as

(current assets-inventory)/(current liabilities)

when is each rate used?

- INOM: written into contracts, quoted by banks and brokers. not used in calculations or shown on time lines. - IPER: used in calculations and shown on time lines. if m=1, !NOM = 1PER = EAR - EAR: used to compare returns on investments with different payments per year. used in calculations when annuity payments don't match compounding periods

loan amortization

- amortization tables are widely used for home mortgages, auto loans, business loans, retirement plans, etc - financial calculations and spreadsheets are great for setting up amortization tables EXAMPLE: construct an amortization schedule for a $1,000, 4% annual rate loan with 3 equal payments

assumptions of pure expectations

- assumes that the maturity risk premium for treasury securities is zero - long-term rates are an average of current and future short-term rates - if the pure expectations theory is correct, you can use the yield curve to "back out" expected future interest rates

pure expectations theory

- contends that the shape of the yield curve depends on investors' expectations about future interest rates - if interest rates are expected to increase, l-t rates will be higher than s-t rates, and vice-versa. thus, the yield curve can slope up, down, or even bow

relationship between treasury yield curve and yield curves for corporate issues

- corporate yield curves are higher than that of treasury securities, though not necessarily parallel to the treasury curve - the spread between corporate and treasury yield curve widens as the corporate bond rating decreases - since corporate yields include a default risk premium (DRP) and a liquidity premium (LP), the corporate bond yield spread can be calculated as: corporate bond yield spread = corporate bond yield - treasury bond yield = DRP + LP

find the PV of this 3 year ordinary annuity

- could solve by discounting each cash flow, or... - use the EAR and treat as an annuity to solve for PV INPUTS: 3=N 4.04=I/YR 100=PMT 0=FV OUTPUT: PV=-277.30 excel=PV(.0404,3,100,0,0)

present value

- discounting (the reverse of compounding): finding the PV of a cash flow or series of cash flows - the PV shows the value of cash flows in terms of today's purchasing power what is the present value (PV) of $100 due in 3 years, if I/YR=4%? PV=FVN/(1+I)N PV=FV3/(1+I)3 =$100(1.04)3 =$88.90

macroeconomic factors that influence interest rate levels

- federal reserve policy - federal budget deficits or surpluses - international factors - level of business activity

effects of debt on ROA and ROE

- holding assets constant, if debt increases: equity declines, interest expense increases- which leads to reduction in net income - ROA declines (due to the reduction in net income) - ROE may increase or decrease (since both net income and equity decline)

why is it important to consider effective rates of return?

- investments with different compounding intervals provide different effective returns - to compare investments with different compounding intervals, you must look at their effective returns (EFF% or EAR)

what four factors affect the level of interest rates?

- production opportunities the investment opportunities in productive (cash-generating) assets - time preferences for consumption the preferences of consumers for current consumption as opposed to saving for future consumption - risk in a financial market context, the change that an investment will provide a low or negative return - expected inflation the amount by which prices increase over time

market value ratios

- ratios that relate the firm's stock price to its earning and book value per share - used in 3 primary ways: * investors- when they are deciding to buy or sell a stock * bankers- when they are setting the share price for a new stock issues (an IPO), and *firms- when they are deciding how much to offer for another firm in a potential merger

asset management

- right amount of assets vs sales - set of ratios that measure how effectively a firm is managing its assets - answers this question: does the amount of each asset seem reasonable, too high, or too low in view of current or projected sales?

conclusions about pure expectations

- some would argue that the MRP does not equal 0, and hence the pure expectations theory is incorrect - most evidence supports the general view that lenders prefer s-t securities, and view l-t securities as riskier - thus, investors demand a premium to persuade them to hold l-t securities (i.e., MRP >0)

ratios- why are they useful?

- standardize numbers and facilitate comparisons -used to highlight weaknesses and strengths -should be made through time and with competitors * industry analysis *benchmark (peer) analysis * trend analysis

solving for FV: calculator

- what is the future value (FV) of an intial $100 after 3 years, if I/YR = 4%? INPUTS: N=3 I/YR=4 PV=-100 PMT=0 OUTPUT: FB=112.49

suppose you had invested $5000 in a fund that generated 5.5% returns compounded annually. at the end of the investment period the value was $8,771.17. for approximately how many years were you invested in the fund?

10.5 solve for n

river corp's current assets at the end of 2014 were $335,000, net fixed assets were $600,000, net profit margin was 4.75% and over 2014 the firm posted sales of $3 million. what was its return on total assets? (HINT: net income = net profit margin x sales)

15.0% (.0475 x 3,000,000)/(600,000 + 335,000)

highland corp's total common equity at the end of last year was $405,000 and its net income was $70,000. what was its ROE?

17.28%

ovo co's total common equity at the end of last year was $555,000, total debt was $675,839, total assets was $567,789 and its net income was $100,000. what was its ROE?

18.00% 100,000/555,000

cardinals corp's sales last year were $38,000, and its total assets were $16,000. what was its total assets turnover ratio (TATO)?

2.38

Solving for FV

3 year annuity due of $100 at 4% 1. set calculator to "BEGIN" mode and solve for the FV of the annuity due: INPUTS: 3=N 4=I/YR 0=PV -100=PMT OUTPUT: FV=324.65

solving for PV

3 year ordinary annuity of $100 at 4% INPUTS: 3=N 4=I/YR 100=PMT 0=FV OUTPUT: PV=-277.51

solving for FV

3 year ordinary annuity of $100 at 4% INPUTS: N=3 I/YR=4 PV=0 PMT=-100 OUTPUT FV=312.16

suppose 1-year t-bills currently yield 7.00% and the future inflation rate is expected to be constant at 3.20% per year. what is the real risk-free rate of return, r*? disregard any cross-product terms, i.e., if averaging is required, use the arithmetic average.

3.80% 1 year t bill rate 7.00% inflation 3.20% difference = real risk-free rate, r* = 3.80%

suppose 1 year t-bills currently yield 9.00% and the future inflation rate is expected to be constant at 4.60% per year. what is the real risk-free rate of return, r*? (hint: the assumption here is that all of the other factors used to calculate interest rates are equal to 0.)

4.40% 9%=r* + 4.60% + 0% + 0% + 0%

suppose the real risk-free rate is 3.50% and the future rate of inflation is expected to be constant at 2.20%. what rate of return would you expect on a 1-year treasury security, assuming the pure expectations theory is valid? disregard cross-product terms, i.e., if averaging is required, use the arithmetic average

5.70% real risk-free rate, r* 3.50% inflation 2.20% yield on 1-year t-bond 5.70%

suppose the yield on a two-year treasury security is 5.83% and the yield on a five-year treasury security 6.20%. assuming that the pure expectations theory is correct, what is the market's estimate of the 3-year treasury rate two years from now?

6.45%

suppose the real risk-free rate is 4.20%, the average expected future inflation rate is 3.10%, and a maturity risk premium of 0.10% per year to maturity applies, i.e., MRP=0.10%(t), where t is the number of years to maturity, hence the pure expectations theory is NOT valid. what rate of return would you expect on a 4-year treasury security? disregard cross-product terms, i.e., if averaging is required, use the arithmetic average.

7.70% real risk-free rate, r* 4.20% MRP years:4 per year:0.10% 0.40% yield on t-year t-bond= r* + IPt + MRPt 7.70%

havanna corp's total assets at the end of last year were $415,000 and its net income was $32,750. what was its return on total assets?

7.89%

a company has current liabilities of $700 million, and its current ratio is 3.0. what is the total of its current assets? if this firm's quick ratio is 1.4, how much inventory does it have?

CA/CL=CA/700=3.0 CA=(700)(3.0) CA=2100 inventory= *(CA-inventories)/CL=(2100-inventories)/700=1.4 *2100-inventories=1.4(700) *2100-inventories=980 *2100-980=inventories *1120=inventories

see how the effective return varies between investments with the same nominal rate, but different compounding intervals

EARannual 4.00% EARsemiannually 4.04% EARquarterly 4.06% EARmonthly 4.07% EARdaily (365) 4.08%

basic earning power

EBIT/total assets

ROIC

[EBIT(1-T)]/total invested capital total invested capital = debt + equity = total equity + long term debt + notes payable

the power of compound interest

a 20 yr old student wants to save $5 a day for her retirement. every day she places $5 in a drawer. at the end of the year, she invests the accumulated savings ($1,825) in a brokerage account with an expected annual return of 8%. how much money will she have when she is 65 years old? solving for FV if she sticks to her plan, she will have $705,373 when she is 65. INPUTS: 45=N 8=I/YR 0=PV -1825=PMT OUTPUT: FV=705,373

annuity

a series of equal payments at fixed intervals for a specified number of periods - for example, $100 paid at the end of each of the next 3 years is a 3-year annuity types: ordinary annuity- payments occur at the end of each year - annuity due- payments are made at the beginning of each year

periodic rate (IPER)

amount of interest charged each period, e.g. monthly or quarterly - IPER = INOM/M, where M is the # of compounding periods per year - M =4 for quarterly and M=12 for monthly compounding

which of the following would be most likely to lead to a higher level of interest rates in the economy?

corporations step up their expansion plans and thus increase their demand for capital

the current ratio is defined as:

current assets/current liabilities

times-interest-earned ratio

debt-to-capital ratio= total debt/total invested capital TIE=EBIT/interest

future value

ending amount, of your account after n periods.

compounding

finding the FV of a cash flow or series of cash flows

fixed assets and total assets turnover ratios

fixed asset turnover - measures how effectively the firm uses its plant and equipment - fa turnover = sales/net fixed assets ta turnover=sales/total assets

what is the future value (FV) of an initial $100 after 3 years, if I/YR = 4%?

formula after N years: FVn=PV(1+I)N After 1 year: FV1=PV(1+I)=$100(1.04)=$104.00 after 2 years: FV2=PV(1+I)2=$1001.04)2=$108.16 after 3 years: FV3=PV(1+I)3=$100(1.04)3=$112.49

solving for PMT

how much must the 40 yr old deposit annually to catch the 20 yr old? 1. enter # of yrs until retirement and the final goal of 705,372.75 and solve for PMT INPUTS 25=N 8=I/YR 0=PV FV=705373 OUTPUT: PMT=-9648.64

IP

inflation premium - a premium equal to expected inflation that investors add to the real risk-free rate of return - inflation rate built into interest rates is the inflation rate expected in the future

will the FV of a lump sum be larger or smaller if compounded more often, holding the stated I% constant?

larger, as the more frequently compounding occurs, interest is earned on interest more often

uneven cash flows

life of pablo co will see the following cash flows over the next 4 yrs. what is the PV of their cash flow? yr 1: 100 yr 2: 300 yr 3: 300 yr 4: -50 input cash flows into the calculator's CFLO register: CF0=0 CF1=100 CF2=300 CF3=300 CF4=-50 enter I/YR=4, press NPV button to get NPV=597.48

M/B

market price/book value per share (higher number, better)

assume that the current corporate bond yield curve is upward sloping. under this condition, then we could be sure that

maturity risk premiums could help to explain the yield curve's upward slope

example of observes treasury rates and pure expectations

maturity/yield 1 yr/6.0% 2 yrs/6.2% 3 yrs/6.4% 4 yrs/ 6.5% 5 yrs/ 6.5% if the pure expectations theory holds, what does the market expect will be the interest rate on one-year securities, one year from now? three-year securities, two years from now?

what's the FV of a 3 year $100 annuity, if the quoted interest rate is 4% compounded semiannually? - payments occur annually, but compounding occurs every 6 months - cannot use normal annuity valuation techniques

method 1: compound each cash flow FV3=$100(1.02)4+$100(1.02)2+$100 FV3=$312.28 Method 2: financial calculator or excel - find EAR and treat as an annuity - EAR = (1+0.04/2)2-1=4.04% INPUTS: 3=N 4.04=I/YR 0=PV -100=PMT OUTPUT: FV= 312.28 EXCEL: =FV (.0404,3,-100,0,0)

ROA

net income/total assets

ROE

net income/total common equity

a firm wants to strengthen its financial position. which of the following actions would increase its quick ratio?

offer price reductions along with generous credit terms that would (1) enable the firm to sell some of its excess inventory and (2) lead to an increase in accounts receivable

P/E

price/earnings per share (higher number, better)

determinants of interest rates

r = r* + IP + DRP + LP + MRP r= required return on a debt security r* = real risk-free rate of interest IP = inflation premium DRP = default risk premium LP = liquidity premium MRP = maturity risk premium

"nominal" vs "real" rates

r = represents any nominal rate r* = represents the "real" risk-free rate of interest (like a t-bill rate, if there was no inflation. typically ranges from 1% to 4% per year.) rRF = represents the rate of interest on treasury securities

r*

real risk-free rate of interest - the rate of interest that would exist on default-free U.S. treasury securities if no inflation was expected. - factors that affect the r*: * the rate of return that corps and other borrowers expect to earn on productive assets and * people's time preferences for current versus future consumption

DSO: days sales outstanding

receivables are evaluated by the days sales outstanding ratio - also called the ACP (avg collection period) - represents the avg length of time a firm must wait after making a sale before receiving cash DSO = receivables/avg sales per day = receivables/(annual sales/365)

profitability ratios

reflect the net result of all of the firm's financing policies and operating decisions

premiums adde to r* for different types of debt

s-t treasury: IP l-t treasury: IP, MRP s-t corporate: IP, DRP, LP l-t corporate IP, MRP, DRP, LP

inventory turnover ratio

sales/inventories

if a 40 yr old investor begins saving today and sticks to the plan, how much will she have?

she will have $133,418 at age 65. this is 571,954 less than if starting at age 20. INPUTS: 25=N 8=I/YR 0=PV -1825=PMT OUTPUT FV=133,418

constructing the yield curve: inflation

step 1: find the average expected inflation rate over years 1 to n assume inflation is expected to be 5% next year, 6% the following year, and 8% thereafter IP1=5%/1=5.00% IP10=[5%+6%+8%(8)]/10=7.50% IP20=[5%+6%+8%(18)]/20=7.75% must earn these IPs to break even vs inflation; these IPs would permit you to earn r* (before taxes) step 2: find the appropriate maturity risk premium (MRP). for this example, the following equation will be used to find a security's appropriate maturity risk premium MRPt=0.1%(t-1) use the given equation: MRP1=0.1%x(1-1)=0.0% MRP10=0.1%x(10-1)=0.9% MRP20=0.1%x(20-1)=1.9% notice that since the equation is linear, the maturity risk premium is increasing as the time to maturity increases, as it should be step 3: adding the premiums to r* rRF,t=r*+IPt+MRPt assume r*=3%, rRF,1=3%+5%+0.0%=8.0% rRF,10=3%+7.5%+0.9%=11.4% rRF,20=3%+7.75%+1.9%=12.65%

loan amortization steps

step 1: find the required annual payment. - all input information is already given, just remember that FV=0 bc the reason for amortizing the loan and making payments is to retire the loan INPUTS: 3=N 4=I/YR -1000=PV 0=FV OUTPUT: Pmt=360.35 excel=pmt (.04,3,-1000,0,0) step 2: find the interest paid in year 1 - the borrower will owe interest upon the initial balance at the end of the first year. interest to be paid in the first year can be found by multiplying the beginning balance by the interest rate. INT1=beg bal1(I) INT1=$1,000(0.04)=$40 step 3: find the principal repaid in year 1 - if a payment of $360.35 was made at the end of the first year and $40 was paid toward interest, the remaining value must represent the amount of principal repaid PRIN=PMT-INT =$360.35-$40=$320.35 step 4: find the ending balance after year 1 - to find the balance at the end of the period, subtract the amount paid toward principal from the beginning balance END BAL=BEG BAL - PRIN = $1000-$320.35=679.65

yield curve and the structure of interest rates

term structure: relationship between interest rates (or yields) and maturities. the yield curve is a graph of the term structure.

effective (or equivalent) annual rate (EAR = EFF %)

the annual rate of interest actually being earned, considering compounding - EFF% for 4% semiannual interest EFF% = (1+INOM/M)M-1 = (1+0.04/2)2-1=4.04%

casey communications recently issued new common stock and used the proceeds to pay off some of its short-term notes payable. this action had no effect on the company's total assets or operating income. which of the following effects would occur as a result of this action?

the company's current ratio increased

which of the following statements is CORRECT?

the inventory turnover ratio and days sales outstanding (DSO) are 2 ratios that are used to assess how effectively a firm is managing its current assets

because the maturity risk premium is normally positive, the yield curve is normally upward sloping

true

during periods when inflation is increasing, interest rates tend to increase, while interest rates tend to fall when inflation is declining

true

if the pure expectations theory is correct, a downward-sloping yield curve indicates that interest rates are expected to decline in the future

true

which of the following yield factors is not used in calculating interest rates?

yield-to-maturity premium

what is the net present value of the following uneven cash flows; $100 1 year from today, $300 2 years from today, $300 three years, and $-50 four years from today if the discount rate is 4.0%?

$597.48

hypothetical yield curve

- an upward-sloping yield curve - upward slope due to an increase in expected inflation and increasing maturity risk premium