FINANCE FINAL
annuity present value factor
(1-present value factor)/r
Present Value (PV)
$ / (1+ r)^t
You want to save $X in a retirement account today (year 0) so that when you retire in 28 years you can make annual withdrawals of $137,000 for 15 years (your first annual withdrawal is at time 28). At the end of the 15 annual withdrawals you want to have $230,000 left in your retirement account so that you can bequeath them to your grandchildren. If the interest rate is 9.00%, how much is $X?
$113,953.02
Assume your company's pension plan promises to pay you $50,000 per year starting when you retire in 34 years (the first payment is 34 years from now) and increase the payment by 3% every year after the first to compensate for inflation. You hope to live 21 years after you retire (you collect 22 payments). If your interest rate is 4%, what is the value today of your pension plan?
$262,431.25
A rich donor will give a hospital $1.1 million in exactly 2 years from today. Each year after that, she will donate to the hospital the same amount until year 11 (i.e. her last donation is at time 11). What is the present value of this donation today (time 0) given that the interest rate is 7%?
$7.22
Assume your company's pension plan promises to pay you $43,000 per year starting when you retire in 33 years (the first payment is 33 years from now) and increase the payment by 1% every year after the first to compensate for inflation. You hope to live 23 years after you retire (you collect 24 payments). If your interest rate is 6%, what is the value today of your pension plan?
$91,472.34
simple interest =
($) + ($ * r * t)
Future Value =
($)(1 + r)^t
rE= (the return in decimal form)
((div+Psell)/Pbuy)-1
holding period return (hpr) =
((pricesell-pricebuy)+dividend)/pricebuy
suppose we invest in a stock for N periods with returns R1, R2 .... Rn. the HPR is:
(1+R1)(1+R2)...(1+Rn) - 1
future value factor
(1+r)^t
For the past 4 years, General Motors (ticker GM) has the following annual returns: -15%, 15%, 2%, -2%. If you were invested for the full four years, what was your holding period return?
(1-.15)(1.15)(1.02)(1-.02)-1 = -2.29
annual returns for the last 5 years of Best Buy: 13.6%, 65.7%, -22.6%, 60.4%, and 42.9%. what is your HPR if you were invested in Best Buy the full 5 years?
(1.136)(1.657)(1.226)(1.604)(1.429) -1 =2.34 -> 234%
You have a 7-year bond, with $1,000 face value, 4.50% coupon rate, and quarterly coupon payments. It is currently trading at a price of $970.622. Which of the options below corresponds to this bond's yield to maturity (in APR)?
(1.25/(.05/4) * (1-(1/(1+.05/4)^28)+ (1000/(1+.05/4)^28) = 970.622
A rich donor will give a hospital $1.4 million in exactly 2 years from today. Each year after that, she will donate to the hospital an amount 3% larger than the previous donation, with her last donation occurring in ten years (year 10). What is the present value of this donation today (time 0) given that the interest rate is 6%?
(1.4/.06-.03)(1-(1.03/1.06)^9)(1/(1.06)^1)=10.2
You have a 9-year bond, with $1,000 face value, 5.00% coupon rate, semiannual coupon payments, and yield to maturity of 6.50%. What is its price?
(2.5/.0325)(1-(1/1.0325^18)+(1000/1.0325^18) = 899
you own a small piece of commercial land. you have two options: 1) sell it for $300,000 2) open a bar. you estimate an initial investment of $400,000, profits of $60,000 the first year and then annual growth of 5%. your bank would charge you 12% to lend you the money.
(60/0.12-1.05)-400 = 457.157
Four years ago you bought a 11-year bond with $100 face value trading at par with a coupon rate of 5.00% paid annually. Today, after 4 years (7 years left in maturity), you decide to sell it and you find that the new yield to maturity is 11.00% APR. What is the percentage change in the bond's price?
(71.727-100)/100 = -28.27%
quick ratio =
(Current Assets - Inventory) / Current Liabilities
when dividends grow at a constant rate of g... P0=
(D1/1+rE)+(D1(1+g)/(1+rE)^2)+(D1(1+g)^2)/(1+rE)^3)+...
when dividends grow at constant rate we can invert to find rE=
(D1/P0)+g ^ this is the dividend yield + capital gain rate
cash coverage ratio =
(EBIT + Depreciation) / Interest
capital gains rate
(Psell-Pbuy)/Pbuy
sustainable growth rate =
(ROE x b) / (1 - ROE x b)
total debt ratio =
(Total Assets - Total Equity) / Total Assets
bond price=
(c/r)(1-(1/(1+r)^n)+(c/(1+r)^n)
HPR =
(capital gains+dividend yield)/buyingprice
it always makes more sense to have money now rather than in the future
(doesnt matter what inflation or the interest rate is)
coupon
(face value)(coupon rate/n)
coupon =
(face value)(coupon rate/n)
return on equity (du pont style)
(net income/assets) * (assets/total equity)
ROE dupont style
(net income/sales)*(sales/assets)*(assets/equity) profit margin asset turnover equity mult. profit margin represents operating efficiency asset turnover represents asset use efficiency equity multiplier represents financial leverageF
averages over standardized periods of time can obscure the true investor experience
(the HPR)
two potential sources of benefits when owning stocks
- dividend payments - capital gains
weaknesses of the payback method
- ignores the time value of money - ignores cash flows after the payback period -biased against long-term projects -requires an arbitrary acceptance criteria
we can refer to stocks thru their ticker symbol
- maximum of 4 letters - uniquely identify a company in a point in time -(ex) Apple=APPL
coupon bonds
- pay face value at maturity - make regular coupon interest payments
payday loans are particularly tough for the interest-on-interest they create
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Bond
-a financial security where the issuer promises to make payments to the holder over time -its an IOU -not a standardized security like a share of stock -one bond may have very different characteristics than the next one -*an enforceable legal contract*
pure discount bond
-also called zero coupon bonds bc they make no coupon payments -sell at a discount(under face value) -typically for short maturity -treasuring bills are examples of pure discounts -only one branch of the government that can borrow money on behalf of the govt(US treasury)
value of financial securities = PV of expected future cash flows
-bond value is determined by the present value of the coupon payments and par value -getting the expectation of future cash flows can be really complicated sometimes
bonds are said to be sold at...
-discount if the market price is less than face value -premium if market price is greater than face value -at par if market price is equal to face value
disadvantages of IRR
-does not distinguish between investing and borrowing -IRR may not exist, or there may be multiple IRRs -scaling and timing problem
advantages of the payback method
-easy to understand -biased toward liquidity
advantages of IRR
-easy to understand and communicate
beta coefficient
-measures systematic risk in an asset relative to a large portfolio of assets in the market(M) -if M is truly large, it should have only systematic risk -typically M is the S&P 500 index
pure discount bonds are usually super short term
-remember these don't make coupon payments -in the US zero coupon bonds arent as common, but in other countries in europe they can have super long bonds (like 30 years) that are still pure discount/zero coupon
replacement chain
-repeat projects until they begin and end at the same time -compare NPV for the "repeated projects"
risk
-returns show deceptively little variation -false sense of security so you end up taking on more risk -then a surprise hits and you lose big -fat tails are embedded in financial assets: sporadic releases of info mean sporadic big shocks -standard deviation is a measure of risk -returns are not perfectly normal or symmetric though -fat tails in normal stats jargon: called excess kurtosis
capital intensity ratio
-total assets/sales -amount of assets needed to generate $1 of sales
typical timeline of payments in a bond with T years maturity and n payments per year. this is just the basic/standard case, remember bonds can get exotic
0---1:coupon---2:coupon---nT:coupon+face value
X Inc. has the following expected dividends: $0.50 in one year, $5.00 in two years, and $2.10 in three years. After that, its dividends are expected to decrease by 4.00% per year forever (so that year 4's dividend will be 4.00% less than $2.10 and so on). If X Inc.'s equity cost of capital is 6.00%, what is its current stock price?
0.5/1.06 + 5/1.06^2 + 2.1/0.06+.04 * 1/1.06^2 =23.61
Suppose a savings account offers you an annual interest rate of 15.00%. if the annual inflation rate is 10.00%, what is your real rate?
1 + real = (1+1.15)/(1+1.10) real = 4.55
You want to achieve a real return of 10.50% in your investments. If you expect the inflation rate to be 16.00%, what nominal return do you need?
1 + real = (1+nom)/(1+inf)
Retention Ratio (Plowback Ratio)
1 - dividend payout ratio addition to retained earnings / net income
going from APR to EAR (EAR=)
1+ EAR = (1+(APR/M))^M
interest rates and inflation
1+RealRate= 1+NominalRate/1+Inflation
Suppose you bought a new home for $340,000 using a 30-year mortgage with monthly payments of $1,825.19. The annual interest rate of the mortgage is 5%. After the first 4years (48 monthly payments), how much money have you paid in interest and how much in principal?
1. find how much is the new balance of the loan after the first year of payments. the new balance represents the PV of all the remaining payments: C/(r/paymentsperyear)*(1-1/(1+r)^remaining pmts ^ this shows how much is still owed on the mortgage. the amount of money paid in principal is the difference between the original balance and this new balance original balance-new balance (the new balance is how much money is left to be paid on the mortgage) the amount of money you paid in interest is the difference between the 12 monthly payments made so far and the amount of money paid in principal: (payments per year)(remaining years)(original balance)-principle= amount of money paid in interest answer: Interest: $65,951.28; Principal: $21,658.00
Suppose you bought a new home for $330,000 using a 30-year mortgage with monthly payments of $1,894.46. The annual interest rate of the mortgage is 5.6%. After the first 4 years (48 monthly payments), how much money have you paid in interest and how much in principal?
1. find how much is the new balance of the loan after the first year of payments. the new balance represents the PV of all the remaining payments: C/(r/paymentsperyear)*(1-1/(1+r)^remaining pmts 1894.46/(.056/12)*(1-1/(1.056/12)^312 ^ this shows how much is still owed on the mortgage. the amount of money paid in principal is the difference between the original balance and this new balance original balance-new balance (the new balance is how much money is left to be paid on the mortgage) principle = 330,000-310979.1. the amount of money you paid in interest is the difference between the 12 monthly payments made so far and the amount of money paid in principal: (payments per year)(remaining years)(original balance)-principle= amount of money paid in interest (12)(26)(1894.46)-19020.81 = 71,913.30
Each year for the next 25 years (years 1 to 25) you will deposit $X dollars in your retirement account. When you retire you want to make 20 annual withdrawals (Your first withdrawal will be at time 26). The first withdrawal is for $55,000, and each withdrawal after will increase by 2%. If the interest rate on your retirement account is 6.9%, how much is $X?
1. find the PV of all the withdrawals, and then that will be equal to the PV of all deposits. PV of withdrawals: (55000/0.069-0.02)(1-(1.02/1.069)^20)/(1.069)^25 = 128,874 2. solve for X by making the PV of deposits match the value found above: 128,875=(X/.069)(1-(1/1.069)^25) so X equals 10,959.33
the YTM is the return if we buy the bond right now and:
1. keep it until it matures 2. issues does not default -this makes bonds unique in the asset world, as you know your return ahead of time. great for planning -you do not have to keep the bond all the way until the end. but if you do keep it all the way to the end, you know for sure how much money you're getting
from survey evidence, we know firms use more decision rules than NPV
1. payback method 2. internal rate of return (IRR)
most common types of bonds
1. pure discount 2. coupon bonds 3. consols
2 types of US Treasury coupon securities:
1. treasury notes: maturities from 1 to 10 years 2. treasury bonds: 10+ years maturities
Suppose an investment gave you a real return of 7.00%. If the inflation rate was 15.00%, what was your nominal return?
1.07=(1+nominal)/(1+1.15) nominal = 23.05
X Inc. has the following expected dividends: $1.50 in one year, $2.50 in two years, and $2.20 in three years. After that, its dividends are expected to grow at 2.00% per year forever (so that year 4's dividend will be 2.00% more than $2.20 and so on). If X Inc.'s equity cost of capital is 6.00%, what is its current stock price?
1.5/1.06 + 2.5/1.06^2 + 2.2/(.06-.02) * 1/(1+.06)^2 = 52.59
X Inc. has the following expected dividends: $1.50 in one year, $3.00 in two years, and $1.70 in three years. After that, its dividends are expected to grow at 2.00% per year forever (so that year 4's dividend will be 2.00% more than $1.70 and so on). If X Inc.'s equity cost of capital is 11.00%, what is its current stock price?
1.5/1.11 + 3/(1.11)^2 + 1.7/(.11-.02) * 1/1.11^2 =19.12
Suppose a 5-year bond with $100 face value, 4.00% coupon rate and quarterly coupons is trading for $101.50. If the yield to maturity of the bond changes to 10.00%, what is the percentage change in its price?
1/(.1/4) * (1-1/(1+.1/4)^20)+ 100/(1+.1/4)^20 =76.616 to find the change in price: (76.616-101.5)/101.5 =-24.52%
Present Value Factor
1/(1+r)^t
present value factor
1/(1+r)^t
X Inc. has the following expected dividends: $1.00 in one year, $4.00 in two years, and $2.40 in three years. X Inc. will pay a final dividend of $15.00 at time 4 and then will cease to exist. If X Inc.'s equity cost of capital is 6.00%, what is its current stock price?
1/1.06 + 4/1.06^2 + 2.4/1.06^3 + 15/1.06^4 = 18.40
you can buy a 100 euro zero-coupon one year German bond for 100.424 euros. find its YTM
100.424=100/(1+YTM)^1 YTM = 100/100.424 -1 = -0.005
You have $10,000 you want to invest for the next 32 years. You are offered an investment plan that will pay you 3% per year for the first 16 years and then 6% per year for the last 16 years. How much will you have at the end of the 32 years?
10000(1.03)^16 = 1604.706 1604.706(1.06)^16 = answer: $40,765.19
germany sold 31 year zero coupon bonds with a face value of 100 euro for a price of 103.35. find the YTM
103.35(100/(1+YTM)^31 YTM=(100/103.35)^1/31 -1
suppose you invest $50 for 1 year at 12% compounded semi-annually. what is your FV1?
12%/2 compounding periods = 6% = r 50(1.06) = 53 53(1.06) = 56.18 FV = C(1+r)^n 56.18 = 50(1+r)^1 r = 58.16/50 -1 EAR = 12.36%
******** You receive a credit card offer from Bank X offering an introductory rate of 1% per year, compounded monthly, for the first six months. After that, it increases to 23% per year, compounded monthly. What is the EAR of this credit card for the first whole year?
12.63%
Suppose Oil Company XYZ plans to pay a dividend of $2.25 in one year (this is time 1), $4.50 in two years, and then increase this dividend by 11.00% every year (i.e. the dividend at time 3 is $4.50 ×\times 1.11 ) until time 9, after which the company will cease to operate and no more dividends will be paid. If the required rate of return on this company is 14.00%, what is its current price?
2.25/1.14 + 4.5/(.14-.11) * 1-(1.11/1.14)^8 / 1-0.14 = 27.25
X Inc. has the following expected dividends: $2.00 in one year, $2.50 in two years, and $2.10 in three years. X Inc. will pay a final dividend of $16.00 at time 4 and then will cease to exist. If X Inc.'s equity cost of capital is 6.00%, what is its current stock price?
2/1.06 + 2.5/1.06^2 + 2.1/1.06^3 + 16/.06^4 = 18.55
Question Suppose Oil Company XYZ plans to pay a dividend of $2.00 in one year (this is time 1), $1.25 in two years, and then increase this dividend by 3.00% every year (i.e. the dividend at time 3 is $1.25 ×\times 1.03 ) until time 15, after which the company will cease to operate and no more dividends will be paid. If the required rate of return on this company is 12.00%, what is its current price?
2/1.12 + 1.25/.12-.03 * (1-1.03/.12^14) / 1.12 =10.35
You have a 10-year bond, with $1,000 face value, 7.00% coupon rate, semiannual coupon payments, and yield to maturity of 6.00%. What is its price?
3.5/(.06/2) * 1-1/(1+.06/2)^20+ 1000/(1+.06/2)^20 = 1074.39
Suppose Ford Motor Company plans to pay a dividend of $3.75 in one year and $4.50 in two years. Afterward, the company will not pay any dividend for 8 years. At time 10, the company will pay a dividend of $3.25 per share and will increase the dividend by 10.00% every year thereafter. If Ford's equity cost of capital is 14.00%, what is its current price?
3.75/1.14 + 4.5/1.14^2 + 3.25/(.14-.1) / 1.14^9 = 31.74
Suppose Procter & Gamble Co. plans to pay a dividend of $3.00 in one year (year 1) and $2.25 in two years (year 2). Following this, the company will not pay any dividends for 8 years. At the end of year 10 (year 10), the company will start paying a fixed annual dividend of $3.00 per share every year for eternity. If Procter & Gamble Co.'s equity cost of capital is 14.00%, what is its current price?
3/1.14 + 2.25/1.14^2 + 3/.14-0 / 1.14^9 =1
ABC Corp. will pay a dividend (at time 1) of $5.0. It is expected the company will keep its dividend at the same level forever. If the ABC Corp.'s equity cost of capital is 13.00%, what is the price of its stock today?
5/0.13 = 38.46
Suppose Ford Motor Company plans to pay a dividend of $5.00 in one year and $3.00 in two years. Afterward, the company will not pay any dividend for 4 years. At time 6, the company will pay a dividend of $2.00 per share and will increase the dividend by 7.00% every year thereafter. If Ford's equity cost of capital is 11.00%, what is its current price?
5/1.11 + 3/1.11^2 + 2/.11-.07 / 1+0.11^5 = 36.61
in exchange for $500 today, your firm will receive $550 in one year. the interest rate is 8% annual. would you go ahead with this investment?
550/1.08 = 509.25 NPV = 509.25-500 = 9.25
You have a bond with face value of $100, coupon rate of 7.50%, annual coupon payments, maturity of 10 years, and a yield to maturity of 5.00%. This bond allows the issuer to not make coupon payments for the first 2 years. Find its price.
7.5/0.05 (1-1/(1+.05)^8)+ 100/(1+.05)^8) /(1+.05)^2 =105.36
You want to save $X in a retirement account today (year 0) so that when you retire in 27 years you can make a one-time withdrawal of $280,000 and travel the world for a year. After that, starting at year 28 you plan to withdraw $98,000 every year for 15 years (your first withdrawal is at time 28). If the interest rate is 6.50%, how much is $X?
98000*((1-(1/(1.065)^15)/.065) + 280,000 = 1201461.548 1201461.548 = C * (1.065)^27 1201461.548 / (1.065)^27 answer: $219,417.10
a 10 year treasury note with coupon rate of 1.625% and face value of $100 currently sells for $99. find its YTM
99 = (0.8125/(YTM/2))*(1-(1/(1+YTM/2)^20)+(100/(1+YTM/2)^20) (0.01625/2)(100) = 0.8125
normal distribution
99.74% - 95.44% - 68.26%
you can buy a $100 zero-coupon one year Treasury bill for $99.934. find its YTM
99.934= (100/1+(YTM))^1 YTM = 100/(99.934)-1=.0006
ABC Corp. has a share price of $9.00 today. In one year, it is expected ABC Corp. will pay dividend of $1.00 and its stock price is expected to be $12.00. What is ABC Corp.'s equity cost of capital (rE)?
9= (12+1)/(1+rE) rE = 44.444%
by law, credit card companies have to disclose their APR interest rate on each statement. Most credit cards compound their APR daily, why?
? not seeing this anywhere online
annuity
A level stream of cash flows for a fixed period of time
If the economy enters a recession, MCD will probably not do great. Why? Are all of your other assets insensitive to a recession?
A recession is a systematic risk because it affects every asset in the market.
interest rate per compounding period =
APR / M (where M is the number of compounding periods)
a typical payday loan will charge $15 for every $100 loan every two weeks. What is the APR of this?
APR = 0.15*26 = 390% EAR = (1+(3.9/26))^26 -1 = 36.85 -> 3685%
interest rates are usually quoted as Annual Percentage Rates(APR). this is the rate that does not take into account the effect of compounding
APR is useful because it tells us how much the interest rate is per compounding period; however, the APR does not tell us what the true annual interest rate is
If MCD is only 1 stock out of 100 in your investment portfolio, then you only feel about 1/00 of the 10% risk the new CEO is clueless.
All of your other assets are insensitive to this risk. If you have 500 stocks in your portfolio, then you feel it even less. As you add more assets to your portfolio, you feel the unsystematic risk of each less and less. At the limit (as you add many many assets) you no longer care about unsystematic risk.
what does the total debt ratio indicate ?
how does your debt compare to your equity when put against your assets
NWC turnover ratio indicates?
how much "work" we got out of our net working capital
suppose you have a business opportunity where you can receive $1 million today if you agree to pay $500,00 each year for the next 3 years. find the IRR
NPV = 1-(0.5/r*)(1-(1/(1+r*)^3)) = 0 r*= 23.34%
PE ratio measures?
how much investors are willing to pay per dollar of current earnings
Growing annuity present value
C X [(1-((1+g)/(1+r))^t)/(r-g)]
growing annuity present value
C X [(1-((1+g)/(1+r))^t)/(r-g)]
annuity present value
C X [(1-Present Value Factor)/r]
growing perpetuity present value
C/(r-g)
PV of a perpetuity
C/r
present value for a perpetuity =
C/r
cash ratio =
Cash / Current Liabilities
Dividend payout ratio
Cash Dividends/Net Income
inventory turnover =
Cost of Goods Sold / Inventory
interval measure =
Current Assets/Average Daily Operating Costs
internal growth rate
maximum growth rate a firm can reach without external financing
suppose you buy a stock today and sell NEVER
pt=0=PV(Div1+Div2+Div3+Div4+...)
when dividends grow constant D2=
D1(1+g)
when dividends grow constant D3=
D2(1+g)
dividend yield=
Div/Pbuy
when dividends grow at constant rate Dt=
Dt-1(1+g)
Modify the gamble: we flip a coin→ Heads you win $1 million +X, Tails you lose $1 million -X. how much is expected return how much does X need to be so that you'll play rather do one flip or many flips? ^ x is linked to your individual risk aversion
E(gamble) = 1/2(1+x)+1/2(-(1-x)) =x your risk aversion is individual and is typically dependent on your wealth
Think about the following gamble: we flip a coin → Heads you win $1 million but Tails you lose $1 million.
E(x)= SUMi * Xi * Pi =1(1/2)+-1(1/2)=0 each outcome has half probability don't play this
what is the EAR of 12% APR compounded monthly? compounded daily?
EAR = (1+(0.12/365))^12 -1 = 0.1236 EAR = (1+(0.12/365))^365 -1 = 0.1274
suppose your credit card charges 25% APR compounded daily. what is the EAR?
EAR = (1+(0.25/365))^365 -1 = 0.2839
earnings before taxes
EBIT + non-operating income - interest expense
taxable income =
EBIT - interest paid
Interest Coverage Ratio
EBIT/ interest expense
times interest earned ratio =
EBIT/Interest
suppose you save $5000 in a savings account that offers a 3.5% interest rate compounded monthly. what is your balance after 48 years?
FV48 = 5000(1+(0.035/12))^48 = 5750
You are schedule to receive $9,000.00 in 4 years. When you receive it, you will immediately invest it for 5 more years in a savings account that earns 7% annually. How much money will you have in year 9?
FV9=9000(1.07)^5 = 12,623.0
how to find HPR from per-period returns?
FVn = C(1+r)^n
what is the HPR of a stock that was purchased for $25, sold for $27 and distributed $1.25 in dividends?
HPR = (27-25+1.25)/25 3.25/25= 0.13
look back at the fertilizer example. find the IRR by solving r* in the following NPV equation: (if the cost of capital is 10% do you go ahead with it?)
NPV = -81.6+(28/r*)(1-1/(1+r*)^4) = 0 r* = 0.14
X~N(Mu, naut)
N(0,1)
find the YTM of a semiannual bond w/ face value of $100, coupon rate of 8%, maturity of 6 years, and price of $105.50
N=12 PV=-105.50 PMT=4 FV=100 P/Y=2 select I% press ALPHA then ENTER answer =
suppose you borrow $300,000 on a 30 year mortgage with monthly payments and 5% interest rate. what is your monthly payment
N=30 I%=5 PV=300000 P/Y=12 select PMT press ALPHA then ENTER answer = $1,610.46
a fertilizer company can create a new environmentally friendly fertilizer. the fertilizer will require a new factory that can be built at a cost of $81.6 million after the first and last four years. if the firm's cost of capital is 10%, is the project profitable?
NPV = -81.6 + (28/.10)(1-(1/(1.10)^4)) = 7.15
You are evaluating a project with initial investment (at year 0) of $4,300 that is expected to produce annual profits of $1,300 at year 1 and $2,200 at year 2. What is the net present value of this project if the cost of capital is 8.00%?
NPV = PV(B)-PV(C) (1300/1.08)+(2200/1.08^2)-4300 = -1210
retained earnings =
Net Income - Dividends
Return on Sales (ROS)
Net Income/Sales
Return on Assets (ROA)
Net Income/Total Assets
proper cost benefit analysis must be done in present value terms:
Net Present Value = PV(Benefits) - PV(Costs)
net working capital to total assets =
Net Working Capital / Total Assets
cash flow from assets formula
Operating Cash Flow - Net Capital Spending - Change in NWC
case one: dividend discount model(DDM) of Williams (1938)
P0=(D1/(1+rE)+(D2/(1+rE)^2)+(D3/(1+rE)^3)+....
suppose Target plans to pay $2.64 per share in dividends in the coming year(time 1). if its equity cost of capital is 10% and dividends are expected to grow by 5% per year in the future, estimate the value of Target's stock.
P0=D1/(rE-g) 2.64/(0.10-0.03) =$52.8
You have a bond with face value of $100, coupon rate of 7.00%, semiannual coupon payments, maturity of 7 years, and a yield to maturity of 6.50%. This bond allows the issuer to not make coupon payments for first the 2 years. Find its price
P4 =(3.5/0.0325)(1-(1/1.0325)^10)+(100/(1.0375)^10) take this ^ price back to time zero P0=(P4)(1/(1.0325^4))
price=
PV of all future expected payments
Suppose you win a big prize in the lottery. The prize is a sequence of annual payments where you receive $1.00 million at year 0 and every year after the annual payment increases by 5.00% until year 6 (there are a total of 7 annual payments). What is the present value (in millions) of this prize at 9.00% annual interest rate?
PV of growing annuity * (1 + r) $6.27
????P0=
PV(D1+P1)
P1=
PV(D2+P2)
P2=
PV(D3+D4+P4)
consider a factory that must have an air cleaner that is mandated by law. there are two choices: 1. the expensive choice costs $4,000 today, has annual operating costs of $100, and lasts 10 years 2. the cheap choice costs $1,000 today, has annual operating costs of $500, and lasts 5 years assuming a 10% cost of capital, which one should we choose?
PV1= 4000+(100/.10)(1-(1/1.10)^10) PV2= 1000+(500/.10)(1-(1/1.10)^10)+(1000/1.10)^5)
Suppose we have 10 independent business ventures:V1,V2,...,V10.Each one has 50% of going bankrupt. What is the probability all 10 go bankrupt?
PV1×PV2×...PV10= 0.510= 0.0009 = 0.09%
X Inc has the following expected dividends: 2.00 in one year, 4.00 in two years, and 2.00 in three years. After that, all dividends are expected to grow at 4% per year forever(so that year 4's dividend will be 4% more than 2.00 and so on). if x Inc's cost of capital is 11%, what is its current stock price?
Po= (2/1.11)+ (4/1.11^2)+ (2/1.11^3)+ (2*1.04)/(0.11-0.04)*(1/1.11^3) = $28.24
X Inc has the following expected dividends: $1 in one year, $4 in two years, and $1.90 in three years. X Inc. will pay a final dividend of $18.00 at time 4 and then will cease to exist. If X Inc's cost of capital is 11%, what is the current stock price?
Po=(1/1.11)+(4/(1.11)^2)+(1.90/(1.11)^3)+(18/(1.11)^4) = $17.39
ABC Corp has a share price of $10.50 today. in one year, it is expected ABC corp will pay a dividend of $0.75 and its stock price is expected to be $12.00. what is ABC corp's equity cost of capital(rE)?
Po=(D1+P1)/(1+rE) solve for rE (0.67+12)/(1+rE) =10.50 rE=(12.75/10.5)-1 answer: 21.429%
ABC corp will pay a dividend at time 1 of $2.5. it is expected the company will increase its dividend by 10% per year forever. if the ABC corp's equity cost of capital is 4.5%, what is the price of its stock today?
Po=2.5/(0.045-0.10)= -45 answer: $45.5
today the price of one share of Microsoft is $242, and it will pay an annual dividend of $2.14 per share. if you expect its price in 1 year to be $276.93, what is Microsoft's growth rate (g)?
Po=D1/(rE-g) Po=(D1+P1)/(1+rE) solve for RE 242=(2.14+276.93)/(1+rE) rE= 15.3% now find g 242= 2.14/(0.153-g) g=0.153-(2.14/242) g= 14.4%
probability distribution
Possible outcomes with probabilities
ROE =
Profit Margin x Total Asset Turnover x Equity Multiplier
suppose you buy a stock and sell IN FOUR PERIODS
Pt=0=PV(Div1+Div2+Div3+Div4+P4)
suppose you buy a stock and sell IN ONE PERIOD
Pt=0=PV(Div1+P1)
Netflix just paid a dividend of $2.9 this year (year 0). You expect Netflix's dividend to grow by 1% per year. If the firm's equity cost of capital is 8%, what is the price per share of Netflix 3 years from now?
Pt=Dt+1/(rE-g) 2.9*(1.01)^4 / 0.08-.01 = 43.11
if the YTM on a 1-year Treasury is 0.065% and the current inflation rate is 1.8%, what is the real return?
REAL = (1.00065)/(1.018) -1 = -0.017
internal growth rate formula
ROA x b / 1 - ROA x b
corporate finance
Relationship between business decisions and the value of stock in the business
Suppose you invest $100,000 (total value of portfolio) and buy 200 shares of Apple at $200 per share ($40,000) and 1000 shares of Coca-Cola at $60 per share ($60,000). If Apple's stock goes up to $240 per share and Coca-Cola stock falls to $57 per share and neither paid dividends, What return did the portfolio earn? what is the new value of the portfolio?
Return of Apple:(RA) =240−200/200= 20% Return of Coca-Cola:(RC) =57−60/60= −5% Weight of Apple:(wA) =40,000/100,000= 40% Weight of Coca-Cola:(wC) =60,000/100,000= 60% Return of the portfolio is: Rp=wARA+wCRC= [(0.40)×(0.20)] + [(0.60)×(−0.05)] = 5% New Value of Portfolio:$100,000×(1 + 0.05) = $105,000
NWC turnover =
Sales / NWC
fixed asset turnover =
Sales/Fixed Assets
total asset turnover =
Sales/Total Assets
Suppose you invest today (time 0) $1,200 into a certificate of deposit that is expected to earn an annual rate of return of 6%. After 20 years, how much is the simple interest and interest on interest you earned?
Simple interest: $1,440.0 & Interest on Interest: $1,208.6
best bond-rating companies
Standard & Poor's Moody's
with amortized loans, though the payment (C) is fixed, the interest payment is reduced while the principle payment is increased. why?
The periodic payment amount is fixed, but the breakdown of interest and principal on each payment is determined by the interest balance on the day the payment is received. If a borrower makes their payment early, there will be less interest to pay; therefore, more of their payment will be applied to principal. Conversely, if they pay late, there will be more interest to cover, and so less will apply to principal.
If the interest rate on savings accounts is 0.0%, the value of having one dollar today is ______________ having one dollar in one year.
The same nominal quantity of money today is always better because you use it today (save it, consume it, invest it, donate it, etc.)
McDonalds (ticker MCD) recently hired a new CEO. Suppose we have the following probabilities that the new CEO 1. a genius: 10% 2. a normal person: 80% 3. clueless: 10%
This is an unsystematic risk, it is unique to MCD. If all of your investments are MCD, then you are exposed completely to this risk (i.e. you feel all the 10% risk the new CEO is clueless).
Equity Multiplier
Total Assets/Total Equity
debt-equity ratio
Total Debt/Total Equity
Wi is the fraction of the total portfolio held in each investment in the portfolio
Wi = value of stocki / total value of portfolio
Approximately, what is the yield to maturity of a pure discount bond with 7 years maturity, face value of $100 and price of $101.00.
YTM = (100/101)^1/7 -1 answer: -.142%
dupont identity
an expression that breaks the ROE ratio into three different parts to determine operating efficiency, asset use efficiency, and financial leverage
generalization of scenario analysis
state of economy, returns, and probability -good(20%, 0.35) -normal(7%, 0.50) -bad(15%, 0.15)
annuity future value factor
[(1+r)^t-1]/r
indications of a declining current ratio
a declining current ratio could indicate a deteriorating liquidity position OR that changes have been made to more efficiently use current assets etc.
percentage of sales approach
a financial planning method in which accounts are varied depending on a firm's predicted sales level
what does the cash coverage ratio indicate?
a firm's ability to generate cash from operations
bond indenture
a legal document that details all the conditions relating to a bond issue -face/par value: principal amount of the bond -maturity: date when the principal amount is to be repaid - coupon rate: interest rate of the bond(APR) -payment frequency: # of payments within the year -coupon payment = (coupon rate * face value)/frequency
Suppose you win a big prize in the lottery. The prize is a sequence of annual payments where you receive $4.00 million at year 0 and every year after the annual payment increases by 2.00% until year 11 (there are a total of 12 annual payments). What is the present value (in millions) of this prize at 5.00% annual interest rate?
annuity due situation: (growing annuity present value)(1 + r) answer: $41.13
X Inc. has the following expected dividends: $2.50 in one year, $5.00 in two years, and $1.50 in three years. After that, its dividends are expected to decrease by 5.00% per year forever (so that year 4's dividend will be 5.00% less than $1.50 and so on). If X Inc.'s equity cost of capital is 11.00%, what is its current stock price?
answer: $13.92 de
bond characteristics
all payments in a bond are promised, issuer can default
cash flow to stockholders =
dividends paid (income statement) - net new equity raised
Suppose Intel Co. plans to pay a dividend of $3.25 in one year (year 1) and $1.25 in two years (year 2). Following this, the company will not pay any dividends for 5 years. At the end of year 7 (year 7), the company will start paying a fixed annual dividend of $3.50 per share every year for eternity. If Intel Co.'s equity cost of capital is 14.00%, what is its current price?
answer: $15.20
ABC Corp. will pay a dividend (at time 1) of $2.9. It is expected the company will increase its dividend by 5.00% per year forever. If the ABC Corp.'s equity cost of capital is 9.00%,what is the price of its stock at time 3?
answer: $83.93 look at netflix problem
You have a 8-year bond, with $1,000 face value, 6.00% coupon rate, annual coupon payments, and yield to maturity of 7.00%. What is its price?
answer: $940.29 literally how!?
Your investment portfolio comprises of 250 shares of Cisco Systems, Inc. and 300 shares of Exxon Mobil Co., which you bought a year ago at $381 per share and $99 per share, respectively. If Cisco Systems, Inc.'s share price has changed to $374, and Exxon Mobil Co.'s share price has changed to $101, and assume no dividends have been given, then what is the return of your portfolio?
answer: -0.92%
Your investment portfolio comprises of 200 shares of Exxon Mobil Co. and 300 shares of Boeing Co., which you bought a year ago at $423 per share and $86 per share, respectively. If Exxon Mobil Co.'s share price has changed to $345, and Boeing Co.'s share price has changed to $111, and assume no dividends have been given, then what is the return of your portfolio?
answer: -7.34%
Microsoft just paid (year 0) a dividend of $1.80. If you expect Microsoft's dividends to grow at 2% per year forever, what is the current price of Microsoft's share if its equity cost of capital is 7%?
answer: 36.72
capital gains
appreciation in price between buying and selling the shares
pro forma
as a matter of form; financial statements are the form we use to summarize the different events projected for the future
comparing companies through time
balance sheet: item / total assets income statement: item / sales no obvious denominator for statement of cash flows
Publicly traded companies are required to make public the following financial statements:
balance statement, income statement, statement of cash flow, statement of stockholder's equity
the return from investing $1 has...
been increasing over time (between 1926-2016)
the probability of default is clearly important to the price you are willing to pay for a corporate bond. how do you assess a firms likelihood of default?
bond ratings
interest only loans
borrower pays interest each period and repays the entire principal at some point in the future
pure discount loan
borrower receives money today and repays the loan in a single lump sum at some time in the future
annuity present value =
c*(1-[1/(1+R)^T)]) / R
case 1: dividends don't grow
dividends stay constant D=D1=D2=D3=... then P0=D/rE ^^^not a good assumption!!!!!!
A perpetuity will pay $600 per year, starting 5 years after the perpetuity is purchased. What is the present value (PV) of this perpetuity on the day that it is purchased (consider this time 0), given that the interest rate is 3%?
calculate the present value of the perpetuity which will show how much the cash flow is over the course of the 5 years, then take the present value number and calculate the present value for the date of purchase: pv at time 5 = 600/.03 pv at time 0 = 20,000/1.03^4 $17,769.74
some risk is eliminated or greatly reduced through diversification
call this unsystematic risk or idiosyncratic risk some risk is common to all instruments that cant be diversified-systematic risk
A stock is bought for $26 and sold for $33 one year later, immediately after it has paid a dividend of $2.10. What is the capital gains rate for this transaction?
capital gains rate = 26.923
cash flow from assets =
cash flow to creditors + cash flow to stockholders
portfolios
collections of securities or stocks
two types of equity
common and preferred
Suppose you need to borrow money. Bank X charges 10.000% compounded monthly on its loans; Bank Y charges 10.100% compounded semiannually; Bank Z charges 10.600% compounded annually. Which bank is best for you?
compute the EAR of all three options and choose the one with the lowest EAR(since we are borrowing)
corporate bonds
corporations issue bonds but they could also could go bankrupt. this is called credit risk. corporations with higher default risk will need to pay higher coupons to attract buyers to their bonds
agency costs
costs of the conflict of interest between stockholders and management
consols price =
coupon/YTM
current ratio =
current assets / current liabilities
working capital
day to day operations
return=
dividend yield + capital gains rate
A stock is bought for $19 and sold for $14 one year later, immediately after it has paid a dividend of $1.70. What is the dividend yield for this transaction?
dividend yield = 8.947
Returns =
dividends + capital gains
Suppose you borrow$1,000 today at a 6% interest rate and you make annual interest payments (interest-only loans)
each year you pay 6% of the 1000 dollars which is the interest. so that's 60 dollars per year in interest payments across the three years
operating cash flow =
earnings before interest and taxes (EBIT) + depreciation - taxes
net income
earnings before taxes - taxes
examples of systematic risk
economic crisis, increasing interest rates, changes in consumer purchasing power, and wars
Change in NWC (net working capital)
ending NWC - beginning NWC
net capital spending =
ending net fixed assets - beginning net fixed assets + depreciation
TI calculator
enter the finance app by pressing the apps button and select Finance and then TVM solver. for all the cases below, the last row PMT should highlight END
find the PV of $10,000 in 10 years if the interest rate is 5%
enter this: N=10 I%=5 FV=10000 P/Y=1 select PV press ALPHA then ENTER
find the price of a semiannual bond with face value of $100, coupon rate of 5%, YTM of 3%, and maturity of 10 years
enter this: N=20 I%=3 PMT=2.5 FV=100 P/Y=2 select PV press ALPHA then ENTER answer= $117.1686
find the Present Value of an annuity that pays you $5,000 each year for the next five years(starting in one year) if the interest rate is 5%
enter this: N=5 I%=5 PMT=50000 P/Y=1 select PV press ALPHA then ENTER answer = $21,647.38
suppose you have a 25-year mortgage with monthly payment of $1,500 and interest rate of 6%. find your outstanding balance.
enter: N=25*12 I%=6 PMT=1500 P/Y=12 select PV press ALPHA then ENTER answer = $232,810
preferred equity
entitled to receive dividends every year but do not have control over the company
the essence of capital budgeting
evaluating the size, timing, and risk of future cash flows
amortized loans
every period, some portion of the principal amount is being paid. typically, the borrower makes the same payment every period, some amount goes to interest, and the rest toward reducing the balance on the loan
common equity
exercise control over the company but receive dividends last
statistics
expected value: mean, variance: expected value of squared deviation from mean, standard deviation: square root of variance
Relative to the normal distribution, stock returns have "fat tails" (or excess kurtosis). This means:
extreme returns happen more often
how to calculate how much interest on interest has been incurred
find regular future value and then find the value of simple interest and subtract them
Pawn Shop XYZ charges an interest rate of 20% per month (i.e. this is the monthly rate, not the annual rate). By regulation, they must disclose (in the fine print) an APR to their customers. What is the APR they disclose and what is their EAR?
find the APR, which is the per period interest rate multiplied by the number of periods in a year: 20%(12) = 240% for the EAR, use the formula to go from APR to EAR: (1+20^12)-1 = 791.61%
Assume your company's pension plan promises to pay you $57,000 per year starting when you retire in 37 years (the first payment is 37 years from now) and increase the payment by 1% every year after the first to compensate for inflation. You hope to live 19 years after you retire (you collect 20 payments). If your interest rate is 5%, what is the value today of your pension plan?
find the value of all withdrawals at the time of 36 where t=20 and c=57,000. this will be 769,675.57 then discount this back to PV: 769,675.57/(1.05)^36=132,890.19
return on equity is?
for every dollar in equity, x amount of profit is generated in accounting terms
Earnings before interest and taxes (EBIT)
gross profit - selling/admin/general - r&d - depreciation
Tesla Motors has a beta coefficient (β\beta) of 0.72, this means Tesla
has less systematic risk than the overall market
we record info standardized to a measure of time: day, week, month, year, etc
holding periods do not have to be standardized (ex: you can invest for 1.5 months)
the problem w investing is that its about the future and the future is uncertain
how do we deal with uncertainty? statistics
******* You are evaluating a project with initial investment (at year 0) of $49,000 that is expected to produce annual profits of $24,000 for 5 years starting at year 1. A year after the project ends, there is an abandonment cost of $22,000 (at year 6). If your firm's cost of capital is 6.00%, what is the net present value (NPV) of this project, and should you accept the project?
how to deal with the abandonment cost?? answer: $36,587.60
for for stocks, there is no obvious interest rate used to compute PV
however, when an investor buys a stock she expects to make a return. this expected return E(rE) is what we use to discount PV
default
if default, then issuer is forced into bankruptcy court. the case can end in liquidation(like toys are us) or reorganization(like GM)
Suppose we have two companies, A and B, and it is expected both will pay $1.50 in dividends every year forever. However, the stock price of A is higher than the stock price of B. Which of the following must be true?
if dividends and the growth rate are the same across the 2 companies, the only way the prices can be different is if the rE is different, so the equity cost of capital of B is more than the one of A
Suppose the Texas lottery advertises that it pays its winner $28 million. However, this prize money is paid at the rate of $7.00 million each year (with the first payment being at year 0) for a total of 4 payments. What is the present value (in millions) of this prize at 10% annual interest rate?
if the first payment is at time 0, then are are a total of 3 future payments which we discount as an annuity. PV: 7/0.1(1-(1/(1.1)^3)+7=24.41
YTM=
if there's no year factor: face value/price) -1
in general, the NPV will vary with the cost of capital
if we have multiple mutually exclusive projects, the NPV rule is: choose the one with highest NPV
bond prices will vary with interest rates
in general, prices move opposite to interest rates (why is this?)
Goal of Financial Management
increase in the value of a stock
Your investment portfolio comprises of 250 shares of Shoelace Inc. and 350 shares of Johnson & Johnson, which you bought a year ago at $515 per share and $119 per share, respectively. If Shoelace Inc.'s share price has changed to $413, and Johnson & Johnson's share price has changed to $102, and assume no dividends have been given, then what is the return of your portfolio?
initial value of the portfolio: (250*515)+(350*119)= 170,400 portfolio weights: 128750/170400= 0.7556 (shoelace) .2444(j and j) return: .7555751* -.1980583+ .2444249* -.14285 =-18.96
interest on interest
interest earned on the reinvestment of previous interest payments always assume interest on interest unless otherwise specified
simple interest
interest paid on the principal alone
cash flow to creditors =
interest paid(income statement) - net new borrowing(from balance sheet; change in long term debt)
suppose you save $12,000 in an account that pays a 6.6% interest rate compounded monthly. What is your balance after 2 years?
interest rate per compounding period = rate as a decimal/compounds per year ^ plug this in for the rate answer: $13,688.35
real rates
interest rates or rates of return that have been adjusted for inflation
nominal rates
interest rates or rates of return that have not been adjusted for inflation
if the interest rate on savings accounts is 0.0%, the value of having one dollar is _________ having one dollar is one year
less than
categories of financial ratios:
liquidity, leverage, profitability, market value
long-term debt ratio =
long term debt / (long term debt + total equity)
capital budgeting
long term investments
all else equal,
longer maturities have greater sensitivity to changes in interest rate
inflation has the capacity to affect our returns
making a 10% return sounds great, but if inflation is also 10% then we haven't really gained anything
boeing spent 32 billion dollars to build the 787 during the 2000s but it didnt start to fly commercially until 2011
many airlines dont buy the airplane but instead lease it
Market to Book Ratio
market value per share/book value per share
what is the goal when the firm has no traded stock
maximize the market value of the existing owners' equity
amazon's annual returns for the past 5 years: 25%, 42%, 13%, 77%, -25% find the mean and standard deviation
mean (25+42+13+77-25)/5 = 26.4% standard deviation (25-26.4)^2+(42-26.4)^2+(13-26.8)^2+(77-26.4)^2+(-25-26.4)^2 /4 all of the above to the power of 1/2 = 33.6%
examples of amortized loans
mortgage, car loan
Mu w a hat = x with a line on top
naut with a hat = standard deviation
profit margin (PM)
net income / sales
return on equity (ROE) =
net income / total equity
earnings per share
net income / total shares outstanding
Earnings Per Share (EPS)
net income/shares outstanding
Earnings before interest and taxes (EBIT) =
net sales - cost of goods sold - depreciation
assume a company requires all projects to have a payback period of three years or less. for the project below, would the firm undertake the project under this rule? year net cash flow 0 -10,000 1 1,000 2 1,000 3 1,000 4 1,000,000
no because at year three, there is still a need for 7,000 more dollars in order to pay back the 10,000 spent at the beginning
cash from from assets (amount going to creditors/shareholders) =
operating cash flow - net capital spending - change in NWC
cash flow from assets involves three components:
operating cash flow, capital spending, and change in net working capital
Annuity Due Value (equation)
ordinary annuity value * (1 + r)
for stocks s1,s2...2n, a portfolio p is
p= w1S1+w2S2+...wNSM
Find the price of a zero-coupon bond with a face value of $1,000, yield to maturity of 3.00%, and 7 years to maturity.
p= face value/1+(r)^time answer: $813.09
find the price of a one year pure discount bond with a face value of $100,000 and YTM of 2%
p=(100/(1.02)^1)= 98.4
Suppose you borrow$1,000 today at a 6% interest rate and have to pay it all back in three years.
pay back = $1000(1+0.06)^3 in one lump sum at the end of the three years
how long does it take a project to pay back its initial investment
payback method = number of years to recover initial costs payback period rule: investment is acceptable if the calculated payback period is less than some pre-specified number of years
You are evaluating a project with initial investment (at year 0) of $220,000 that is expected to produce annual profits of $21,000 for 15 years starting at year 1. Your firm's cost of capital is 10.00% and their preferred payback period is 5 years or less. Will your firm accept or reject the project if they follow the payback rule?
payback rule = need to recover costs within specified amount of time find the PV of the benefits using 5 as the time(the longest it could be) and see if it has matched or surpassed the PV of the costs PV(B) = 79606.52216 in five years so it has not recovered the costs within the preferred payback period answer: reject
Netflix just paid a dividend of $0.4 this year (year 0). You expect Netflix's dividend to grow by 4% per year. If the firm's equity cost of capital is 10%, what is the price per share of Netflix 10 years from now?
price = .6157816/(.1-.04) =10.26
Apple will pay a dividend of $4.20 this coming year (year 1). If you expect Apple's dividend to grow by 9% per year, what is its current price per share if the firm's equity cost of capital is 14%.
price = 4.2/(.14-.09) =84
PE ratio =
price per share (stock price) / earnings per share
You have a 10-year bond, with $1,000 face value, 6.50% coupon rate, annual coupon payments, and yield to maturity of 4.50%. What is its price?
price= 65/0.045 * (1-1/(1+.045)^10)+ 1000/(1+.045)^10 answer: 1,158.25
You want to save $X amount of dollars today (time 0) in a savings account that pays an annual interest rate of 9.00% so that starting at time 5 you can withdraw $65 every year forever. How much is X?
pv at time 5 = 65/.09 = 722.2222.. pv at time 0 = 722.22/1.09^4 = 511.6404 $511.64
Holding Period Return
rate of return over a given investment period
what does the quick ratio indicate?
ratio more than one = good ratio less than one = need to create more liquidity to sell more of that inventory; you might not be able to turn inventory into cash at any given time
product costs
raw materials, direct labor expense, and manufacturing overhead
gordon and shapiro growth model (1956)
reasonable extension: dividends grow at constant rate g
Preferred shareholders:
receive a dividend every period
Each year for the next 28 years (years 1 to 28) you will deposit $X dollars in your retirement account. When you retire you want to make 20 annual withdrawals (Your first withdrawal will be at time 29). The first withdrawal is for $46,000, and each withdrawal after will increase by 1%. If the interest rate on your retirement account is 4.6%, how much is $X?
refer to the formula on formula sheet to solve for the PV of withdrawals and then use that number to solve for X answer: $11,734.23
fixed assts are:
relatively liquid
Suppose you need to borrow money. Bank X charges 10.000% compounded monthly on its loans; Bank Y charges 10.150% compounded semiannually; Bank Z charges 10.650% compounded annually. Which bank is best for you?
remember m = # of compounding periods compute the EAR for each bank and pick the lowest EAR = (1+(APR/m)^m -1 X- .10471 Y- .10407 Z- .1065 Bank Y has the lowest EAR by just a little bit answer: Bank Y
what does the times interest earned ratio indicate?
represents how well a company has interest obligations covered. if the ratio is less than one, need to bring in more interest
income
revenue - expenses
gross profit
revenues - cost of goods sold
finding the YTM of a coupon bond analytically is quite difficult
see below example
period costs
selling, general, and administrative expenses
capital gains=
sellingprice - buyingprice
You have been offered a unique investment opportunity. If you invest $2,900 today (at year 0), you'll receive annual payments of $900 at the end of each of the next 7 years, starting at year 1. Approximately, what is the internal rate of return (IRR) of this investment opportunity?
set up NPV equation and honestly just plug in answer choice for the rate that will make the equation equal to 0 answer: 24.44%
expected value =
sigmaN * Ri / N
variance =
sigmaN(Ri-expected value)^2 / N-1
multiple cash flows
simply look at the problem as a series of single payments and calculate their PVs and FVs separately
aggregation
smaller investment proposals are added up and treated as one big project
a fertilizer company can create a new environmentally friendly fertilizer. the fertilizer will require a new factory that can be built at a cost of $81.6 million after the first and last four years. the firm's cost of capital is 10%. if the firm requires all projects to have a payback period of two years or less, would the frim undertake the project under this rule? what if the company requires 3 years?
solve for PV at year 2 and compare to cost. solve for PV at year 3 and compare to cost
A janitorial services firm is considering two brands of industrial vacuum cleaners to equip their staff. Option A will cost $1900, require servicing of $500 per year, and it will last 8 years. Option B will cost $300, require servicing of $700 per year, and it will last 2 years. If the cost of capital is 7.00%, which is the better option, given that the firm has an ongoing requirement for vacuum cleaners?
solve for the PV of each option using this formula: costs+(annual op costs/rate)(1-(1/1+r)^years) compare the PVs and accept the one with the better PV(one with the higher PV) answer: option A
You are considering an investment. If you make the investment, you will receive $5,000each of the next 4 years (these are years 1, 2, etc.). The opportunity requires an initial investment of $2,000 at time 0 plus and additional investment of $2,000 at year 2. What is the NPV of this investment if the cost of capital is 4%?
solve for the present value of the benefits by using the PV of annuity formula. then subtract the flat 2000 investment and the 2000 in two years investment(2000/1.04^2) from the benefits PV. answer: 14,300.36
diversification
spitting capital among many instruments reduces instrument-specific risk -insurance principle: many small bets are safer than one big bet
standard deviation =
square root of the variance
suppose you buy a stock for two years. in the first year the stock is up 50%; in the second year it is down 50%. what is your HPR?
t = 0 -> 1 -> 2 50% up, 50% down 0.75-1 / 1 HPR = -25%
In a well functioning market (lots of informed buyers and sellers) the expected return of an asset (rE) is related to its systematic risk only
take any asset that has systematic and unsystematic risks: -a diversified investor will see only the systematic risk -an undiversified investor will see the total risk -the diversified investors required return(rE) is lower, why? -price= D1/(rE-g) -> the diversified investor is willing to pay a higher price -the diversified investor in the one that actually buys the asset in the market
the beta coefficient of the S&O 500 is normalized to 1, every other asset is measured relative to this
take asset i with Bi, -Bi>1: asset i has more systematic risk than the market -Bi<1: asset i has less systematic risk than the market -Bi=1: asset i has the same systematic risk than the market
efficiency in asset management/turnover
talks about the asset management within the firm and how quickly assets are converted into sales quickly and efficiency inventory needs to turn into sales which turns into a collection of accounts receivable
taxes =
taxable income * tax rate
Pawn Shop XYZ charges an interest rate of 27% per month(i.e. this is the monthly rate, not the annual rate). By regulation, they must disclose (in the fine print) an APR to their customers. What is the APR they disclose and what is their EAR?
the 27% per month within a year is the interest rate per compounding period: .27 = r/12 -> .27*12 = 3.24 = APR now convert the APR to ear using the EAR formula: EAR = 16.605 answer: APR: 324.00%; EAR: 1,660.53%
what does the market to book ratio measure
the M/B ratio compares the market value of the firm's investments to their costs. ratio less than one could mean that the firm has not been successful overall in creating value for its stockholders
You want to save $X in a retirement account today (year 0) so that when you retire in 31 years you can make a one-time withdrawal of $330,000 and travel the world for a year. After that, starting at year 32 you plan to withdraw $63,000 every year for 17 years (your first withdrawal is at time 32). If the interest rate is 8.50%, how much is $X?
the PV of a one-time withdrawal: 330,000/(1.085)^31=26,314.31 the PV of the annual withdrawals(the annuity) is: (63,000/0.085)(1-(1/(1.085)^17)/(1.085)^31=44,334.60. find the sum of the two PVs to get the answer which is: 70,648.92
why are treasuries risk free?
the US government will always pay then back, though their price still fluctuates
most business decisions(from the financial perspective) come down to cost-benefit analysis.
the analysis is complicated because the Cost and the Benefits typically happen at different points in time
You have a 10-year bond, with $1,000 face value, 6.50% coupon rate, and quarterly coupon payments. It is currently trading at a price of $1,205.217. Which of the options below corresponds to this bond's yield to maturity (in APR)?
the answer: 4% confused tbh
the plug
the designed source(s) of external financing needed to deal with any shortfall or surplus in financing and thereby bring the balance sheet into balance
liquidity
the ease with which an asset can be converted into the economy's medium of exchange
suppose you want to open a savings account and you are offered two choices by your bank. 1. 10% annual rate paid at the end of the year 2. 10% annual interest rate paid every month (compounded monthly) do you have a preference and why?
the frequency of payments in a year (or in compounding periods) matters because it builds interest on interest
inventory turnover indicates?
the higher the inventory turnover ratio is, the more efficiently the inventory is being managed
Suppose you invest $1,800 into a mutual fund that is expected to earn an annual rate of return of 7%. After 16 years, how much is the interest on interest you earned?
the interest on interest is the difference between the FV WITH COMPOUNDING and the FV with just simple interest.
Yield to Maturity
the interest rate that sets the present value of the promised bond payments equal to the current market price of the bond
the Effective Annual Rate (EAR)
the interest rate that takes into account the effect of compounding; the EAR is the rate with annual compounding that gives the same result as the APR with the true compounding; the EAR is the rate with annual compounding that achieves the same FV1
what does the structure of assets for a firm reflect?
the line of business the firm is in and the managerial decisions about how much cash and inventory to have and about credit policy, fixed asset acquisition, and so on
Capital Structure
the mixture of debt and equity maintained by a firm
You need a 30-year, fixed rate mortgage to buy a new home for $250,000. Your mortgage bank will lend you the money at an annual interest rate of 6.40%. What is your monthly payment?
the monthly interest rate is 6.4%/12 = 0.5333%, and there are 30*12 = 360 monthly payments. the monthly payment is then: (250000*.00533)/(1-(1/(1.0053))^360) = 1563.76
Suppose you save $11,000 in an account that pays a 5.8% interest rate compounded monthly. What is you balance after 2 years?
the monthly interest rate will be 0.48333%. solve for the future value at time 24: 11000(1+.004833)^24 = 12,349.50
the equilibrium price is set by the diversified investor
the only risk that carries an expected return is the systematic risk *how can we measure systematic risk in an asset??* see next card
variable "C"
the payment in one type of loan
(amortized loan example) you want to buy a house worth $200,00. your bank offers you a 30-year mortgage with a 6% interest rate and monthly payments. what is your monthly payment?
the present value is the 200,000 dollars, the rate is .06 divided by the 12 months in a year(which is 0.005). 30 years times 12 months per year is a time of 360. plug this into the annuity formula and solve for c. C = 1.999
You need a 30-year, fixed rate mortgage to buy a new home for $250,000. Your mortgage bank will lend you the money at an annual interest rate of 5.20%. What is your monthly payment?
the present value is the 250,000 dollars, the rate is 5.2% divided by the 12 months in a year(which is 0.0043). 30 years times 12 months per year is a time of 360. plug this into the annuity formula and solve for c. c= answer: $1,372.78
Which of the following is a systematic risk for Exxon (an oil company)?
the price of oil declines by half
return on assets is?
the profit per dollar of assets
You want to buy a car that costs $67,000. The car dealer offers to finance the purchase with a 4 year loan with an interest rate of 8.00% and quarterly payments (first payment in one quarter). What is your quarterly payment?
the quarterly interest rate is 8%/4=2% payment = (67000*.02)/(1-(1/(1.02)^16)= 4934.56
can the Real Rate be negative? if so what would that mean?
the real rate can be negative but im pretty sure the nominal rate has to be at least 0%
financial leverage
the use of debt in a firm's capital structure
return of a portfolio is:
the weighted average of the returns on the investments in the portfolio
risk and return seem to go hand in hand
there is no free lunch!
consols are bonds without maturity, they are perpetuities
they only make coupon payments by never a face value most of the time, the issuer can recall(buy back) the bonds paying the PV of its payments
IRR is defined as the rate r that makes the NPV equal 0
think of this like the break-even cost of capital
what if the current ratio is less than 1?
this means there are less assets to pay for your liabilities; more short term bills than short term assets; not the end of the world, just need to borrow money to pay bills
Suppose you open a savings account today (time 0) so that starting at time 4 you can withdraw $75 and every year after you can increase the amount withdrawn by 7.00% with respect to the prior year. How much do you have to deposit today?
this question is broken answer: $2,895.69
net working capital =
total current assets - total current liabilities
dividends per share
total dividends / total shares outstanding
you can lose money trading treasuries even if they are risk free
treasuries are free from default risk but not PRICE RISK
Attached are the Income Statement and Balance Sheet for Company X and Company Y. If Company X could match the return on sales (ROS) of Company Y, what would be Company X's new return on equity (ROE) if all else stays equal?
use DuPont identity formula for ROE we know company Y's ROS is .3649 now we can plug that into the ROE equation along with other values found on the balance sheet (.3649)(3800/14706)(14706/7959.48) = .174209... answer: 0.174
Microsoft is considering a new investment opportunity. If they take the investment they will receive $600 million each of the next 4 years (these are years 1, 2, . . . , 4). The opportunity requires an initial investment of $150 million at time 0 and has a cost of capital of 4%. What is the net present value of this investment?
use PV of annuity equation to find the the PV of the benefits and subtract the initial investment around that to obtain the NPV answer: $2,027.94 billions
(amortized loan example) You want to buy a car that costs$36,000. Your dealer offers you 5year financing at a 7% interest rate. Find your annual payment and does it matter if you make your first payment today or in one year?
use annuity formula where we know the PV is 36,000 and we're solving for C (the annual payment) C = 8.78
(amortized example) the interest rate is 5%. when you are 30, you will deposit X in your retirement account every year so that when you retire in 35 years you can make annual withdrawals every year for 20 years (last deposit is when you are 65, first withdrawal is when you are 66). you want to withdraw $100,000 when you are 66 and then increase the amount by 2% each year to compensate for inflation. how much is x?
use growing annuity formula and solve for the PV where C=65, r=.05, g=.02, and t=20 for the 20 withdrawals. so, PV=1466. now, discount it: 1466/1.05^36 = 253.2 (66 years - 30 years). now to find x. substitute everything into the regular annuity formula with the present value = to 253.2 and solve for C. t is 36 (for the 36 deposits)
almost everywhere we use rE when we really mean E(rE)
we call rE the equity cost of capital or the required return
the price of a stock should reflect the OV of all its future dividends
we need to make assumptions about future dividends
investments in stocks have no maturity
you can buy or sell any moment
You have a 9-year bond, with $1,000 face value, 6.50% coupon rate, and semiannual coupon payments. It is currently trading at a price of $967.026. Which of the options below corresponds to this bond's yield to maturity (in APR)?
you have to plug in the value of each YTM/frequency and check which one gives you the correct price
Suppose you buy a bond with a 5% yield to maturity (YTM). This means
your annual investment return will be 5% if you do not sell the bond and the issuer makes all of its payments
