week 4 chapter 6
what is the IRR for a project with an inital investment of $250 and subsequent cash flow of $100 per year for 3 years?
9.70%
ABC CO. issues 1 million 6 percent annual coupon bonds that mature in 10 years. The face value is $1,000 per bond what are the expected cash flow from one of these bonds?
$60 in interest at the end of each year for 10 years and a $1,000 repayment of principle at the end of 10 years 6% * 10 years = $60
discount bond
A bond that sells below its par value; occurs whenever the going rate of interest is above the coupon rate discount bonds are bonds that sell for less than the face value
the payback period rule ___ a project if it has a payback period that is less than or equal to a particular cutoff date
accept
the basic NPV investment rule
accept if the NPV is greater than zero reject if less than zero if the NPV is equal to zero its is a matter of indifference to accept or reject
a project should be __ if its NPV is greater than zero
accepted
Match each information type to the form of market efficiency that identifies that type of information as being quickly and accurately reflected in the stock price.
all information - strong form efficiency all public information - semi strong form effiency historical stock prices - weak form effciency
Capital ___ is the decision- making process for accepting and rejecting projects
budgeting
The second lesson from studying capital market history states that the ______ the potential rewards the ____ the risk
pg 327 greater greater lower lower
the year 2008 was
pg 328 one of the worst years for stock market investors in US history
Two ways of calculating average returns are ___ and ___.
pg 333 geometric average return arithmetic average return
The arithmetic average rate of return measures the _____
pg 333 return in an average year over a given period
Finding a firm's overall cost of equity is difficult because:
pg 391 cannot be observed directly
to estimate the dividend yield of a particular stock we need
pg 391 forecasts of dividend growth rate g the last dividend paid D the current stock price
the growth rate of dividends can be found using
pg 392 historical dividend growth rates security analysts forcasts
The dividend growth model is applicable to companies that pay ____
pg 393 dividends
The following are advantages of the SML approach
pg 394 adjust for risk does not require the company to pay a dividend
The following are disadvantages of SML approach
pg 394 require estimation of Beta and market risk premium
What is the equation for finding the cost of preferred stock
pg 396 Rp= D/ P0
if D is the market value of a firms debt E the market value of that same firm equity V the total value of the firm (E+D)R the yeild on the firm debt T is the corporate tax rate and R the cost of equity the weight average cost of capital is
pg 397 [E/V] * Re + [D/V] * Rd * (1-t)
What is the coupon rate on a bond that has a par value of $1,000 a market value of $1,000 and a coupon interest payment of $100 per year?
pg166 annual coupon interest (C) = 100 Par value (F) = 1000 coupon rate = C/F 100/1000 = .1 or 10%
What is the definition of a bond's time to maturity
pg166 the number of years until the face value is paid off
according to the basic IRR rule we should :
pg236 reject a project if the IRR is less than the required return
Some projects as mines have cash outflows followed by cash inflows and cash outflows again giving the project multiple internal rates of return
pg252 true whenever subsequent cash flows are both negative and positive multiple internal rates of return mat occur
an efficient market is one that fully reflects all available ______
pg336 information
The NPV is ___ if the required return is less that the IRR and it is _____ if the required return is greater than the IRR
positive negative
A part of the indenture limiting certain actions during the term of the loan are termed?
protective covenant
Which of the following are true about a bond's face value?
pg 166 is also know as the par value the principle amount repaid at maturity
What is the current yield on a $1,000 par value bond that sells for $900 if the coupon rate is 10%
pg 166 (.10 * 1,000) /900 = 11.11%
When interest rates in the market fall bond values will increase because the present value of the bonds remaining cash flow?
pg 166 increases
what is the real rate of return
-it is a rate of return that has been adjusted for inflation -it is a percentage change in buying power
If stock ABC has a mean return of 10 percent with a standard deviation of 5 percent then the probability of earning a negative return is approximately ___ percent
0.05/2 - 2.5
If the arithmetic average return is 10% and the variance of return is 0.05 find the approximate geometric means
0.10 - 0.05/2 = 0.075 or 7.5%
Air Taxi, Inc has common stock with a Beta of 1.32. If the risk free rate is 2.75% percent and the expected return on the market is 10.00% percent, what is Air Taxi's cost of equity capital? Beta1 0.32 Risk-Free rate 2.75% Market return 10.00%
2.75 +(10-2.75)*1.32 = 12.32
if analyst forecast for a firm earnings growth is 7 percent and its dividend yield is 3 percent its cost of equity will be___
3 + 7 = 10%
Suppose the risk-free rate is 5 percent the market rate of return is 10 percent and beta is 2 find the required rate of return using the CAPM
5 + (2 (10-5)) = 15% pg393 SML
Your sister just deposited $6,000 into an investment account. She believes that she will earn an annual return of 8.9 percent for the next 7 years. You believe that you will only be able to earn an annual return of 8.2 percent over the same period. How much more must you deposit today in order to have the same amount as your sister in 7 years?
6000(1.089)^7 = 10897.99 6000(1.082)^7= 10416.99 10897.99 - 10416.99 = 481 To find the value of deposit today, we can find it by calculating PV of the difference. PV of th difference = FV/(1 + r)n 481/(1.082^7) = 277.05 or FV = $6,000 × 1.0897 = $10,897.99 PV = $10,897.99/1.0827 = $6,277.05 Difference = $6,277.05 − 6,000 = $277.05
A firms capital structure consist of 30 percent debt and 70 percent equity its bonds yield 10 percent pretax its cost of equity is 16 percent and the tax rate is 40 percent what is its WACC
70 * 16 + 30 * 10* (1+.40) =13%
which of the following is a disadvantage of Profitability index?
pg 257 cannot rank mutually exclusive projects
Power Manufacturing has equipment that it purchased 5 years ago for $3,050,000. The equipment was used for a project that was intended to last for 7 years. However, due to low demand, the project is being shut down. The equipment was depreciated using the straight-line method and can be sold for $500,000 today. The company's tax rate is 35 percent. What is the aftertax salvage value of the equipment?
Annual depreciation=(Cost-Salvage value)/Useful Life =(3050000/7)=$435714.2857/year Hence book value as on date of sale=Cost-Accumulated depreciation =3050000 - (435714.2857*5)=$871428.571 Hence loss on sale=$871428.571-$500,000=$371428.571 Aftertax salvage value=Sale proceeds+(loss on sale*Tax rate) =500,000+(371428*0.35) 629999.9999
The ______ rate of return is the difference between the rate of return on a risky asset and the risk free rate of return
pg 321 excess
Some important characteristics of the normal distribution are that it is:
pg 326 bell-shaped symmetrical
arrange the following investments starting from lowest historical risk premium to highest historical risk premium
US Treasury bills long term government bonds large term corporate bonds 2.8% large company stocks 8.6% small company stocks
The WACC is the overall rate of return the firm must earn on its existing assets to maintain the ____ of its stock
Value pg 397
Kasey Corp. has a bond outstanding with a coupon rate of 5.9 percent and semiannual payments. The bond has a yield to maturity of 6.3 percent, a par value of $2,000, and matures in 16 years. What is the quoted price of the bond?
Coupon = .059*2000/2 = 59 Number of Periods = 2*16 = 32 YTM semiannually = .063/2 = .0315 Price of Bond = PV of Coupon + PV of Par Value = 59*(1-(1+.0315)^-32)/.0315 +2000/(1+.0315)^32 =1920.08 price of blindquoted bond Quoted Price = 1920.08/2000*100%= 96.004 or PV = $59{[1 − (1/1.0315^32)]/.0315} + $2,000/1.0315^32 PV = $1,920.08
There is a project with the following cash flows : Year Cash Flow 0 −$25,700 1 7,500 2 7,950 3 7,350 4 5,600 What is the payback period?
Cumulative cash flow for period 0 = -25,700 Cumulative cash flow for period 1 = -25,700 + 7500 = -18200 Cumulative cash flow for period 2 = -18200 + 7950 = -10250 Cumulative cash flow for period 3 = -10250 + 7350 = -2900 Cumulative cash flow for period 4 = -2900+ 5600 = 2700 2900 / 5,600 = 0.517857142 +3 = 3.52 years
Santa Klaus Toys just paid a dividend of $2.00 per share. The required return is 11 percent and the perpetual dividend growth rate is 2.9 percent. What price should this stock sell for five years from today?
Current Price = Expected Dividend / ( Required Return - Growth Rate) = [ Current Dividend * ( 1+ Growth Rate) ] / ( Required Return - Growth Rate) = ( $ 2.00 * 1.029) / ( 11 - 2.9) = $ 25.41 Price five years from now = Current Price * ( 1+ Growth Rate) ^ 5 = $ 25.41 * (( 1+.029) ^ 5) = $ 29.31 P = [$2.00(1 + .029)^6]/(.110 − .029) P = $29.31
Ghost Riders Co. has an EPS of $1.57 that is expected to grow at 7.7 percent per year. If the PE ratio is 18.35 times, what is the projected stock price in 4 years?
Current price=EPS*PE ratio 1.57 *.1835 = .288095 current price= 28.81 Price in Year 1= current price*(1+growth) 28.81 *(1+.077)= 31.02 price in a year Price in Year 2= current price*(1+growth)^2 28.81 *(1+.077)^2 = 33.42 Price in Year 3= current price*(1+growth)^3 28.81 *(1+.077)^3 =29.42 Price in Year 4= current price*(1+growth)^4 28.81 *(1+.077)^4 =38.76 or EPS4 = $1.57(1.077)^4 = $2.11 P4 = $2.11(18.35) = $38.76
If the economy booms, RTF, Inc., stock is expected to return 13 percent. If the economy goes into a recessionary period, then RTF is expected to only return 3 percent. The probability of a boom is 81 percent while the probability of a recession is 19 percent. What is the variance of the returns on RTF, Inc., stock?
Expected Return = 81%*13 + 19%*3 Expected Return = 11.10% Variance = (13%-11.10%)^2* 81% + (3%-11.10%)^2*19% Variance = 0.001539 Answer B) 0.001539
Airfoil, Inc. announced yesterday that they earned $25,000,000 million this year. They also stated the firm's return on equity is 12% percent. Airfoil retains 90% percent of their earnings. What is the firms earnings growth rate? Earnings $25,000,000 ROE 12% Retention ratio 90%
Explanation: Present Earnings: $ 25000,000 Retention ratio: 90% Earnings reinvested: 25000,000*90% = 22500,000 Additonal earnings earned on reinvested amount: 22500,000 *12% = $2700,000 Therefore, Growth rate in earnings(as compared to previous earnings) = 2700,000 /25000,000 *100 = 10.80%
Which of the following is true about bonds
They are issued by both corporations and governments they are normally intrest only loans
The Ibbotson-Sinquefield data shows that
US T bills had the lowest risk or variability long term corporate bonds had less risk or variability than stocks
McCanless Co. recently purchased an asset for $2,750,000 that will be used in a 3-year project. The asset is in the 4-year MACRS class. The depreciation percentage each year is 33.33 percent, 44.45 percent, 14.81 percent, and 7.41 percent, respectively. What is the amount of depreciation in Year 2?
amount of depreciation in Year 2=Cost of asset*Depreciation Rate for Year 2 =$2,750,000*44.45% which is equal to 122237500
dividends paid to common stockholders____be deducted fro the payers taxable income for tax purposes
cannot
A corporate bond's yield to maturity
changes over time is usually not the same as a bonds coupon rate
Which of the following are components used in the construction of the WACC
cost of common stock cost of preferred stock cost of debt
which of the following tax deductible to the firm
coupon interest paid on bonds
Air Taxi, Inc. has issued a bond with the following characteristics: par Value = 1000 Settlement date= 1/1/2000 Maturity date = 1/1/2015 annual coupon rate = 7% Coupon per year = 2 Yield to maturity = 7%
coupon rate = market rate + bond priced at par $1,000 When the YTM and the coupon rate are equal, the bond will sell at par. The price of any bond is the PV of the interest payment, plus the PV of the par value.
Historically there is a ______ relationship between risk and expected return in the financial market
direct or positive
An advantage of AAR is that it is based on book values, not market values
false
if a bond is selling at a discount from its par value the YTM must be ___ the coupon rate
greater
The second lesson from studying capital market history is that risk is
handsomely rewarded
You purchased a bond at a price of $1,400. In 25 years when the bond matures, the bond will be worth $10,000. It is exactly 17 years after you purchased the bond and you can sell the bond today for $7,300. If you hold the bond until it matures, what annual rate of return will you earn from today?
$10,000 = $7,300 × (1 + r)8 r = ($10,000/$7,300)1/8 r = .040, or 4.0%
The risk-return relationship states that a riskier investment should demand a ______ return
higher
You expect to receive $3,900 upon your graduation and will invest your windfall at an interest rate of .59 percent compounded quarterly until the account is worth $5,350. How many years do you have to wait until you reach your target account value?
(1 + .0059)^4-1 = .023809 or 2.381 future value / present value 5350/3900 = 1.371794872 log(1.3718) / log (1.023809) = 13.43 or $5,350 = $3,900(1.0059)t t = 53.74 quarters Years to wait = 53.74/4 = 13.43 years
Giving the following information what would you expect the treasury bill rate to be? Real rate = 4.20% inflation rate = 5.80%
(1 + Treasury rate) = (1+ real rate) * (1+ inflation rate) (1+ .042 )*(1+.058) = 1.102436 or 10.24% (1 + R) = (1 + r)(1 + h).
If stock ABC has a mean return of 10 percent with a standard deviation of 5 percent, then the probability of earning a negative return greater than 15 percent is about ______precent
(1-.68)/2=16%
If stock GHI returns of 6% and -2% over 2 years the geometric average rate of return is _____
(1.06)(.98^5) -1 = 1.92%
MNO preferred stock pays a dividend of $2 per year and has a price of $20 if MNO tax rate is 40% the after tax rate of return on its preferred stock is
10%
perferred stock______
pays dividends in perpetuity pays a constant dividends
Treasury bills yielded a nominal average return over 86 years of 3.5% verse an average inflation rate of 3.0% over the same period . This makes the real return on T-bills approximately equal to ____
3.5 - 3.0 = 0.5%
An asset has an average return of 11.09 percent and a standard deviation of 21.18 percent. What range of returns should you expect to see with a 95 percent probability?
95% probability means the range is between 2 standard deviations range of return @ 95% probability = return +/- 2SD lower limits = 11.09 - (2*21.18) = -31.27% upper limits = 11.09 + (2 * 21.18) = 53.45 % range = -31.27 , 53.45 =
Which one of the following stocks is correctly priced if the risk-free rate of return is 4.0 percent and the market risk premium is 8.5 percent? Stock Beta Expected Return A .79 12.30% B 1.56 17.26 C 1.37 11.34 D 1.35 16.68 E .95 8.65
A = .04 + .79 * 8.5 = 10.72 B= 4% + 1.56 *8.5% = 17.26% C=4%+1.37*8.5% = 15.65% D4% + 1.35 * 8.5% = 15.48% E = 4% +.95 * 8.5% = 12.08%
WACC was used to compute the following project NPV project A = 100 Project B = -50 project C = -10 Project D = 40 which project should the firm accept
A and D
A stock had returns of 14.35 percent, 18.75 percent, −14.55 percent, 12.35 percent, and 25.03 percent for the past five years. What is the variance of the returns?
Average return = (.1435 + .1875 − .1455 + .1235 + .2503)/5 Average return = .11186 Variance = (.1435 - .11186)^2 +.(1875 - .11186)^2 - (.1455 -.11186)^2 + (.1235 - .11186)^2 + (.2503 - .11186)^2 ) /4 =.2306
A stock had returns of 18.54 percent, 21.88 percent, −15.08 percent, 9.08 percent, and 28.15 percent for the past five years. What is the standard deviation of the returns?
Average return = (.1854 + .2118 − .1508 + .0908 + .2815)/5 Average return = 12.51% Variance = [(.1854 - .1251)^2 + (.2118 -.1251)^2 +(-.1508 - .1251)^2 + (.0908 - .1251)^2 + (.2815 - .1251)^2 = .114717404 /4 Variance = ..285% Standard deviation = ..02854351 ^.5 Standard deviation = 16.89%
A stock had returns of 18.58 percent, −5.58 percent, and 20.81 percent for the past three years. What is the variance of the returns?
Average return = (.1858 − .0558 + .2081)/3 Average return = .1127, or 11.27% Variance = 1/2[(.1858 − .1127)2+ (−.0558 − .1127)2+ (.2081 − .1127)2]Variance = .02142
Air Taxi, Inc. is considering a new 3-year expansion project that requires an initial fixed asset investment of $1,500,000 million dollars. The asset will be depreciated over a 3 year tax life and have no salvage value. The project is estimated to have annual cash flows of $1,210,000 with a cost of $475,000. The tax rate is 35% percent and the required rate of return is 11% percent. What is the project NPV? Asset investment $1,500,000 Estimated annual sales $1,210,000 Costs $ 475,000 Tax rate 35% *Depreciation straight-line to zero over tax life 3 Required return 11%
Depreciation as per straight line method= $15,00,000/3=$5,00,000 Tax rate= 35% Depreciation Tax Shield=$5,00,000*35%=$1,75,000 Annual sales=$12,10,000 Annual cost=$4,75,000 Annual pre-tax earnings=$(12,10,000-4,75,000)=$7,35,000 Post tax earnings=$(7,35,000*65%)=$4,77,750 Thus, post tax annual cash flow= Post tax annual earnings + Depreciation Tax Shield =$(4,77,750+1,75,000) =$6,52,750 Since cash flow is same in each year, we will use Present Value Annuity Factor. Required return= 11% and Time=3 years PVAF( (1/(1+.11^1) + (1/(1.11^2) +(1/(1+.11^3) = .9009+ .8116+ 7312 =2.4437 NPV = post - tax annual cash flow * PVAF - initial investment = (652750 * 2.4437) - 1500000 = 1595125.175 - 1500000 = 95125 Using the tax shield approach to calculating OCF, we get: OCF = (Sales - Costs)(1 - tC) + tCDepreciation; Therefore NPV = Asset Investment + the Present Value Interest factor of the OCF.
Shares of common stock of the Samson Co. offer an expected total return of 15.80 percent. The dividend is increasing at a constant 5.00 percent per year. The dividend yield must be:
Dividend yield=Expected total return-Constant growth rate .1580 - .05 = 10.8% or Dividend yield = 15.80% - 5.00% = 10.80%
Which of the following are ways to make money by investing in stocks
Dividends capital gain
as a general rule which of the following are true of debt and equality?
Equity represents an ownership interest the maximum reward for owning debt is fixed
Given the following information what is the percentage change in the price of the bonds if interest rates suddenly rise by 7%? Wing Air Inc. Coupon rate 7% Settlement date 1/1/2000 Maturity date 1/1/2002 Face value 1,000 # of coupons per year =2 Airfoil, Inc. Coupon rate = 7% Settlement date 1/1/2000 Maturity date 1/1/2015 Face value =1,000 # of coupons per year =2 Change in interest rate =2%
N=4 FV = 1,000 PMT =
If a project has multiple internal rates of return, which of the following methods should be used?
NPV MIRR
What is the NPV of a project with an initial investment of $95, a cash flow in one year of $107, and a discount rate of 6%?
NPV = -95 + (107/1.06) = 5.94
the spreadsheet function for calculating net present value is ____
NPV(rate,CF1...,CFn) +CFO
Jenny Enterprises has just entered a lease agreement for a new manufacturing facility. Under the terms of the agreement, the company agreed to pay rent of $10,500 per month for the next 6 years with the first payment due today. If the APR is 6 percent compounded monthly, what is the value of the payments today?
Number of months = 6*12 = 72 monthly rate= 6/12= .50% Value of payment today = PVAD .50%,72 * Rent amount = 60.64121* 10500 = $ 636,732.71 **Find present value annuity due factor from table at .50%,for 72 periods .or using the financial calculator. or PV = $10,500(1.0050)[(1 −1/1.005072) / .0050] = $636,732.72
Sun Brite has a new pair of sunglasses it is evaluating. The company expects to sell 6,100 pairs of sunglasses at a price of $156 each and a variable cost of $108 each. The equipment necessary for the project will cost $320,000 and will be depreciated on a straight-line basis over the 9-year life of the project. Fixed costs are $220,000 per year and the tax rate is 40 percent. How sensitive is the operating cash flow to a $1 change in variable costs per pairs of sunglasses?
OCF at ((156 - 108) * (6100) - 220000) * (.6) + .40 * (320000/9) =57902.22 ((156 - 107) * (6100) - 220000) * (0.6) +.4 *(320000/9) = 181122.2222 (181122.22 - 57902.22) / (107 - 108) = -123220
Maxxie purchased a tract of land for $32,000. Today, the same land is worth $48,400. How many years have passed if the price of the land has increased at an annual rate of 5.2 percent?
P(1+r/100)^n 48400= 32000(1+.052)^n in cal log(48400/32000)/log (1.052) = 8 years
What is the profitability index for a project with an inital cash outflow of $30 and subsequent cash inflows of $80 in year one and $20 in year two if the discount rate is 12%
PI = (PV/inital cost) (80/1.12) +(20/(1.12^2) = 87.3724 / 30 = 2.91
Contrail Air Inc. runs a small drone manufacturing business. For this year, the company expects real net cash flow of $175,000. The company expects its cash flow to erode at a rate of 2% percent per year in perpetuity. The appropriate real discount rate for the company is 9% percent. Assume all cash flows received at the end of the year. What is the present value of the cash flows? Cash flow $175,000 Cash flow growth rate -2% Required return 9%
PV of Caash Flows = CF1 / ( Req Ret - g) = $ 175,000 / ( 9% - (-2%) ) = $ 175,000 / (9% + 2%) = $ 175,000 / 11% = $ 1590909.091 PV=C1/(R-g)
Bond Value
PV of coupons + PV of par OR PV of annuity + PV of lump sum
Cavu Air Inc., a drone manufacturer, is reviewing its annual budget. It is considering investments in three different technologies. Consider the following cash flows of the three independent projects. Assume a discount rate of 12% percent. The company has $20 million to invest in projects this year. Required return is 12% Annual cash flows Projects A year 0 =8,500,000 B year 0 =12,500,000 C year 0 = 18,000,000 Year 1 A $11,000,000 B $10,000,000 C $18,000,000 Year 2 A $7,500,000 B $25,000,000 C $32,000,000 Year 3 A $2,500,000 B $20,000,000 C $20,000,000 Based on the NPV, rank these investments.
PVCF = CF /(1+R^Y) PV = PVCF/CF project A PV@12% year 0 8500,000 PV=1 PVCF = 8500,000 year 1 11,000,000 PV =.8929 PVCF= 9,821,429 year 2 7,500,000 PV=.7972 PVCF= 5978954 Year 3 2,500,000 PV= .7118 PVCF = 1779451 9821429+5978954+1779451= 17579834 - 9079834 NPV Project B 12% year 0 (12500000) pv =1 PVCF = (12500000) year 1 10000000 PV= .8929 PVCF=8928571 year 2 25000000 PV .7972 PVCF= 19929847 year 3 20000000 PV .7118 PVCF = 14235605 NPV=8928571+19929847+14235605 = 43094023 - 12500000 = 30594023 PROJECT C 12% year 0 18000000 PV=1 PVCF= 18000000 year 1 18000000 PV= .8929 PVCF = 16071429 year2 32000000 PV=.7972 PVCF= 25510204 year 3 20000000 PV .7118 PVCF 14235605 1607149+25510204+14235605 = 55817238 - 18000000 NPV = 37817238 answer CBA NPV implies we accept project C since it has the highest NPV. This is the correct decision if the projects are mutually exclusive. The next project with the highest NPV is project B.
A project with an initial investment of $446,900 will generate equal annual cash flows over its 8-year life. The project has a required return of 8.7 percent. What is the minimum annual cash flow required to accept the project?
Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate 446900 =Annuity[1-(1.087)^-8]/0.087 446900=Annuity*5.597072728 Annuity=446900/5.597072728 79845.31
A project with an initial cost of $62,400 is expected to provide annual cash flows of $12,900 over the 7-year life of the project. If the required return is 8.1 percent, what is the project's profitability index?
Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate =$12900[1-(1.081)^-7]/0.081 =$66933.08632 PI=Present value of inflows/Present value of outflows =$66933.08632/$62400 which is equal to =1.072645614(Approx).
A company. has a project available with the following cash flows: Year Cash Flow 0 −$34,550 1 12,750 2 14,740 3 20,080 4 11,360 If the required return for the project is 8.5 percent, what is the project's NPV?
Present value of inflows=cash inflow*Present value of discounting factor(rate%,time period) =12750/1.085+14740/1.085^2+20080/1.085^3+11360/1.085^4 =$48190.00 NPV=Present value of inflows-Present value of outflows =$48190.00 - $34550 = 13640.00
What is the price of a 15 year zero coupon bond paying $1,000 at maturity if the YTM is 5% percent? years to maturity = 15 years Face Value = $1,000 Yeild to Maturity= 5%
Price of Bonds: Value of bonds = F/(1+r)^t 1000/(1+.05)^15 = $476.74 PV=FV/(1+r/2)^t
POD has a project with the following cash flows: Year Cash Flows 0 −$285,000 1 145,300 2 162,800 3 127,900 The required return is 8.1 percent. What is the profitability index for this project?
Profitability index = Present vaue of cash inflows / Initial investment Present value of cash inflows = 145300 / ( 1 + 0.081)1 + 162800 / ( 1 + 0.081)2 + 127900 / ( 1 + 0.081)3 Present value of cash inflows = 374978.8618 Profitability index = 374978.8618 / 285000 Profitability index = 1.316
The formula for calculating the cost of equity capital that is based on the dividend discount model is
RE = D1 / P0 + g pg391
An asset has an average return of 10.43 percent and a standard deviation of 19.26 percent. What range of returns should you expect to see with a 68 percent probability?
Range of Returns = (Average Return - Standard Deviation) to (Average Return + Standard Deviation) 10.43 - 19.26 = -8.83 10.43 + 19.26 = 29.69
What is required return on a stock R according to the constant dividend growth model if the growth rate (g) is zero
Re= D1/P0 pg391
Given the following information, what is the historical real return for long-term government bonds? Long-term government 6.00% Long-term corporate 6.10% Inflation rate 2.95%
Real return = [( 1 + nominal return) / ( 1 + inflation)] - 1 [ (1+ .06) / (1+.0295) ] -1 =.0296260321 2.96%
The common stock of Flavorful Teas has an expected return of 16.00 percent. The return on the market is 15 percent and the risk-free rate of return is 3.7 percent. What is the beta of this stock?
Required Return = Risk free rate + beta * (market return - risk free rate) 0.1600 = 0.037 + beta*(0.15 - 0.037) 0.123 = beta*0.113 beta = 1.0884
You want a seat on the board of directors of Four Keys, Inc. The company has 285,000 shares of stock outstanding and the stock sells for $52 per share. There are currently 4 seats up for election. The company uses straight voting. How many shares do you need to guarantee that you will be elected to the board?
Shares necessary = 285,000/2 + 1 = 142,501 shares or
Consider the following information about two stocks and indicate which stock has the most systematic risk. State Probability Stock A Stock B Recession 0.15 0.11 (0.35) Norman 0.55 0.18 0.11 Boom 0.30 0.08 0.31 Market risk premium 8.50% Risk-free rate 3.00%
Stock A expected return = (.15*.11) + (.55*.18) + (.30*.08) = .1395 Beta = (Expected Return - Risk-free Rate) / Market Risk Premium (.1395 - .03) / .0850 = .117647059 Stock B Expected return = (.15 * -.35) + (.55* .11)+ (.30 *.31) =.101 stock A is risker The amount of systematic risk is measured by the Beta of an asset. Since we know the market risk premium and the risk-free rate, if we know the expected return of the asset we can use the CAPM to solve for the Beta of the asset. Although Stock B has more total risk than A, it has much less systematic risk, since its beta is much smaller than A's. Thus, A has more systematic risk, and B has more unsystematic and more total risk.
CDB stock is currently priced at $67. The company will pay a dividend of $4.97 next year and investors require a return of 11.3 percent on similar stocks. What is the dividend growth rate on this stock?
Stock price = Dividend next period/(Requires rate- growth rate) 67=4.97/(0.113-d) 0.113-d=4.97/67 0.113-d=0.0741791045 .0741791045 - .113 = 38.88% or Dividend yield = $4.97/$67 = 7.42% Dividend growth rate = 11.30% − 7.42% = 3.88%
A prominent alumnus of your university has just donated $2,700,000 to fund a scholarship that will distribute $101,000 per year forever beginning in one year. For this to be true, what rate of return is expected on the donation?
Total Amount = Per Year Distributions / rate of Return rate of Return = Per Year Distributions / Total Amount = $ 101,000 / $ 2,700,000 * 100 = 3.74% or R = $101,000/$2,700,000 = .0374, or 3.74%
A portfolio consists of $13,800 in Stock M and $19,900 invested in Stock N. The expected return on these stocks is 8.20 percent and 11.80 percent, respectively. What is the expected return on the portfolio?
Total investment=(13800+19900)=$33700 Hence expected return of portfolio=Respective return*Respective weights =(13800/33700 *8.20) +(19900/ 33700*11.80) 10.32
There are zero coupon bonds outstanding that have a YTM of 5.13 percent and mature in 15 years. The bonds have a par value of $10,000. If we assume semiannual compounding, what is the price of the bonds?
Value of zero-coupon bond = Face vale / (1+required return) ^time to maturity 10000= (1+(.0513/2)^15*2 10000 / 1.02565 ^15*2 10000 / 1.02565 ^30 10000/2.137841635 4677.61 or PV = $10,000/(1 + .0513/2)^30 PV = $4,677.61
A firms capital structure consist of 40 percent debt and 60 percent equity. The after tax yield on debt is 2.5 percent and the cost of equity is 15 percent the project is about as risky as the overall firm what discount rate should be used to estimate the projects net present value
WACC = (.4* .025) +(.6* .15) = .1 = 10%
Assuming an interest rate of 4.8 percent, what is the value of the following cash flows five years from today? year 1 = 3,465 year 2= 4,595 year 3 =5,555 year 4=6,820
We use the formula: A=P(1+r/100)^n where A=future value P=present value r=rate of interest n=time period. Hence A=$3465(1.048)^4+4595(1.048)^3+5555(1.048)^2+6820(1.048)^1 which is equal to =$22717.12(Approx). or FV = $3,465(1.048)4 + $4,595(1.048)3 + $5,555(1.048)2 + $6,820(1.048) = $22,717.12
You need to have $33,500 in 14 in years. You can earn an annual interest rate of 5 percent for the first 4 years, 5.6 percent for the next 3 years, and 6.3 percent for the final 7 years. How much do you have to deposit today?
We use the formula: A=P(1+r/100)^n where A=future value P=present value r=rate of interest n=time period 33500 = P*(1.05)^4*(1.056)^3*(1.063)^7= 2.195238964 33500/2.195238964 = 15260.29765 or PV = $33,500/1.0637 = $21,842.98 PV = $21,842.98/1.0563 = $18,548.99 PV = $18,548.99/1.0504 = $15,260.30
A bond with a coupon rate of 5.24 percent and semiannual coupon payments matures in 14 years. The YTM is 6.43 percent. What is the effective annual yield?
YTM=6.43 semi YTM= 6.43/2 = 3.215 / 100= .03215 Effective Annual Yield = (1 + Semiannual YTM)^2 - 1 (1+.03215)^2-1 6.53% or PV = $59{[1 − (1/1.0315^32)]/.0315} + $2,000/1.0315^32 PV = $1,920.08 ffective rate = (1 + .0643/2)^2 − 1 = 6.53%
if a stock has returns of 10 percent and 20 percent over 2 years the geometric average rate of return can be calculated by _____
[(1.10) (1.20)]^5 -1
advantages and disadvantages of IRR
crossly related to NPV with simulare results easy to understand disadvantages: multiple answers with noncomvential cash flows may lead to incorrect decisions
to estimate the dividend yield of stock we need
current stock price forecast of dividends growth rate g the last dividend paid D0
When calculating NPV the present value of n^th cash flow is found by dividing the n^th cash flow by 1 plus ____ rate raised to the n^th power
discount
Contrail Air Inc., Just paid a dividend of $1.75 per share on its stock. The dividends are expected to grow at a constant rate of 4% percent per year, indefinitely. If investors require a return of 13% percent, what is the current price? Dividend paid $1.75 Dividend growth rate 4% Required return 13% Requested year 0
dividend $1.75 which will grow every year at 4%. Next dividend = Dividend just paid * (1+ Growth rate) = $1.75 * 1.04 = $1.82 Current price of share = Next dividend/(Required return - Growth rate) Current price of share = $1.82/(0.13 - 0.04) = $20.22 or The constant dividend growth model is Pt = Dt × (1 + g) / (R - g).
what can we say about dividends paid to common and preferred stockholders
dividends to preferred stockholders are fixed Dividends to common stockholder are not fixed
Which of the following is NOT a difference between debt and equity
equity is public traded where debt is not
if a stocks return for years 1 to 4 were 3% 5% 8% and 2% what is the standard deviation of these returns
in calculator stat>edit> enter list>stat calc>1 var >enter Sx is your SD 4.203%
Stock prices fluctuate day to day because of
information flow
Internal Rate of Return (IRR) formula
investment / annual cash flows = PV factor
Components of the WACC include funds that come from ____________
investors
which is true about a firms cost of debt
it is easier to estimate than the cost of equity yields can be calculated from observing data
The most appropriate weights to use in the WACC are the _____ weights
market value
The normal distribution is completely described by the_____ and _______
mean variance or standard deviation
High cash flows earlier in a projects life are ____ valuable than higher cash flows later on
more present value is inversely related to time. cash flows early are more valubale for reinvestments
You just won the $90 million Ultimate Lotto jackpot. Your winnings will be paid as $4,500,000 per year for the next 20 years. If the appropriate interest rate is 7.8 percent, what is the value of your windfall?
n=20 pmt= 4500000 rate= .078 4500000[1-(1.078^-20]/.078 4500000 * 9.966011947 44847053.76 or PV = $4,500,000[(1 −1/1.07820)/.078] = $44,847,053.76
If you use an arithmetic average to project long-run wealth levels your results will most likely be _______
optimistic
Thom owes $4,000 on his credit card. The credit card carries an APR of 16.8 percent compounded monthly. If Thom makes monthly payments of $100 per month, how long will it take for him to pay off the credit card assuming that he makes no additional charges?
owe = 4000 APR =16.8 monhly intrest r = .168/12 = .014 month payment = 100 PV = P* [ 1 - (1/ (1+r)^n)/ r ] 4000=100 (1-1.014)^n/ .014 4000/100= 40 40 * 0.014 = 1 - (1 / (1.014)^n ) 0.56 = 1 - (1 / (1.014)^n ) -0.44 = - (1 / (1.014)^n ) 0.44 = (1 / (1.014)^n ) 1.014^n = 1/ 0.44 1.014^n = 2.27272 How We have to find the value of n where 1.014 become equal to 2.27272 Using Calculator at 59 payments value is = 2.23975 hence the payment period is near around 59 months. So the answer is 59.05 months. or $4,000 = $100{[1 − 1/(1 + .168/12)t]/.168/12} t = 59.05 months
Equity represents a _________interest of a firm
ownership
Cavu Air Inc., issued 15 Year bonds 2 years ago at a coupon rate of 5.30% percent. The bonds make semi annual payments. If these bonds currently sell for 102 percent of par value, what is the YTM? Settlement date1/1/2000 Maturity date=1/1/2013 Annual coupon rate =5.30% Coupons per year=2 Face value (% of par) =100 Bond price (% of par)= 102
par value = 1000 coupon rate = .053 semi coupon rate = coupon rate /2 =.0265 maturity years =13 number period= maturity*2 = 26 current selling price = 1025 %*1000= 10200 semi coupon paymeny = semi coupon rate * par value = 26.5 YTM= # period, semial coupon payment, current selling, par value) see excel
A firm decides to raise money by issuing 5 million bonds with a par value of $5,000 each for 10 years at a coupon rate of 7 percent. AT the time of issue the bonds were sold for $5,500 each what will the par value of the bonds be in year 5?
par value is not effected by the interest rate, market price or time so it would remain 5,000
An investment project provides cash flows of $595 per year for 5 years. What is the project payback period if the initial cost is $5,500. Annual cash inflow $595 # of years 5 Initial cost $5,500
payback period = inital cost / annual cash inflow 5500 / 595 = 9.24
Assuming a bond has a $1,000 par value a coupon rate of 6 % annual interest payments and 7 years to maturity. If the yield on similar bonds is 8 percent what is the current market value of this bond
pg 167 P= bond price C = coupon (6%*1000) =60 y= current rate interest = 8% FV=1000 T= time of maturity 4 (60/.08)*(1-1/(1.08)^7) = 312.38 1000 /(1.08)^7)=583.49 312.38+383.49= 895.87
if the present value of the interest payments on bonds is $320 and the present value of the par value to be paid at maturity is $900 the total value of the bonds must be?
pg 167 bond value= 320 + 900 = 1,220
If a $1,000 par value bond is trading at a premium the bond is
pg 168 trading for more than $1,000 on the market
Which of the following is the most important source of risk from owning bonds?
pg 170 market interest rates fluctuations coupon interest rate are fixed
The sensitivity of a bond's price to interest rate changes is dependent on which of the following two variables?
pg 170 coupon rate time to maturity
If you are holding two bonds one with a 5% coupon rate and the other with a 8% coupon rate which one is more sensitive to interest risk all other things are equal
pg 170 the lower the coupon rate the higher the risk so the bond at 5%
What is a bond's current yield?
pg 172 current yield = annual coupon payment / price
if the IRR is greater than the _____ _______ we should accept the project
pg 236 required return
PI rule for an independent project is to _____ the project if the PI is greater than 1
pg 236 accept
the internal rate of return is a function of
pg 236 dependent on the cash flow
The present value of the future cash inflows are divided by the _____ to calculate the profitability index
pg 236 initial investment
in capital budgeting____ determines the dollar value of a project to the company
pg 238 net present value
payback period ignores time value of money
pg 244 true
The payback period can lead to foolish decisions if it is used too literally because:
pg 244 it ignores cash flows after the cutoff date
in general NPV is
pg 248 Positive for discount rates below the IRR. Negative for Discount rates above the IRR Equal to zero when the discount rate equals the IRR.
A_____ project does not rely on the acceptance or rejection of another project
pg 250 independent
A project with non-conventional cash flow will produce two or more IRRS
pg 250 true
If a firm is evaluating two possible projects both requiring the use of the same production facilities and take one project means that we cannot take the others these projects would be considered____________
pg 252 mutually exclusive
which of the following are reasons why IRR continues to be used in practice?
pg 254 IRR can be calculated without the discount rate they are easier to communicate information about a proposal business people prefer to talk about rate of return
which of the following methods of calculating the MIRR of a project
pg 255 reinvestment approach discounting approch combination approach
studying market history can reward us by demonstrating
pg 310 greater the potential reward is the greater the risk there is a reward for bearing risk
What does WACC Stand for?
pg 389 weighted average cost of capital
which of the following are weaknesses of the payback method?
pg243 cash flows received after the payback period are ignored time value of money principles are ignored the cutoff date is arbitary
The efficient hypothesis contends that ____ capital markets such as the NYSE are effcient
pg337 well organized
If a stock had an initial price of $75 per share, paid a dividend of $1.50 per share during the year, and had an ending share price of $90. Compute the percentage total return. Initial price $75 Dividend paid $1.50 Ending share price $90
precentage total return of the stock = (ending price of share + dividends paid) / inital paid -1 (90 +1.50) /75 +1 = 22.2%
Wing Air, Inc. has a project with the following cash flows: Required Return of 8%. Annual cash flows: Year 0 $(15,000) Year 1 $5,800 Year 2 $7,600 Year 3 $8,200 What is the internal Rate of Return (IRR)?
present value = cash flow /(1+R^Y) PVF @20% = PV / cashflow year 1 CF= -5800 PVF = .8333 PV= 48333.33 year 2 CF= 7600 PVF= .69444 PV = 5277.778 year 3 8200 PVF = .578704 PV= 4745.37 add all pv 48333.33 +5277.778+475.37 = 14856.483 -5000 NPV=-143.519 PVF @19% repeat top year 1 = 5800 PVF=.840336 PV=4873.95 year 2 = 76000 PVF= .706165 PV=536.853 year 3 = 8200 PVF = .593416 PV=4866.01 4873.95 + 536.853 + 4866.01 = 15106.813 - 15000 = npv=106.813 IRR= LOWER RATE + NPV AT LOW RATE / DIFFERANCE OF RATES .19 + (107/ (143+107) *1% = 19.42% or CO +C1 / (1+IRR) +C2 / (1+IRR)2 + C3 / (1+IRR)3/ (1+IRR)3
You purchase a bond with an invoice price of $1,069. The bond has a coupon rate of 5.84 percent, it makes semiannual payments, and there are 4 months to the next coupon payment. The par value is $1,000. What is the clean price of the bond?
purchas price = 1069 par value =1000 coupon rate = .0584 2 month intreast =1000* coupon rate * (2/12) 1000* .0584 * (2/12)= 9.73 purchase price - accrued interest 1069 - 9.73 = 1059.27 or Coupon payment = .0584($1,000)/2 = $29.20 Accrued interest = $29.20[(6 − 4)/6] = $9.73 Clean price = $1,069 − 9.73 = $1,059.27
There is a zero coupon bond that sells for $435.47 and has a par value of $1,000. If the bond has 14 years to maturity, what is the yield to maturity? Assume semiannual compounding.
rate = (FV/PV)^(1/t)-1 435.47=1000/(1+rate/2)^(2*14) 435.47=1000/(1+rate/2)^28 1000/435.47= 2.29636944 ^(1/28) = 1.030135487 1.030135487 -1 = .030135487 *2 =.060270974 6.03% or $435.00 = $3/(1 + r)^28 r = .0301, or 3.01% YTM = 3.01% × 2 = 6.03%
suppose the risk free rate is 5.5% the market rate of return is 8.5% and the beta is 1.25 find the required rate of return using the CAPM
risk free rate +(beta *(market rate - risk free rate )) = 9.25
A 4-year project has an annual operating cash flow of $54,500. At the beginning of the project, $4,550 in net working capital was required, which will be recovered at the end of the project. The firm also spent $23,000 on equipment to start the project. This equipment will have a book value of $4,900 at the end of the project, but can be sold for $5,850. The tax rate is 34 percent. What is the Year 4 cash flow?
salvage value = 5850 book value = 4900 salvage - book value = 950 tax gained = 950 * .34 = 323 after tax salvaged = 5850 - 323 = 5527 operating cost = 54500 net WC = 4550 after tax salvage = 5527 add them up = 64577
to estimate a firms equity cost of capital using the CAPM we need to know the ____
see # 156 stock beta risk free rate market premium
If a study of firms financial information will not lead to gains in the market that the market must be at least ______ effcient
semi strong form
Geometric averages are usually ______ arithmetic averages
smaller
if a series of stock returns has a variance of .0068 what is the standard deviation?
square .0068 = 8.246%
The ____________________ tells us that the expected return on a risky asset depends only on that asset's nondiversifiable risk.
systematic risk principle
The Ibbotson SBBI show that over the long term____
t-bills had lower risk and lower return small companies stock have higher return small company stocks have higher risk
according to the average accounting return rule a project is acceptable if it averages accounting return exceeds:
targeted average accounting return
If you are holding two identical bonds except that one matures in 10 years and the other matures in 5 years which bond's price will be more sensitive to interest rate risk
the 10 year bond since the longer the terms the greater the intrastate rate sensitivity pg170
par value
the amount that an investor pays to purchase a bond and that will be repaid to the investor at maturity
SmartKids a textbook publisher iss considering investing in a software company that collects and stores data what beta should SmartKids use to assess the risk of the project
the beta for software companies that hold and store data
Specifying variables in the Excel NPV function differs from the manner in which they are entered in a financial calculator in which of the following ways?
the discount rate in excel in entered as a decimal or percentage the range of cash flow specified in excel begins with cashflow #1 not cashflow 0 withe excel NPV function cashflow #0 must be handled outside the NPV function excels NPV function is actually a PV function
what are the advantages of the payback period method for management
the payback period method is easy it allows for level managers to make small decisions payback period method is ideal for minor projects
Airfoil, Inc. has issued a bond with the following characteristics: Par Value=1,000 Settlement date=1/1/2000 Maturity date=1/1/2015 Annual coupon rate =7.00% Coupons per year=2 Yield to maturity=9% What is the price of the bond?
the price of the bond = 837.11 semi annual coupon = (7% / 2)*1000=35 semi annual maturity = 9%/2=.045 time = (20015 -2000) *2=30 price of bond= coupon *(1-1+r)^-n)R+F/(1+r)^n ((35 * (1-.045^-30)/.045)+1000/1.045^30 price of bond = 570.11 +267.00 = 837.11
according to the CAPM what is the expected return on stock if beta is equal to zero
the risk free rate
What four variables are required to calculate the value of a bond?
time remaining to maturity par value coupon rate yield to maturity
You own a portfolio that has $1,800 invested in stock A and $3,900 invested in stock Z. If the expected returns on these stocks are 14% percent and 10% percent respectively, what is the expected return on the portfolio? Stock A $ value $1,800 Stock A E(R) 14.00% Stock Z $ value $3,900 Stock Z E(R) 10.00%
total value = stack A + stock Z 1800 + 3900 = 5700 expected return = (1800 / 5700*14) + (3900 / 5700 * 10) = 11.26
The square of the standard deviation is equal to the _______
variance
Which are true
we should use the market value in the WACC the market value of debt and equity are not reliable for a privatly owned company false statements: book value is used in WACC book value and market value are simular
If a study of past prices and volumes to find mis-priced securities will not lead to gains in the market then the market must be at least _______ efficient
weak form
You own a portfolio that has a total value of $255,000 and it is invested in Stock D with a beta of .78 and Stock E with a beta of 1.47. The beta of your portfolio is equal to the market beta. What is the dollar amount of your investment in Stock D?
wieght of stock D=d wieght of stock E=e Now e=(1-d) since there are two stocks Hence 0.78*d + 1.47 (1-d)=1 0.78d +1.47 -1.47d=1 -0.69d=-0.47 d=(0.47/0.69) Hence Value of stock D= (0.47/0.69) *255,000=17369565
Cirice Corp. is considering opening a branch in another state. The operating cash flow will be $151,600 a year. The project will require new equipment costing $565,000 that would be depreciated on a straight-line basis to zero over the 6-year life of the project. The equipment will have a market value of $159,000 at the end of the project. The project requires an initial investment of $36,500 in net working capital, which will be recovered at the end of the project. The tax rate is 40 percent. What is the project's IRR?
year 0 cash flow = -565000 - 36500 =-601500 year 1 =151600 year 2 151600 year 3 151600 year 4 151600 year 5 = (151600 + 36500 + (159000 * .60) =283500 in excel IRR year 0: year 5)
For a firm with outstanding debt, the cost of debt will be the ____________ on that debt.
yields to maturity
The IRR is the discount rate that makes NPV equal to ________________.
zero
