finance quiz 3 questions
Compute the NPV for Project X with the cash flows shown below if the appropriate cost of capital is 8 percent. Time: 0 1 2 3 4 5 Cash flow: -110 -110 0 170 145 120 $111.35 $103.10 $323.20 $111.90
$111.35
Compute the Payback statistic for Project X and recommend whether the firm should accept or reject the project with the cash flows shown below if the appropriate cost of capital is 12 percent and the maximum allowable payback is 4 years. Time: 0 1 2 3 4 5 Cash flow: -2,100 350 700 800 750 525
3.33 years, accept (bc it is less than the max allowable payback, if this isnt given, assume the max allowable payback is 2 yrs)
Compute the Payback statistic for Project X and recommend whether the firm should accept or reject the project with the cash flows shown below if the appropriate cost of capital is 10 percent and the maximum allowable payback is 4 years. Time: 0 1 2 3 4 5 Cash flow: -2,300 250 550 900 800 575
3.75 accept
A preferred stock from Duquesne Light Company (DQUPRA) pays $2.60 in annual dividends. If the required return on the preferred stock is 5.50 percent, what's the value of the stock?
47.27
Ultra Petroleum (UPL) has earnings per share of $1.69 and a P/E ratio of 33.20. What's the stock price? (Round your answer to 2 decimal places.) Stock price $
56.11
Financial analysts forecast Safeco Corp.'s (SAF) growth rate for the future to be 13 percent. Safeco's recent dividend was $1.70. What is the value of Safeco stock when the required return is 15 percent?
96.05
Stock price equation
=Price/Earnings ratio * EPS
growing vs. ordinary perpetuity
ordinary:cash inflows of the project go on forever, growing:cash flows here grow at a constant rate forever
This is the process of estimating expected future cash flows of a project using only the relevant parts of the balance sheet and income statements. incremental cash flows cash flow analysis substitutionary analysis pro forma analysis
pro
This is the process of estimating expected future cash flows of a project using only the relevant parts of the balance sheet and income statements. incremental cash flows substitutionary analysis pro forma analysis cash flow analysis
pro forma analysis
A preferred stock from Duquesne Light Company (DQUPRA) pays $4.10 in annual dividends. If the required return on the preferred stock is 7.00 percent, what's the value of the stock?
value of stock = $58.57
Financial analysts forecast Safeco Corp.'s (SAF) growth rate for the future to be 10 percent. Safeco's recent dividend was $1.30. What is the value of Safeco stock when the required return is 12 percent?
value of stock= $71.50
what is 20/20 preferred stock?
we have a stock that pays no dividends for 20 years. Once the stock begins paying dividends, it will have the same dividends forever
when do you find the crossover rate?
when deciding between which projects to choose over a range of discounts that you have to find To find the crossover rate, we subtract the cash flows from one project from the cash flows of the other project. Here, we will subtract the cash flows for Project B from the cash flows of Project A. Once we find these differential cash flows, we find the IRR by entering the new cfs into the calc & CPT IRR
when do you know not to multiply the $ amount given by 1+ g when calculating price per share?
when it says "the next dividend for the company will be $X per share" and you are calculating price per share
when do you accept a project when using required return and IRR
when the cash flows are conventional and the IRR is greater than the required return, we would accept the project.
Ultra Petroleum (UPL) has earnings per share of $1.49 and a P/E ratio of 32.80. What's the stock price?
$48.87
Calculating NPV if all cash flows are "blocked" by the government (ex: blocked for 1 year)
1 First, we need to find the future value of the cash flows for the one year in which they are blocked by the government. Do this by multiplying each cash flow by (1+ reinvestment rate) 2 calculate NPV by multiplying the FVs we just found by (1+ req. return)^n and then adding them together 3 enter FVs that we calculated in step 1 into the calculator as cash flows and CPT NPV
Calculating IRR if all cash flows are "blocked" by the government (ex: blocked for 1 year)
1 First, we need to find the future value of the cash flows for the one year in which they are blocked by the government. Do this by multiplying each cash flow by (1+ reinvestment rate) 2 enter FVs that we calculated in step 1 into the calculator as cash flows and CPT IRR
How to calculate NPV of each project at the crossover rate
1 calculate IRR of crossover rates between projects 2 use the IRR to calculate the NPV of the projects separate cash flows **The NPV of the projects at the crossover rate must be equal
Calculate aftertax salvage value
1 calculate annual depreciation and accumulated depreciation 2 Calculate ending book value 3The asset is sold at a loss to book value, so the depreciation tax shield of the loss is recaptured. 4 Taxes on salvage value = (BV - MV)TC
calculating dividend yield for stocks w same req. return
1 calculate current price(P0) of each stock 2 calculate dividend yield (D1/P0)- dont forget to multiply the dividend by 1+constant growth rate to get D1 3 use capital gains equation to calculate cap gains
How to calculate profitability index
1 enter the cash flows in calculator, only for CF0, instead of entering the negative number (today's cost), enter 0. 2 NPV CPT 3 Divide the NPV calculated by today's cost (the negative number) 4 accept: if P1 (Project Index) is greater than 1, reject: if P1 is less than 1 *Using the profitability index to compare mutually exclusive projects can be ambiguous when the magnitude of the cash flows for the two projects are of different scale.
How to find high/low target stock price in one year
1 find earnings per share 2 find the average high/low PE ratio each year (using high prices /EPS) 3 use PE ratio to find P1
how to calculate AAR
1 find net income (add projected net incomes and divide by Xyears) 2 divide net income by average book value
Reinvestment Approach calculation
1 find the time (end year) cash flow by multiplying each CF by (1+interest rate)^n and then adding them together, dont forget that when reinvesting you ignore the initial CF. 2 find the MIRR by using the reinvestment approach: 0=(initial CF)+ (((time end year CF)/1+MIRR)^n)) you will have to rearrange the equation to find MIRR (which is a %)
Combination Approach calculation
1 find time 0 CF(which is the same answer and calculation as the discounting approach) and also find the time (end year) CF 2 plug in these numbers to the MIRR equation using the discounting approach and rearrange to find MIRR (chapter 8 practice #21)
how to find the target share price in X years (aka the projected stock price)
1 use EPS equation 2 use PE ratio (questions 29, 30 in Ch. 7 practice)
how to calculate the current share price on an annual dividend, on it's common stock in a single annual installment, and management plans on raising this dividend by X% per year, indefinitely
1 use the constant growth model to find the price of the stock paying annual dividends
Compute the NPV for Project X with the cash flows shown below if the appropriate cost of capital is 10 percent. Time: 0 1 2 3 4 5 Cash flow: -125 -125 0 200 175 150 $362.93 $112.99 $162.01 $124.29
124.29
Paychex Inc. (PAYX) recently paid an $0.80 dividend. The dividend is expected to grow at a 16 percent rate. The current stock price is $47.31. What is the return shareholders are expecting?
17.96
how to calculate highest dividend over the last year:
1: The highest dividend yield will occur when the stock price is the lowest. So, using the 52-week low stock price, the highest dividend yield was: Dividend yield = D/PLow Dividend yield = $1.66/$32.90 Dividend yield = .0505, or 5.05%
(CH7 practice 26) Given EPS, Benchmark PE, and growth rate, estimate the current stock price calculate the target stock price in 1 year and assuming that the company pays no dividends, what is the implied return on the company's stock over the next year?
1Using the equation to calculate the price of a share of stock with the PE ratio: P = Benchmark PE ratio × EPS So, with a PE ratio of 21, we find: P = 21($2.35) P = $49.35 2First, we need to find the earnings per share next year, which will be: EPS1 = EPS0(1 + g) EPS1 = $2.35(1 + .07) EPS1 = $2.51 Using the equation to calculate the price of a share of stock with the PE ratio: P1 = Benchmark PE ratio × EPS1 P1 = 21($2.51) P1 = $52.80 3To find the implied return over the next year, we calculate the return as: R = (P1 - P0) / P0 R = ($52.80 - 49.35) / $49.35 R = .07, or 7% Notice that the return is the same as the growth rate in earnings. Assuming a stock pays no dividends and the PE ratio is constant, this will always be true when using price ratios to evaluate the price of a share of stock.
If the discount rate is zero, what is the NPV?
At a zero discount rate (and only at a zero discount rate), the cash flows can be added together across time. So, the NPV of the project at a zero percent required return is: the sum of the cash flows + today's cost (installed cost)
present value of cash flows on a growing perpetuity equation
C1/(R-g) which = C0(1+g)/(R-g)
Capital gains yield equation
Capital gains yield = Total return - Dividend yield
if we have the dividend in one year, what is the dividend in 4 years equal to?
D1*(1+g)^3
Dividend per share equation
D1=D0(1+g)
Depreciation tax shield equation
Depreciation tax shield = Depreciation(TC) T=taxes C=Depreciation The depreciation tax shield shows us the increase in OCF by being able to expense depreciation.
MIRR- Discounting approach Reinvestment approach Combination approach
Discounting: In the discounting approach, we find the value of all cash outflows at time 0, while any cash inflows remain at the time at which they occur. Reinvestment: we find the future value of all cash except the initial cash flow at the end of the project. Combination: we find the value of all cash outflows at Time 0, and the value of all cash inflows at the end of the project.
EPS equation
EPS1 = EPS0(1 + g)
TwitterMe, Inc., is a new company and currently has negative earnings. The company's sales are $1,200,000 and there are 130,000 shares outstanding. Requirement 1: If the benchmark price-sales ratio for the company is 5.2, how much will you pay for the stock?
First, we need to find the sales per share, which is: Sales per share = Sales / Shares outstanding Sales per share = $1,200,000 / 130,000 Sales per share = $9.23 Using the equation to calculate the price of a share of stock with the PS ratio: P = Benchmark PS ratio × Sales per share 1: With a benchmark PS ratio of 5.2, we find: P = Benchmark PE ratio × EPS P = 5.2($9.23) P = $48.00
what does it mean if cash flows change signs twice?
From Descartes' rule of signs, we know there are two IRRs since the cash flows change signs twice. When there are multiple IRRs, the IRR decision rule is ambiguous. Both IRRs are correct in this example. That is, both IRRs make the NPV of the project equal to zero. If we are evaluating whether or not to accept this project, we would not want to use the IRR to make our decision. the BA II Plus will calculate only one IRR. The second IRR must be calculated using another program, by hand, or trial and error.
E-Eyes.com has a new issue of preferred stock it calls 20/20 preferred. The stock will pay a $20 dividend per year, but the first dividend will not be paid until 20 years from today. Required: If you require a return of 8 percent on this stock, how much should you pay today?
Here, we have a stock that pays no dividends for 20 years. Once the stock begins paying dividends, it will have the same dividends forever, a preferred stock. We value the stock at that point, using the preferred stock equation. It is important to remember that the price we find will be the price one year before the first dividend, so: P19 = D20/ R P19 = $20 / .08 P19 = $250 The price of the stock today is simply the present value of the stock price in the future. We simply discount the future stock price at the required return. The price of the stock today will be: P0 = $250 / 1.0819 P0 = $57.93
Metallica Bearings, Inc., is a young start-up company. No dividends will be paid on the stock over the next nine years, because the firm needs to plow back its earnings to fuel growth. The company will then pay a dividend of $15 per share 10 years from today and will increase the dividend by 5 percent per year thereafter. Required: If the required return on this stock is 14 percent, what is the current share price?
Here, we have a stock that pays no dividends for 9 years. Once the stock begins paying dividends, it will have a constant growth rate of dividends. We can use the constant growth model at that point. It is important to remember the general constant dividend growth formula is: Pt = [Dt × (1 + g)] / (R - g) This means that since we will use the dividend in Year 10, we will be finding the stock price in Year 9. The dividend growth model is similar to the present value of an annuity and the present value of a perpetuity: The equation gives you the present value one period before the first payment. So, the price of the stock in Year 9 will be: P9 = D10 / (R - g) P9 = $15.00 / (.14 - .05) P9 = $166.67 The price of the stock today is simply the PV of the stock price in the future. We simply discount the future stock price at the required return. The price of the stock today will be: P0 = $166.67 / 1.149 P0 = $51.25
If the discount rate is infinite, what is the NPV?
If the required return is infinite, future cash flows have no value. Even if the cash flow in one year is $1 trillion, at an infinite rate of interest, the value of this cash flow today is zero. So, if the future cash flows have no value today, the NPV of the project is simply the cash flow today. At an infinite interest rate: the installed cost
Alexander Corp. will pay a dividend of $2.72 next year. The company has stated that it will maintain a constant growth rate of 4.5 percent a year forever. Requirement 1: If you want a return of 12 percent, how much will you pay for the stock?
Here, we need to value a stock with two different required returns. Using the constant growth model and a required return of 12 percent, the stock price today is: P0 = D1 / (R - g) P0 = $2.72 / (.12 - .045) P0 = $36.27
how to calculate the current share price on an annual dividend that pays in equal quarterly installments
If the company pays quarterly dividends instead of annual dividends, the quarterly dividend will be one-fourth of annual dividend, or: Quarterly dividend: $3.20(1.06) / 4 = $.8480} To find the equivalent annual dividend, we must assume that the quarterly dividends are reinvested at the required return. We can then use this interest rate to find the equivalent annual dividend. In other words, when we receive the quarterly dividend, we reinvest it at the required return on the stock. So, the effective quarterly rate is: Effective quarterly rate: 1.12.25 - 1 = .0287 The effective annual dividend will be the FVA of the quarterly dividend payments at the effective quarterly required return. In this case, the effective annual dividend will be: Effective D1 = $.8480(FVIFA2.87%,4) = $3.54 Now, we can use the constant growth model to find the current stock price as: P0 = $3.54 / (.12 - .06) = $59.02 Note that we cannot simply find the quarterly effective required return and growth rate to find the value of the stock. This would assume the dividends increased each quarter, not each year. Assuming you can reinvest the dividends at the required return of the stock, this model would be appropriate.
how to calculate payback period when the future cash flows are an annuity
Just divide the initial cost by the annual cash flow. For the $3,200 cost, the payback period is: Payback = $3,200 / $875 Payback = 3.66 years
how do most corporations pay dividends?
Most corporations pay quarterly dividends on their common stock rather than annual dividends. Barring any unusual circumstances during the year, the board raises, lowers, or maintains the current dividend once a year and then pays this dividend out in equal quarterly installments to its shareholders.
NPV of growing perpetuity
NPV is the PV of the outflows plus the PV of the inflows. accept if NPV is positive
How to find PE ratio for each year
divide each year's stock price by EPS
tax shield approach calculating OCF
OCF = (Sales - Costs)(1 - TC) + Depreciation(TC) Using the tax shield approach to calculating OCF (Remember the approach is irrelevant; the final answer will be the same no matter which of the four methods you use.) after calculating OCF, we can find the NPV as the initial cash outlay, plus the PV of the OCFs, which are an annuity
Operating Cash Flow equation
OCF=EBIT+ Depreciation-Taxes
Constant growth model equation
P0 = D0 (1 + g) / (R - g)
If we are given the stock price, the dividend growth rate, and the required return, and are asked to find the dividend. Using the constant dividend growth model, we use equation:
P0 = D0 (1 + g) / (R - g) -> D0 = P0(R - g) / (1 + g)
growing perpetuity equation
PV of cash inflows = C1 / (R - g) C1= net cash inflow
Constant dividend growth model
Pt=Dt*((1+g)/(R-g))
(Ch.9 pt.1 hw #2) Calculate net sales
Sales due solely to the new product line are: 24,700($27,500) = $679,250,000 Increased sales of the motor home line occur because of the new product line introduction; thus: 4,300($81,500) = $350,450,000 in new sales is relevant. Erosion of luxury motor coach sales is also due to the new portable campers; thus: 1,020($123,500) = $125,970,000 loss in sales is relevant. The net sales figure to use in evaluating the new line is thus: Net sales = $679,250,000 + 350,450,000 - 125,970,000 Net sales = $903,730,000
if you calculate IRR and the percentage is negative
The IRR is the interest rate that makes the NPV of the project equal to zero. The IRR is the interest rate that makes the NPV of the project equal to zero. So, the IRR of the project is: 0 = $35,000 - $27,000 / (1 + IRR) + $29,000 / (1 + IRR)2 Even though it appears there are two IRRs, a spreadsheet, financial calculator, or trial and error will not give an answer. The reason is that there is no real IRR for this set of cash flows. If you examine the IRR equation, what we are really doing is solving for the roots of the equation. Going back to high school algebra, in this problem we are solving a quadratic equation. the square root term works out to be negative, which is a complex number. This means that there is no real solution and the IRR is 0%
how to calculate the NPV of a project
The NPV of a project is the PV of the outflows plus the PV of the inflows. Since the cash inflows are an annuity, the equation for the NPV of this project at an 8 percent required return is: Calculator: CF0: today's cost (the negative number) C01: annual cash flow given amount (positive number) F01: how many years the annual cf lasts (n) At an 8 percent required return, the NPV is positive, so we would accept the project.
(CH7 practice 25) Using the dividend yield, calculate the closing price for Tootsie Roll on this day.
The annual dividend paid to stockholders is $.32, and the dividend yield is 1.3 percent. Using the equation for the dividend yield: Dividend yield = Dividend / Stock price We can plug the numbers in and solve for the stock price: .013 = $.32 / P0 P0 = $.32 / .013 P0 = $24.62
Antiques 'R' Us is a mature manufacturing firm. The company just paid a dividend of $11.45, but management expects to reduce the payout by 4.5 percent per year, indefinitely. Required: If you require a return of 11 percent return on this stock, what will you pay for a share today?
The constant growth model can be applied even if the dividends are declining by a constant percentage, just make sure to recognize the negative growth. So, the price of the stock today will be: P0 = D0 (1 + g) / (R - g) P0 = $11.45(1 - .045) / [(.11 - (-.045)] P0 = $70.55
Requirement 2: Assume the actual closing price for Tootsie Roll was $24.48. Your research projects a 5.5 percent dividend growth rate for Tootsie Roll. What is the required return for the stock using the dividend discount model and the actual stock price?
The dividend yield quoted in the newspaper is rounded. This means the price calculated using the dividend will be slightly different from the actual price. The required return for Tootsie Roll shareholders using the dividend discount model is: R = (D1 / P0) + g R = [$.32(1 + .055) / $24.48] + .055 R = .0688, or 6.88%
Calculate the annual depreciation allowances and end-of-the-year book values for this equipment.
The ending book value for any year is the beginning book value minus the depreciation for the year. Remember, to find the amount of depreciation for any year, you multiply the purchase price of the asset times the MACRS percentage for the year.
after calculating NPV, IRR, payback period, and profitability index, how do you decide which project to accept?
The final decision should be based on the NPV since it does not have the ranking problem associated with the other capital budgeting techniques. IRR, profitability index, and payback period cannot be used to rank mutually exclusive projects. *gr8 practice prob: #15 ch. 8 practice
At what discount rate is the NPV just equal to zero?
The interest rate that makes the NPV of a project equal to zero is the IRR. So calculate IRR
how to calculate lowest dividend over the last year:
The lowest dividend yield occurred when the stock price was the highest, so: Dividend yield = D/PHigh Dividend yield = $1.66/$42.81 Dividend yield = .0388, or 3.88%
calculating minimum growth rate
The minimum growth rate is the growth rate at which we would have a zero NPV. The equation for a zero NPV, using the equation for the PV of a growing perpetuity is: 0=(-initial investment + PV of cash inflows)/(req. return-growth rate), rearrange equation to get g
if total cash flows after X years of annuity are less than the total cash inflows, how do you calculate the payback period?
The payback period for an initial cost of $7,900 is a little trickier. Notice that the total cash inflows after eight years will be: Total cash inflows = 8($875) Total cash inflows = $7,000 If the initial cost is $7,900, the project never pays back. Notice that if you use the shortcut for annuity cash flows, you get: Payback = $7,900 / $875 Payback = 9.03 years This answer does not make sense since the cash flows stop after eight years, so again, we must conclude the payback period is never.
Hot Wings, Inc., has an odd dividend policy. The company has just paid a dividend of $4 per share and has announced that it will increase the dividend by $5 per share for each of the next four years, and then never pay another dividend. Required: If you require a return of 12 percent on the company's stock, how much will you pay for a share today?
The price of a stock is the PV of the future dividends. This stock is paying four dividends, so the price of the stock is the PV of these dividends discounted at the required return. So, the price of the stock is: P0 = $9 / 1.12 + $14 / 1.122 + $19 / 1.123 + $24 / 1.124 P0 = $47.97
when calculating profitability index, if project 2 is greater than project 1,
The profitability index decision rule implies we accept project 2
Definition of profitability index
The profitability index is defined as the PV of the cash inflows divided by the PV of the cash outflows. 1 calculate NPV for each project, but when entering the cash flows, enter 0 as the investment 2 divide the NPV calculated by the investment (negative first CF)
Stock Z is a growth stock that will increase its dividend by 20 percent for the next two years and then maintain a constant 12 percent growth rate, thereafter. Calculate dividend yield and capital gains yield for this kind of stock
To find the price of Stock Z, we find the price of the stock when the dividends level off at a constant growth rate, and then find the present value of the future stock price, plus the present value of all dividends during the supernormal growth period. The stock begins constant growth in Year 3, so we can find the price of the stock in Year 2, one year before the constant dividend growth begins as: P2 = D2(1 + g2) / (R - g2) P2 = D0(1 + g1)2 (1 + g2) / (R - g2) P2 = $2.80(1.20)2(1.12) / (.16 - .12) P2 = $112.90 The price of the stock today is the present value of the first three dividends, plus the present value of the Year 3 stock price. The price of the stock today will be: P0 = $2.80(1.20) / 1.16 + $2.80(1.20)2/ 1.162 + $112.90/ 1.162 P0 = $89.79 Dividend yield = D1/P0 Dividend yield = $2.80(1.20) / $89.79 Dividend yield = .0374, or 3.74% Capital gains yield = Total return - Dividend yield Capital gains yield = .16 - .037 Capital gains yield = .1226, or 12.26%
The Sleeping Flower Co. has earnings of $1.75 per share. Requirement 1: If the benchmark PE for the company is 18, how much will you pay for the stock?
Using the equation to calculate the price of a share of stock with the PE ratio: P = Benchmark PE ratio × EPS So, with a PE ratio of 18, we find: P = 18($1.75) P = $31.50
data from dividends growth model: Required: If investors feel this growth rate will continue, what is the required return for Arch Coal stock?
We need to find the required return of the stock. Using the constant growth model, we can solve the equation for R. Doing so, we find: R = (D1 / P0) + g R = [$0.44(1 + .035) / $14.53] + .035 R = .0663, or 6.63% The required return depends on the company and the industry. As we will see in a later chapter, this required return appears to be low relative to historic stock returns.
Finding stock price today; according to the dividend growth model
With supernormal dividends, we find the price of the stock when the dividends level off at a constant growth rate, and then find the present value of the future stock price, plus the present value of all dividends during the supernormal growth period. Since the first dividend with constant growth is in Year 6, we can find the price of the stock in Year 5, one year before the constant dividend growth begins as: P5 = D6 / (R - g) P5 = D0 (1 + g1)5 (1 + g2) / (R - g2) P5 = $3.00(1.125)5(1.05) / (.11 - .05) P5 = $94.61 The price of the stock today is the present value of the first five dividends, plus the present value of the Year 5 stock price. The price of the stock today will be: P0 = $3.00(1.125) / 1.11 + $3.00(1.125)2 / 1.112 + $3.00(1.125)3 / 1.113 + $3.00(1.125)4 /1.114 + $3.00(1.125)5 / 1.115 + $94.61 / 1.115 P0 = $71.76
Apocalyptica Corporation is expected to pay the following dividends over the next four years: $3, $10, $15, and $3.08. Afterwards, the company pledges to maintain a constant 5 percent growth rate in dividends, forever. Required: If the required return on the stock is 11 percent, what is the current share price?
With supernormal dividends, we find the price of the stock when the dividends level off at a constant growth rate, and then find the present value of the future stock price, plus the present value of all dividends during the supernormal growth period. The stock begins constant growth after the fourth dividend is paid, so we can find the price of the stock at Year 4, when the constant dividend growth begins, as: P4 = D4 (1 + g) / (R - g) P4 = $3.08(1.05) / (.11 - .05) P4 = $53.90 The price of the stock today is the present value of the first four dividends, plus the present value of the Year 4 stock price. So, the price of the stock today will be: P0 = $3 / 1.11 + $10 / 1.112 + $15 / 1.113 + $3.08 / 1.114 + $53.90 / 1.114 P0 = $59.32
Yang Corp. is growing quickly. Dividends are expected to grow at a rate of 25 percent for the next three years, with the growth rate falling off to a constant 6 percent thereafter. Required: If the required return is 13 percent and the company just paid a $2.50 dividend, what is the current share price? (Hint: Calculate the first four dividends.)
With supernormal dividends, we find the price of the stock when the dividends level off at a constant growth rate, and then find the present value of the future stock price, plus the present value of all dividends during the supernormal growth period. The stock begins constant growth after the third dividend is paid, so we can find the price of the stock in Year 3, when the constant dividend growth begins as: P3 = D3 (1 + g2) / (R - g2) P3 = D0 (1 + g1)3 (1 + g2) / (R - g2) P3 = $2.50(1.25)3(1.06) / (.13 - .06) P3 = $73.94 The price of the stock today is the present value of the first three dividends, plus the present value of the Year 3 stock price. The price of the stock today will be: P0 = $2.50(1.25) / 1.13 + $2.50(1.25)2 / 1.132 + $2.50(1.25)3 / 1.133 + $73.94 / 1.133 P0 = $60.45
The NPV decision rule implies
accepting project I, if the NPVI is greater than the NPVII.
Average PE calculation
add all PE ratios together and divide by n
how to calculate the proper cash flow amount to use as the initial investment in fixed assets when evaluating a project
cash flow= current aftertax value+ initial fixed asset investments (cash outlay+ grading expenses)
how to calculate the Internal Rate of Return (IRR) when given cash flows
enter cash flows into calculator, press IRR CPT
Using the company's historical average PE as a benchmark, what is the target stock price in one year?
find PE ratio each year, then find average PE, then use PE ratio equation (P1=Benchmark PE ratio*EPS)
At what discount rate would you be indifferent between accepting a project and rejecting it?
if required return is equal to the IRR of the project, since at that required return the NPV is zero. The IRR of the project is calculated the same way as you calculated the NPV regarding how you enter the cash flows, but then press IRR CPT
how do you decide which project is better when using the crossover rate equation to calculate the interest rate?
if the required return is above this interest rate: project with lower cash flows if the required return is below this interest rate: project with higher cash flows (Ch. 8 practice #18) project I becomes more valuable since the differential cash flows received in the first two years are larger than the cash flows for project J
If a project does not meet it's payback period, but provides the largest increase in shareholder wealth, what do you do?
ignore the payback period, and choose the project with the higher increase in shareholder wealth
definition of AAR (avg accounting return)
is the average net income divided by the average book value.
Paychex Inc. (PAYX) recently paid an $0.80 dividend. The dividend is expected to grow at a 15 percent rate. The current stock price is $50.91. What is the return shareholders are expecting?
shareholders return =16.81%
Discounting Approach calculation
subtract the last cash flow from today's cost, then divide by 1+ interest rate^n
If a firm has already paid an expense or is obligated to pay one in the future, regardless of whether a particular project is undertaken, that expense is a obligated cost sunk cost committed cost complementary cost
sunk
If a firm has already paid an expense or is obligated to pay one in the future, regardless of whether a particular project is undertaken, that expense is a complementary cost committed cost obligated cost sunk cost
sunk cost
0% constant growth rate means
the capital gains yield is the same as the constant growth rate
when finding the current price of preferred stock, what year is the price we are looking for?
the price one year before the first dividend
how to calculate price of a share of stock with the PE ratio
use equation: P1 = Benchmark PE ratio × EPS1