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Final

# FIN 300 Study Guide - Final Guide: Risk-Free Interest Rate, Asset Turnover, Operating Cash Flow

Department
Finance
Course Code
FIN 300
Professor
John Currie
Study Guide
Final

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Current Ratio = CA / CL
Quick Ratio = (CA – Inv) / CL
Cash Ratio = Cash/ Current liabilities
Total asset Turnover = Sales / Total Assets
Inventory Turnover = Cogs / Inventory
Receivables turnover = Sales / Total Assets
Total Debt Ratio = (TATotal equity) / TA
Debt-Equity Ratio = Total Debt / Total Equity
Div Pay. Ratio = Retained earnings / Net income
Div payout ratio: Cash div/ NI
Earn Per Share= Net income / Shares
Div Per Share= Dividends / Shares
Times Interest Earned = EBIT/Interest
Cash Coverage Ratio = (EBIT + Dep) / Interest
Profit Margin = Net income / Sales
Return on Assets = NI / total assets or PM*TAT
Return on Equity Ratio = net income/total asset
ROE = EM x TAT x profit margin
ROE = Equity Multiplier * Return on assets
Full capacity sales = current / %
PM=[(ROE)(TA)]/[(1+D/E)(S)]
Max sales growth = (full/current)-1
Internal growth rate = (ROAxR)/(1-ROAxR)
Total asset turnover = 1/capital intensity ratio
Capital intensity Ratio = TA/Sales
Retention ratio = R = 1-(div./net income) or 1-DPR
Sustainable growth rate = g=(ROE x R) / (1-ROExR)
Net capital spending = Increase in NFA + Depreciation
Required Return = (Share price / currently sells) + % growth
Dividend Yield= Share price / currently sells
Addition to NWC = OCF – Change in NFA-CFS-DIV New equity
CFA = OCF – Net capital spending – Change in NWC
Capital gains yield = Growth rate
CFC = interest exp. + outstanding long-term debt
CFS = Div-new equity
EBIT = sales-cost-dep.
TAX = (EBIT-int)x tax rate
OCF = EBIT+ dep-tax
Sales – costs- tax
Ni + dep + int
(sales-costs)(1-t) + tax shield (i.e. dep*tax rate)
Equity = total (1-Payout Ratio) +original
Cash flow from assets = Cash flow to bondholders + Cash flow to
shareholders
PV=C/(r-g)
PV=c/(r-g) [1-(1+g)/(1+r)]
NWC=Cash+other current assets – liabilities
NWC + FA = Long debt + equity
Capital intensity Ratio = TA/Sales
CFA = CFC + CFS
CFA = OCF – Change in NWC – Net capital spending
Interval measure = Current assets/Average daily operating costs
Long Debt ratio: = LTD/(LTD+equity)
Fixed asset turnover = Sales/Net fixed assets
P/E ratio = Price per share/Earnings per share
Required Return% = PMT / PV
External Finance Needed = A (g) –p(S)R x (1+g)
P0=Div1/(1+r) +Div2/(1+r)2+Div3/(1+r)3…(Div4/(r-g)*1/(1+r)3)
APR = TVM, f5, conv, enter stuff, press f1 for eff then ear is given F2 to
get apr
PV = \$1 × [1/(1 + r)t] = \$1/(1 + r)t PV×(1+r)t =FVt
New TD = [D/(D+E)](TA)
Addition to retained earnings = NI – Dividends
Net capital spending = NFAend – NFAbeg + Depreciation
Stock price willing to pay = PMT / (rr-inc)
Willing to pay for share today = D1/(1+rr)1+…
r = (FV / PV)1 / t – 1
FVA = C{[(1 + r)t – 1] / r}
Pv of pref stock = [Div in perp/%return] / (1+%re)n-1
PVA = C({1 – [1/(1 + r)t] } / r )
APR = m[(1 + EAR)1/m – 1]
EAR = [1 + (APR / m)]m – 1
g=(new sales / old sales) – 1
NI=s-c=taxable income TI-Tax(tax rate*tax inc) = NI
r = [ ((EAR + 1) ^ (1/m)) - 1 ] *m
Fisher equation = (1+R) = (1+r)(1+inflation)
R= nominal rate r = real rate
YTM put nominal rate as % into I
PVIFA= [1-(1+r)-n]/r
PVIF= 1/(1+r)n
If E[rt] > rRequired, then at (t=today),
PE t < PRt à Undervalued
If E[rt] < rrequired, then At (t= Today),
Pet > PRt = à overvalued
Expected real rate of return: 1+Nominal rate = (1+real rate) *(1+inflation
rate)
Beta=(exp return – risk free rate) / risk prem
PV[Tax shield]=C*D*T/(D+r * (1+.5r)/(1+r) – S*D*T/(D+r) * 1/(1+r)n
Price of stock today: div/(rr-g)
Current% of FA= FA/(Current S/%)
TFA required = %FA*New sales
Tax rate = tax/(EBIT-INT)
Return=[(P1-Pt-1)+D1] / Pt-1
A company will purchase a new machine with a cost of \$750,000. The
machine requires an initial investment in net working capital of \$25,000.
Net working capital will remain at this level during the life of the
machine and will be recovered at the end. The machine will be operating
for 3 years. There is no salvage value associated with the machine. The
company does not pay any taxes, the tax rate is zero. The machine will
produce 10,000 units per year. The price per unit will be \$30. The
variable cost per unit is \$7. There are fixed costs of \$50,000 per year. The
required rate of return is 12%.
1.pv of net working capital recovered at end? N=3, i=12 fv=25k, pv=?
2.pv of operating cash flow? 180k/(1+rr)+180k/(1+.12)2+180k/(1.12)3=
3.NPV? = cash flow y1=775k y2=180k y3=180k y3=205k
Your firm is thinking about purchasing a new machine. The new machine
would cost \$4,500,000 today. The new machine would operate for 4
years at which time it could be sold for \$900,000. The CCA rate is 30%.
The asset class will remain open. The new machine will generate
revenues of \$1,750,000 per year. The annual operating costs associated
with the new machine are \$1,100,000 per year. The corporate tax rate is
45%. The required rate of return is 9%.
1.pv of salv? N=4 I=9 pv=? Fv=900k
2.PV CCA tax shield=C*D*T/(D+r)*(1+r/2)/(1+r) – S*D*T/(D+r)*1/
(1+r)n
A firm purchases a Class 8 equipment for \$1,000,000 (CCA Rate 20%)
for a 10 year project. What will be the CCA tax shield in year 4? The
tax rate is 35%. The half-year rule is in effect and the asset class will
remain open.
Y1=1m*.5*20%=100k, y2=[1m-100k]20%= 180k, y3 = [1m-100k-
180k]20%=144, y4=[1m-280k-144k]20%=115200*35%
Loblaws has annual sales of \$1.9 million, depreciation of \$238,000, and
net working capital of \$196,001. The firm has a tax rate of 35% and a
profit margin of 8.2%. The firm has no long-term debt. What is the
amount of the annual operating cash flow?
(S)1.9M*(p)8.2%+D(238k)
Marti purchased a stock one year ago at a price of \$23.89. Over the past
year she has received a total of \$1.63 in dividends. Today she sold the
stock for \$22.84. What total percentage return did Marti earn on this
investment? N=1,pv=-23.80,PMT=1.63,fv=22.84 i=?
What are the arithmetic and geometric average returns for a stock with
annual returns of 21 percent, 8 percent, -32 percent, 41 percent, and 5
percent? Arithmic = average on calc
Arithmic=(p1%+p2%+p3%P4%+p5%)/5
Geo=[(1+p1%)(1+p2%)…]1/Q-1
Which one of the following stocks is correctly priced based on CAPM, if
the risk-free rate of return is 3.8 percent and the market risk premium is
8.5 percent? Guess and check,
Beta=[expected return – risk free rate]/risk premium
Your portfolio has a beta of 1.08. The portfolio consists of 20 percent
Treasury bills, 45 percent in stock A, and 35 percent in stock B. Stock A
has a risk-level equivalent to that of the overall market. What is the beta
of stock B? treasury is risk free beta of 0
0*20%=0, 1*45%=0.45, 1.08-0.45 = 0.63, 0.63/0.35= 1.8
What is the expected return for the following portfolio?
Investment A=200,b=300,c=500 return= a=.15, b = .10, c=.25
Expected return= (200*15%+300*10%+500*25%)/(200+300+500)=.185
You need \$2,000 to buy a new stereo for your car. If you have \$800 to
invest at 5% per year compounded annually, how long will you have to
wait to buy the stereo? N=? i=5, pv=-800, fv=2000
Jacob Money Inc. has a profit margin of 11% and a retention ratio of
70%. Last year, the firm had sales of \$500 and total assets of \$1,000. The
desired total debt ratio is 75%. What is the firm's sustainable growth
rate? P=11%,b=70%,s=500,TD=75%,TA=1k, g=ROE*B/(1-ROE*b)
Dupont identity = ROE = PM*TAT*EM, TAT=s/ta, Debt*equity=1
.75+E=1e=.25, ER=1/Em0.25=1/em, em=4
ROE=0.11*0.5*4=0.22 g=ROE*R/(1-ROE*R)=(.22)(.7)/(1-(.22)
(.7)=18.2% or use TAT=1/Cap int, Tot debt raito=(TA-TE)/TA
Assume that J&F, Inc. is operating at 85 percent of capacity. All costs and
net working capital vary directly with sales. What is the amount of total
fixed assets required if sales are projected to increase by 20 percent?
Current % of FA to Full Cap Sales, %=FA/(Current sales / % of oper)
%FA*New sales = amount of total fixed assets required
A Windsor Ontario firm has a net income of \$32,000 which provides a
12% return on assets. The firm has a debt-equity ratio of .40. What is the
return on equity? Debt equity ratio = debt / equity, ROE=EM*ROA,
1.4*.12
Using the Du Pont Identity Method, calculate the equity multiplier
given the following information: profit margin 14%; total asset turnover
1.7; return on equity 29.08%. ROE/(TAT*PM)=EM EM=29.08%/
(14%*1.7) = 1.2
Current assets of the Smart Inc. are \$94,700. Accounts payable is
\$36,200, net income is \$12,400 and sales are \$110,800. What is the net
working capital turnover rate for Smart Inc.? Another name for asset
turnover ratio: Asset Turnover ratio = sales/NWC
NWC = Current Assets - Current Liabilities = 94700 - 36200 = 58500
AT R = 11 0 , 8 0 0 / 58 5 0 0 = 1 .8 9
DEF's common stock just paid a dividend of \$3 per share. You expect the
dividend to increase by 5% per year in perpetuity. If you require a 15%
rate of return what is the price of the stock today? initial div * (1+g) / (r-
g) Price of stock = Dividend one year from now/ r - growth rate
Dividend one year from now = 3 * 1.05 (this year times the growth rate)
= 3.15
r = 15%
Growth rate = 5%
Price of stock = 3.15/ (.15-.05) = 31.5

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XYZ's stock is currently selling for \$51. The expected dividend one year
from now is \$1.50 and the required return is 10%. The dividends are
expected to grow at a constant rate in perpetuity. What is this firm's
dividend growth rate assuming the constant dividend growth model is
appropriate? D1 (div in a year) = 1.5 r = .1 g = ? P = 51
51 = 1.5/ (.1 - g) : .1-g = 1.5/51 : g = 0.1 - .02941 .1 = .70588 = 7%
XYZ Company's preferred shares will pay a constant dividend of \$2.00
per year forever, starting in 1 year. Given the risk of the shares you think
the appropriate discount rate should be 20% per year for the first 3 years.
You then think the discount rate should drop to 12% per year in year 4
and will last forever. How much would you be willing to pay for these
preferred shares? This is a multi-part annuity and perpetuity question.
Preferred shares still work the same as a bond or annuity.
Step one is to get the PV of the perpetuity 3 years from now:
C = 2 , r = 12% : PV = 2/.12 - 16.67
Carol Singer holds a 5.4% coupon bond that has a quoted price of \$995
and will make its next semi-annual payment in one month. What is the
accrued interest for this bond? annual payment amount is .054 *
1000face value = 54/2times per year = 27 paid semi annually
(Remember the FV for a bond is always 1000 unless its stated otherwise)
Question says there is one month until its semi annual payment. That
means we're 5 months out of 6 of the way to our next payment since
payments happen every 6 months. 5/6 = .8333. We times this with the
coupon payment to say how much we owe so far:
.8333333 * 27 = 22.5
Canadian Treasury bills with 1-year to maturity have a yield to maturity
of 0.98% per year. If you expect inflation to be 1.4% per year over the
upcoming year, what is your expected real rate of return?
1 + R(Nominal Rate) = (1 + r(Real rate)) * (1+ Inflation rate (h)
1 + .0098 = (1 + r) * (1 + .014) : 1.0098/1.014 = 1 + r
: r = .995857988 - 1 = -.00414 = -.414%
You buy a 10-year bond with a 4% coupon rate (paid annually) and a
\$1,000 face value at par. If the yield to maturity increases to 5% per year
compounded annually one year from now, what is your 1-year holding
period return?
N = 9 (10 year bond once 1 year has passed)
PMT = .04 * 1000 = 40
FV = 1000 (make sure sign is same for FV and PMT.
I/Y = 5
CPT PV = 923.92
Year return is equation from yesterday: What you made/What you spent
: Return = [(second price - first price) + Coupons received so far]/First
PV
= [(928.92 - 10000) + 40]/1000 = -3.1%
XYZ Company's preferred shares will pay a constant dividend of \$2.00
per year forever, starting in 1 year. Given the risk of the shares you think
the appropriate discount rate should be 20% per year for the first 3 years.
You then think the discount rate should drop to 12% per year in year 4
and will last forever. How much would you be willing to pay for these
preferred shares?
Step one is to get the PV of the perpetuity 3 years from now:
C = 2 , r = 12% : PV = 2/.12 - 16.67
Couple of ways to solve this. Can do an annuity calculation and then a
separate PV calculation for the 16.67. Also can just plug all into CF mode
of your calculator and find NPV. WIll show both ways:
CF0 = 0 , CF1 = 2, CF2 = 2, CF3 = 2+16.67=18.67. Hit NPV, I = 20%.
CPT for 13.86
OR
Annuity 1: n = 3, PMT = 2, I/Y = 20 CPT PV = 4.21
Annuity 2 : n = 3, FV = 16.67 , I/Y = 20, CPT PV = 9.65
4.21 + 9.65 = 13.86
A bond with a \$5,000 face value and 20 years to maturity has a coupon
rate of 5% per year (paid semi-annually). If its yield to maturity is 3.6%
per year compounded semi-annually, what is its value today? FV = 5000
N = 20 years * 2 (semi annual pmts) = 40 ,
PMT = .05 * 5000 = 250/2(twice a year) = 125
I/Y = 3.6/2 = 1.8
CPT PV = 5991.9
You have borrowed \$12,000 from Rob M. Blind lenders. If they require
you to make payments of \$400 at the end of each month for a period of
six years in order to pay off this loan, what annual percentage rate (APR)
compounded monthly are they charging on this loan? They're looking for
I/Y. APR means they want it for the total year.
PV = 12000 , PMT = 400 (this has to be opposite sign to PV) , N = 6
years * 12 times a year = 72 , CPT I/Y = 2.91
2.91 * 12 times a year = 34.9 APR
The grand prize in the OMG Lottery is a choice between \$1,000 paid at
the beginning of each month for a period of 10 years and a lump sum
paid immediately. If you can invest at an effective annual interest rate of
5%, what is the minimum lump sum you would be willing to accept as
winner of this lottery? find the PV of the lottery payments for 10 years.
Its at the start of each month so need to switch to BGN mode (2nd - PMT
- 2nd - Enter). Also the I/Y is given as an EAR which means we have to
switch it to a monthly rate using EAR Equation rearranged:
r = [ ((EAR + 1) ^ (1/m)) - 1 ] *m
r = [ ((.05+1) ^ (1/12)) -1 ] *12
= (1.05^(1/12) - 1) * 12
= (1.004074 - 1) *12
= .048889485 per year. For this question we we divide that by 12
cause we want monthly I/Y: .048889485/12 = .00407412378*100 = .
407% I/y = .407 , PMT = 1000 , N = 10 years * 12 times = 120 , CPT
PV = 95,173.
What annual percentage rate (APR) compounded monthly is equivalent
to an interest rate of 6.25% per year compounded semi-annually?
Have to plug into ugly EAR/APR formula twice. Don't think there is a
nicer way to do it and it looks really ugly on email but here goes:
Start with an APR so use EAR formula. It starts as semi-annual so m is 2.
Second step will have m of 12 since we'll convert to monthly.
EAR = [1+(APR/m)^m]-1 = [ 1 + (.0625/2)]^2 - 1 = 1.063476563-1 =
0.63476563 We then have to convert this using formula from last
question back to an APR for Monthly. r = [ ((EAR + 1) ^ (1/m)) - 1 ] *m
= [ ((.063476563 + 1) ^ (1/12)) -1 ] * 12 = (1.005141784 - 1) * 12 =
0.0617*100 = 6.17%
Candy Kane has taken out a \$250,000 mortgage at a quoted rate of 6.3%
compounded semi-annually. If the mortgage requires monthly payments
over a term of 20 years, with each payment made at the end of the period,
what is the required monthly payment?
EAR = [1+(APR/m)^m]-1 = [ 1 + (.063/2)]^2 = 1.06399225 - 1 = .
06399225 Plug in this EAR into second formula to get Monthly Rate
r = [ ((EAR + 1) ^ (1/m)) - 1 ] *m = [ ((.06399225 + 1) ^ (1/12)) -1 ] *
12 = (1.00518239 - 1) * 12 = .062188695. Divide by 12 to get monthly
rate: .062188695/12 = .00518239129 * 100 = 0.518239129%
PV = 250,000 , I/Y = 0.518239129 , N = 20 Years * 12 times a year =
240 , CPT PMT = 1822.79
You wish to establish a scholarship fund for students at Clever College.
The fund would pay an annual scholarship that would start at \$5,000
awarded one year from now and increase by 3.5% per year forever. If the
fund could earn an effective annual return of 6%, how much would you
need to contribute to the scholarship fund today for it to be fully funded?
When you see scholarship or bursary its some kind of perpetuity usually.
This one is a growing perpetuity since it says it will increase by a %
forever.
C one year from now: = 5000 (it says it's a year from now so good as is)
r = 6% g = 3.5% PV = 5000/(0.06-.035) = 200000
Holly Daze has taken out a ten-month zero-coupon loan of \$3,000. If the
lender charges 7.2% per year compounded quarterly, what is the amount
she must pay back at the end of the loan?
Zero-coupon bond means its just a regular FV, PV, N, I/Y question. Trick
here is that its a 10 month bond but it's quarterly bond so we have to
remember that for our N:
FV = ? PV = 3000 I/Y = 7.2/4(Times per year for quarterly) = 1.8
N = One quarter is 3 months. 10months/3 = 3.33333333333 (make sure
you enter as many three's as you can. Calculator is stupid with rounding
and will give you wrong answer if you only put two. Have to manually
enter as many 3's as possible.
CPT FV = 3183.81

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