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TYPES OF FIRMS BALANCE SHEET RATIOS

INCOME STMT RATIOS

1annuity) [(1 ) 1]nrFV( C r= +

Annual

Semiannual

Monthly

Daily

Effective Annual Rates for a 6% APR with Different Compounding Periods 2nd CPT, 2nd,2 (ICONV), Nom=APR, EFF=EAR, c/y=times compound per yr c/y = 1, Eff, cpt = 6 C/y = 2, Eff, cpt = 6.09 C/y = 12, Eff, cpt = 6.167 C/y = 365, Eff, cpt = 6.183

Assets = Liabilities + Stockholders Equity Net Working Capital = Current Assets Current Liabilities Market Capitalization = Market Price * Number of Shares Enterprise Value = Market Value of Equity + Debt Cash Gross Profit = Revenue, Net Sales Cost of Sales Operating Income = Gross Profit Operating Expense EBIT = Operating income + Other Income Earnings Per Share = Net Income / Shares Outstanding Retained Earnings = Net Income Dividends Payout Ratio = Dividends / Net Income

CPN payment = (Coupon Rate * Face Value) / no. coupon pmts per year BONDS: N=years or number of payments, I/Y=YTM, PV= bond price, PMT=coupon rate X face value, FV=face value, PMT If Coupon Rate >YTM premium; if CR=YTM, par; if CR

Annuity:Your grandmother putting $1000 into savings every birthday since when you turned one. interest rate of 3%. How much money on your 18th birthday? N=18, I/Y=3%, PV=0, PMT=1000, solve FV=(23,414.43)

Annuity: Parents wanted $160,000 saved for college by your 18 started on 1st bday. Earned 8% per year on their investments. a. How much would they have to save each year to reach their goal? N=18, I/Y=8%, PMT=0, FV=160,000, solve PV=(40,039.84) Annuity pmt N=18, I/Y=8%, PV=40,039.84, FV=0, solve PMT=(4,272) b. If they decided to have $200,000 saved, how much more have to save per year? N=18, I/Y=8%, PMT=0, FV=200,000, solve PV=(50,049.81) !pmt 5340.42

Annuity: How much to save for retirement. plan to save $5000 per year, first investment 1 year from now. can earn 10% per year, retire in 43 years, a) How much have in retirement account on the day you retire? N=43, I/Y=10%, PV=0, PMT=-5000, solve FV=2,962,003.46 b) If wanted to make one lump-sum investment today N=43, I/Y=10%, PMT=0, FV=2,962,003.46, solve PV=(49,169.99) c) Live 20 years in retirement, how much can withdraw every year to exhaust your savings with the twentieth withdrawal (assume earn 10% retirement)? N=20, I/Y=10%, PV=2,962,003.46, FV=0, solve PMT=-347,915.81 d) If you withdraw $300,000 /year in retirement (first withdrawal 1 year after retiring), how many years will it take until you exhaust your savings? I/Y=10%, PV=2,962,003.46, FV=0, PMT=-300,000.00, solve N=45.84 e) Assume $1000/year, retire with $1 million in investment, what rate need to earn? N=43, PV=0, FV=1,000,000, PMT=-1000.00, solve I/Y=11.74291%

Growing perpetuity: You building new machine will save you $1000 in first year. The machine will wear out, savings decline at a rate of 2% per year forever. What is the present value of the savings if the interest rate is 5% per year? PV = 1000 / 0.05 (0.02) = $14,285.71

Growing Annuity: New drug patent will last 17 years. Expect drugs profits $2 million in first year, grow at rate 5% per year for next 17 years. Once expires, competition will drive profits to zero. What is PV of drug if the rate is 10% per year?

Annuity: Piece of art $50,000. Art dealer will lend you the money, you will repay by making same payment every two years for 20 years (10 payments). If the interest rate is 4% per year, how much will you have to pay every two years? Calculate the 2-year interest rate: The 1-year rate is 4%, and $1 today will be worth (1.04)2 = 1.0816 in 2 years, so the 2-year interest rate is 8.16%. Then, N=10, I/Y=8.16%, PV=-50000, FV=0, solve PMT=7505.34

House costs $350,000. You have $50,000 in cash down payment, borrow the rest. Bank offering a 30-year mortgage, annual payments and interest rate 7% per year. How much your annual payment? N=30, I/Y=7%, PV=-300000, FV=0, solve PMT=24175.92 You can afford only $23,500 per year. The bank agrees to allow you to pay this amount each year, yet still borrow $300,000. At the end of the mortgage (in 30 years), you must make a balloon payment; How much? N=30, I/Y=7%, FV=0, PMT=23500, solve PV=-291612.47, less 8387.53. Then, N=30, I/Y=7%, PV=8387.53, PMT=0, solve FV=-63848.02

Annuity: You are 22. Your retirement plan. Every dollar earns 7% per year. No withdrawals until 65. Live to 100, work until 65. You will need $100,000/yr in retirement, you contribute same amount at end of every year you work. How much need to contribute each year to fund retirement? In yr 43, N=35, I/Y=7%, FV=0, PMT=100000, solve PV=-1,294,767.23, Value today, N=43, I/Y=7%, PMT=0, FV=1,294,767.23, solve PV=-70,581.24 Annual pmt N=43, I/Y=7%, PV=70581.24, FV=0, solve PMT=-5225.55

Converting APR to Discount Rate: Suppose bank account pays interest monthly with an effective annual rate of 6%. What interest will you earn each month?

2ND CPT; 2nd, 2 (iCONV); 2nd CLR WORK; UP, UP, (find EFF), 6, ENTER; DOWN, (find c/y), 12, ENTER; down to NOM, CPT = 5.84 " divide by 12 to get periodic rate; STO, 0, RCL, 0, /,12 = 0.486755

If you have no money in the bank today, how much will you need to save at the end of each month to accumulate $100,000 in 10 years?

0.486755, I/Y; 10*12 = 120, N; 100000, FV; CPT, PMT = 615.48

Computing Loan payments: Timeline for a $30,000 car loan with these terms: 6.75% APR for 60 month (assume monthly compounding coz APR is not specifically defined) PV=30000, N=60, I/Y=6.75/12, solve PMT = 590.50 You are now 3 years into loan. You decide to sell the car. After 36 months of payments, how much do you still owe on your car loan? 2nd, PV (AMORT), P2 = 36, P1 = 1, BAL = 13222 or N=24, I/Y=6.75/12, PMT = -590.50, FV=0, solve PV=13222.32 or N=36, I/Y=6.75/12, PMT = -590.50, PV=30000, solve FV=13222.32

Endowment Cash flow needed $10,000. Grow at rate 7%. Endowment starts in 10 yrs PV needed = 10000 0.07 = 142,857.14 = value in year 9 Value today = 142,857.14 (1.07)9 = 77,704.82

Car Payment PMT=5000, N=5, I/Y=6, FV=0, solve value of loan PV = 21061.81 Shift-PV (AMORT), P1=1, P2=1, balance 17325.52 After 4 payments, P1=1, P2=4, balance 4716.98

If $1 invested at 9% APR with daily compounding, Formula: 1 + (0.09/365)365 = 1.09416, so EAR = 9.416% 2nd-2 (ICONV) Nom=9, c/v=365, EFF=9.4162

Firms credit rating AA. Credit spread for 10-year maturity AA debt is 90 basis points (0.90%). Firms ten-year debt coupon rate 5%. New ten-year Treasury notes are $100 issued at par, coupon rate 4.5%. Wuts the price of your outstanding ten-year bonds?

So, debts YTM= 4.5% + 0.9% = 5.4%, 6-mo rate =2.7%. Cash flows 5%=$5 per year, semiannual = $2.5. 10 yrs, 20 pmts. N=20, I/Y=2.7%, PMT=2.5, FV=100, solve PV=$96.94

Coupon Bonds. Spot rates for 6 months=1%, 1 year=1.1%, and 1.5 years=1.3%, semiannually compounded APRs. What is the price of a $1000 par, 4% coupon bond maturing in 1.5 years (the next coupon is exactly 6 months from now)? Payments at 6 months=$20, 1yr=$20, 1.5yrs=$1020. PV= 20/(1.005) + 20/(1.0055)2 + 1020/(10065)3 = $1040.05

Divident Discount Model Store to pay an annual dividend of $0.56 per share, trade $45.50 per share end of year. Expected return of 6.8%, a) what is the most youd pay today for Longs stock? FV=46.06 (45.50 + 0.56), N=1, I/Y=6.8, solve PV=43.13 b) What dividend yield and capital gain rate would you expect at this price? Div yield=0.56/43.13 = $2.37 per share. Cap gain rate = 2.37/43.13 = 5.5%

Constant Dividend Growth. Utility company to pay (div1) $2.30 /share in dividends in the coming year. If equity cost of capital is 7% (rE) and dividends grow by 2% (g) per year in future, estimate the value of stock. P0= Div1 / (rE-g) = 2.30 / (0.07-0.02) = $46.00

Dividends: Profitable-Unprofitable Growth. Crane expects earnings per share of $6 coming year. Firm plans to pay out all of its earnings as dividend. With expectations of no growth, Cranes current share price is $60. Suppose Crane could cut dividend payout rate to 75% and use retained earnings to open new stores. The ROI in these stores is expected to be 12%. If we assume that the risk of these new investments is the same as the risk of its existing investments, then the firms equity cost of capital is unchanged. What effect would this new policy have on Cranes stock price? Div1=EPS1 * 75% = 6 * 75% = $4.50 ; rE=Div1/P0 + g = 6/60 + 0% = 10% g=retention rate * ROI = 25% * 12% = 3% therefore, P0= Div1 / (rE-g) = 4.50/(0.10-0.03) = $64.29 Suppose return on new investments is 8% instead. Expected earnings per share $6, equity cost of capital of 10% (assume risk same), whats Cranes current share price? g=retention rate * ROI = 25% * 8% = 2% therefore, P0= Div1 / (rE-g) = 4.50/(0.10-0.02) = $56.25

Valuing Firm different Growth Rates. Firm reinvesting all earnings to expand. Earnings $2/share this past year, expected growth rate 20% /yr until end of yr 4, when firm will cut investment and begin paying 60% dividends. Its growth will slow to a long-run rate of 4%. If equity cost of capital is 8%, whats todays value of a share? P3= Div1 / (rE-g) = $2.49 / (0.08-0.04) = $62.25 N=3, I/Y=8%, FV=$62.25, solve PV=$49.42

Titan has 217 mil shares outstanding, expects earnings end of year of $860 mil. Titan plans to pay out 50% of its earnings in total, paying 30% as dividend, 20% to repurchase shares. If earnings are expected to grow by 7.5% /year and payout rates remain constant, whats Titans share price assuming equity cost of capital 10%? Total payout = 50% * $860 mil = $430 million PV(Future total divs & repurch) = 430mil / (0.10-0.075) = $17.2 billion P0 = $17.2 bil / 217 mil shares = $79.26 per share

Investments highest avg returns=small stocks, also most volatile. Bonds least volatile. Larger stocks, lower volatility. Portfolio of stocks will have lower volatility than individual stocks which have lower returns and higher risk.

Investors demand higher returns on riskier investments cos averse to fluctuations. Compound annual return is better to describe long-term historical performance,

average of history of returns. Used most often for comparison Arithmetic average return assumes reset investments every year. Used when

estimating expected return over a future horizon based on past performance. Std Deviation. 1sd = 68% confident, 2sd = 95%, 3sd = 99%

Systematic Risk not diversifiable, requires risk premium. Unsystematic Risk - diversifiable, does require risk premium

Bank A has 100 loans outstanding, each $1 million, will be repaid today. Each loan 5% probability of default. Bank B one loan of $100 million repaid today. Also 5% default. Bank A = ($1 million 0.95) 100 = $95 million expected payoff Variance of each loan = (1 0.95)2 0.95(0 0.95)2 0.05 = 0.0475 Std Deviation of each loan = 0.0475 = 0.2179, for portfolio x100=2.179 Bank B = $100 million 0.95 = $95 million, one loan Variance = (100 95)2 0.95 + (0 95)2 0.05 = 475, std dev 475 = 21.79