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Present Value with dividends |
Po= (D1 + P1)/)(1+R) Po is current price of stock P1 is price in one period R is the required return on the market |
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Zero Growth |
D1=D2=D3=D4=constant Po= D1/(1+R)^1 + D2/(1+R)^2….. Ordinary perpetuity Po=D/R |
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Constant Growth |
D1= Do x (1+g) Dt= Do x (1+g)^t |
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Growing perpetutiy |
an asset with cash flows that grow at a constant rate forever |
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Dividend growth model |
Po= Do x (1+g)/(R-g) the rate at which stock price grows |
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Dividend Yield |
next year’s expected cash dividend divided by the current market price per share. D1/Po |
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Capitals gains yield |
dividend growth rate the rate at which the value of the investment grows |
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The price of a stock at year 4 can be expressed as: |
D5/(R – g). |
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When companies don’t pay dividends |
Price at time t = Pt= Benchmark PE Ration x EPS(t) |
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Nonconstant Growth Rate |
D(t)/(1+R)^t + P(t)/(1+R)^t where P(t)= D1 x (1+g)/(R-g) |
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Required Return |
R= D1/Po + g where D1/Po is the dividend yield and g is the capital gains yield |
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Common Stock |
equity without priority for dividends or in bankruptcy |
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cumulative voting |
a procedure in which a shareholder may cast all votes for one member of the board of directors permit minority participation |
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straight voting |
a procedure in which a shareholder may cast all votes for each member of the board of directors |
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Staggering |
1. Makes it more difficult for a minority to elect a director when there is cumulative voting because there are fewer directors to be elected at one time 2. Makes takeover attempts less likely to be successful because it makes it more difficult to cote in a majority of new directors |
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Proxy |
a grant of authority by a shareholder allowing another individual to vote that shareholder’s shares. |
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gingers |
-mystical creatures in which are known to be sexy beasts and sexual predators ;))) |
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dividends |
payments by a corporation to shareholders make in either cash or stock |
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Characteristics of Dividends |
1. not a liability of the corporation 2. not a business expense. paid out of aftertax profits 3. dividends received by shareholders are taxable |
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Preferred Stocks |
stock with dividend priority over common stock, normally with a died dividend rate, sometimes without voting rights holders must receive dividend before common stock |
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Primary Market |
the market in which new securities are originally SOLD to investors |
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Secondary Market |
the market in which previously issued securities are TRADED among investors |
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Dealer |
an agent who buys and sells securities FROM inventory |
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Broker |
an agent who arranges security transactions AMONG investors |
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Member |
As of 2006, a member is the owner of a trading license on the NYSE |
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Designated Market Maker (DMM) |
NYSE members who act as dealers in particular stocks. |
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Floor Brokers |
NYSE members who execute customer buy and sell orders |
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Supplemental Liquidity Providers (SLPs) |
Investment firms that are active participate in stocks assigned to them. Their job is to make a one-died market. They trade purely for their own accountants |
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Order Flow |
the flow of customer orders to buy and sell securities |
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DMM’s post |
a fixed place on the exchange floor where the DMM operates |
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Inside Quotes |
the highest bid quotes and lowest ask quotes for a security |
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Electronic Communications Networks (ECN) |
websites that allow investors to fade directly with one another |
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SUMMARY of CHAPTER 7 |
1. The cash flows from owning a share of stock come in the form of future dividends. In special cases it is possible to calculate the present value of all the future dividends and thus come up with a value for the stock 2. As the owner of shares of common stock in a corporation, you have various rights, including the right to vote to elect corporate directors. Voting can either be cumulative or straight. Most voting is done by a proxy, and proxy battles break out when competing sides try to gain enough votes to have their candidates for the board elected. 3. Some corps have preferred stock. The name stems from the fact that preferred stockholders must be paid first, before common stockholders receive anything. Preferred stock has a fixed dividend 4. NYSE and NASDAQ |
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The required return on a stock is equal to which one of the following if the dividend on the stock decreases by 1 percent per year? |
Dividend yield + capital gains yield |
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Anton, Inc., just paid a dividend of $1.95 per share on its stock. The dividends are expected to grow at a constant rate of 4.1 percent per year, indefinitely. Assume investors require a return of 10.2 percent on this stock. What is the current price? |
Pt = Dt × (1 + g) / (R – g) So, the price of the stock today is: P0 = D0 (1 + g) / (R – g) P0 = $1.95(1.041) / (.102 – .041) P0 = $33.28 P3 = D3(1 + g) / (R – g) P3 = D0(1 + g)4/ (R – g) P3 = $1.95(1.041)4/ (.102 – .041) P3 = $37.54 We can do the same thing to find the dividend in Year 16, which gives us the price in Year 15, so: P15 = D15(1 + g) / (R – g) P15 = D0(1 + g)16/ (R – g) P15 = $1.95(1.041)16/ (.102 – .041) P15 = $60.80 There is another feature of the constant dividend growth model: The stock price grows at the dividend growth rate. So, if we know the stock price today, we can find the future value for any time in the future we want to calculate the stock price. In this problem, we want to know the stock price in three years, and we have already calculated the stock price today. The stock price in three years will be: P3 = P0(1 + g)3 P3 = $33.28(1 + .041)3 P3 = $37.54 And the stock price in 15 years will be: P15 = P0(1 + g)15 P15 = $33.28(1 + .041)15 P15 = $60.80 |
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The next dividend payment by Wyatt, Inc., will be $2.30 per share. The dividends are anticipated to maintain a growth rate of 4.5 percent forever. |
R = (D1 / P0) + g R = ($2.30 / $39.85) + .045 R = .1027, or 10.27% |
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The next dividend payment by Wyatt, Inc., will be $2.30 per share. The dividends are anticipated to maintain a growth rate of 4.5 percent forever. Assume the stock currently sells for $39.85 per share. What is the dividend yield? |
Dividend yield = D1 / P0 Dividend yield = $2.30 / $39.85 Dividend yield = .0577, or 5.77% The capital gains yield, or percentage increase in the stock price, is the same as the dividend growth rate, so: Capital gains yield = 4.5% |
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The stock price of Webber Co. is $68. Investors require an 11 percent rate of return on similar stocks. If the company plans to pay a dividend of $3.85 next year, what growth rate is expected for the company’s stock price? |
g = R – (D1 / P0) g = .11 – ($3.85 / $68) g = .0534, or 5.34% |
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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. If the required return on this stock is 14 percent, what is the current share price? |
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 / (1.14)^9 P0 = $51.25 |
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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. 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 |
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The Sleeping Flower Co. has earnings of $1.75 per share. If the benchmark PE for the company is 18, how much will you pay for the stock? If the benchmark PE for the company is 21, how much will you pay for the stock? |
P= Benchmark PE ratio × EPS So, with a PE ratio of 18, we find: P = 18($1.75) P = $31.50 And with a PE ratio of 21, we find: P = 21($1.75) P = $36.75 |
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Suppose you know that a company’s stock currently sells for $65.70 per share and the required return on the stock is 9 percent. You also know that the total return on the stock is evenly divided between capital gains yield and dividend yield. If it’s the company’s policy to always maintain a constant growth rate in its dividends, what is the current dividend per share? |
We know the stock has a required return of 9 percent, and the dividend and capital gains yield are equal, so: Dividend yield = 1/2(.09) Dividend yield = .045 = Capital gains yield Now we know both the dividend yield and capital gains yield. The dividend is simply the stock price times the dividend yield, so: D1 = .045($65.70) D1 = $2.96 This is the dividend next year. The question asks for the dividend this year. Using the relationship between the dividend this year and the dividend next year: D1 = D0(1 + g) We can solve for the dividend that was just paid: $2.96 = D0(1 + .045) D0 = $2.96 / 1.045 D0 = $2.83 |
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Bui Corp. pays a constant $13.50 dividend on its stock. The company will maintain this dividend for the next eight years and will then cease paying dividends forever. If the required return on this stock is 11 percent, what is the current share price? |
The price of any financial instrument is the present value of the future cash flows. The future dividends of this stock are an annuity for eight years, so the price of the stock is the present value of an annuity, which will be: P0 = $13.50(PVIFA11%,8) P0 = $69.47 69.47/13.50 = 5.15 |
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The Sleeping Flower Co. has earnings of $1.84 per share. If the benchmark PE for the company is 17, 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 17, we find: P = 17($1.84) P = $31.28 2: And with a PE ratio of 21, we find: P = 21($1.84) P = $38.64 |
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Apocalyptica Corporation is expected to pay the following dividends over the next four years: $5.70, $16.70, $21.70, and $3.50. Afterwards, the company pledges to maintain a constant 5.50 percent growth rate in dividends, forever. If the required return on the stock is 9 percent, what is the current share price? |
P4 = D4 (1 + g) / (R – g) P4 = $3.50(1.0550) / (0.09 – 0.0550) P4 = $105.50 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 = $5.70 / 1.09 + $16.70 / 1.092 + $21.70 / 1.093 + $3.50 / 1.094 + $105.50 / 1.094 P0 = $113.26 |
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Net Present Value |
The difference between an investment’s market value and it’s cost |
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Discounted Cash FLow |
the process of valuing an investment by discounting it’s future cash flows |
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Net Present Value Rule |
An investment should be accepted if the net present value is positive and rejected if it is negative. |
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The payback period is the length of time it takes an investment to generate sufficient cash flows to enable the project to: |
recoup its initial cost. |
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Payback Period |
the amount of time required for an investment to generate cash flows sufficient to recover it’s initial cost |
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Payback period Rule |
an investment is acceptable if it’s calculated payback period is less than some pre specified number of years |
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Average Accounting Return |
=some measure of average accounting profit/some measure of average accounting value =Average net income/ Average book value |
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Average Accounting Return Rule |
a project is acceptable if it’s average accounting return exceeds a target average accounting return |
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Internal Rate of Return (IRR) |
the discount rate that makes the NPV of an investment ZERO. |
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Which one of the following defines the internal rate of return for a project? |
Discount rate that results in a zero net present value for the project the required rate that results in a zero NPV when it is used at the discount rate |
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IRR Rule |
an investment is acceptable if the IRR exceeds the required return. It should be rejected otherwise. |
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Net Present Value Profile |
a graphical representation of the relationship between an investment’s PV and various discount rates |
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Multiple Rates of Return |
the possibility that more than one discount rate make the NPV of an investment zero |
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Mutually exclusive investment decisions |
a situation where taking one investment presents the taking of another |
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Which one of the following is generally considered to be the best form of analysis if you have to select a single method to analyze a variety of investment opportunities? |
Net present value |
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Which one of the following indicates that a project should be rejected? |
Profitability index less than 1.0 |
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Discounting Approach |
discount all negative cash flows back to the present at the required return and add them to the initial cost. Then calculate IRR. |
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Reinvestment Approach |
compound all cash flows (positive and negative) except the first out to the end of the project’s life and then calculate the IRR. |
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Combination Approach |
Negative cash flows are discounted back to the present, and positive cash flows are compounded to the end of the project. |
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Profitability Index |
The present value of an investment’s future cash flows divided by it’s initial cost. Benefit-cost ratio. when NPV is positive, present value of future cash flow must be bigger than initial investment and > 1.00 |
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Payback is best used to evaluate which type of projects? |
Low-cost, short-term |
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The payback method of analysis ignores which one of the following? |
Initial cost of an investment Arbitrary cutoff point Cash flow direction Time value of money Timing of each cash inflow |
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The internal rate of return is unreliable as an indicator of whether or not an investment should be accepted given which one of the following? |
One of the time periods within the investment period has a cash flow equal to zero. The initial cash flow is negative. The investment has cash inflows that occur after the required payback period. The investment is mutually exclusive with another investment under consideration. The cash flows are conventional. |
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Discounted Cash Flow Criteria |
A) NPV- the difference between it’s market value and it’s cost. Take project if NPV is positive. NPV is estimated by calculating the present value of the future cash flows and then subtracting the cost. B) IRR- the discount rate that makes the estimated NPV of an investment equal to zero. Take project if IRR > required return. C) MIRR- a project’s cash flows are modified by 1. discounting the negative cash flows back to the present, 2. compounding all cash flows to the end of the project’s life, 3. combining both. Unclear how to interpret them bc they depend on externally supplied discounting or compounding rates D) Profitability Index- ratio of present value to cost. Take an investment if the index exceeds 1. measures the present value of an investment per dollar invested. |
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Payback Criteria |
Payback period- the length of time until the sum of an investment’s cash flows equals it’s costs. Take project if it’s payback is less than some cutoff. Ignores risk, time value of money, and cash flows beyond the cutoff point |
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Accounting Criteria |
Average Accounting Return- a measure of accounting profit relative to book value. NOT related to IRR. Take investment if it’s ARR>a benchmark ARR. |
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If a project with conventional cash flows has a profitability index of 1.0, the project will: |
have an internal rate of return that equals the required return. |
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What is the net present value of a project that has an initial cost of $40,000 and produces cash inflows of $8,000 a year for 11 years if the discount rate is 15 percent? |
CALCULATOR … put initial cash-flow as negative (-40,000) NPV= -40,000 + 8,000x(1-[1/(1.15)^11]/0.15) =$1,869.69 |
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A firm evaluates all of its projects by applying the IRR rule. Year Cash Flow Requirement 1:
Requirement 2: |
CALCULATOR The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equation that defines the IRR for this project is: 0 = – $153,000 + $78,000 / (1 + IRR) + $67,000 / (1 + IRR)2 + $49,000 / (1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 14.02% Since the cash flows are conventional and the IRR is greater than the required return, we would accept the project. |
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For the given cash flows, suppose the firm uses the NPV decision rule. Year Cash Flow Requirement 1: Requirement 2: |
The NPV of a project is the PV of the outflows minus by the PV of the inflows. The equation for the NPV of this project at a 9 percent required return is: NPV = – $153,000 + $78,000 / 1.09 + $67,000 / 1.092 + $49,000 / 1.093 NPV = $12,789.18 At a 9 percent required return, the NPV is positive, so we would accept the project. The equation for the NPV of the project at a 21 percent required return is: NPV = – $153,000 + $78,000 / 1.21 + $67,000 / 1.212 + $49,000 / 1.213 NPV = – $15,116.07 At a 21 percent required return, the NPV is negative, so we would reject the project. |
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A project that provides annual cash flows of $1,930 for 8 years costs $7,700 today. |
1. CALC 2. CALC 3. N=8 PV=-7700 PMT=1930 CPT I/Y 1: 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: NPV = – $7,700 + $1,930(PVIFA8%, 8) NPV = $3,391.01 At an 8 percent required return, the NPV is positive, so we would accept the project. 2: The equation for the NPV of the project at a 24 percent required return is: NPV = – $7,700 + $1,930(PVIFA24%, 8) NPV = -$1,097.04 At a 24 percent required return, the NPV is negative, so we would reject the project. 3: We would be indifferent to the project if the required return was equal to the IRR of the project, since at that required return the NPV is zero. The IRR of the project is: 0 = – $7,700 + $1,930(PVIFAIRR, 8) IRR = .1871, or 18.71% |
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Consider the following two mutually exclusive projects: Year Cash Flow (A) Cash Flow (B) The required return on these investments is 13 percent. Required: |
The payback period for each project is: A: 3 + ($218,000 / $455,000) = 3.48 years B: 2 + ($4,500 / $14,100) = 2.32 years The payback criterion implies accepting project B, because it pays back sooner than project A. The NPV for each project is: A: NPV = – $365,000 + $38,000 / 1.13 + $47,000 / 1.132 + $62,000 / 1.133 + $455,000 / 1.134 NPV = $27,465.34 B: NPV = – $40,000 + $20,300 / 1.13 + $15,200 / 1.132 + $14,100 / 1.133 + $11,200 / 1.134 NPV = $6,509.61 The NPV criterion implies we accept project A because project A has a higher NPV than project B. The IRR for each project is: A: $365,000 = $38,000 / (1+IRR) + $47,000 / (1+IRR)2 + $62,000 / (1+IRR)3 + $455,000 / (1+IRR)4 IRR = 15.41% B: $40,000 = $20,300 / (1+IRR) + $15,200 / (1+IRR)2 + $14,100 / (1+IRR)3 + $11,200 / (1+IRR)4 IRR = 21.51% PI=NPV/initial cash flow PI(a) = $392,465.34 / $365,000 = 1.075 PI(b) = $46,509.61 / $40,000 = 1.163 A: PI = ($38,000/1.13 + $47,000/1.132 + $62,000/1.133 + $455,000/1.134) / $365,000 PI = 1.075 B: PI = ($20,300/1.13 + $15,200/1.132 + $14,100/1.133 + $11,200/1.134) / $40,000 PI = 1.163 The profitability index criterion implies accepting project B because its PI is greater than project A’s. |
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Kerron Company is presented with the following two mutually exclusive projects. The required return for both projects is 15 percent. Year Project M Project N (a) What is the IRR for each project? |
CALCULATORZ (a) M: $125,000 = $57,000 / (1+IRR) + $64,000 / (1+IRR)2 + $59,000 / (1+IRR)3 + $34,000 / (1+IRR)4 IRR = 27.70% N: $310,000 = $135,000 / (1+IRR) + $161,000 / (1+IRR)2 + $129,000 / (1+IRR)3 + $92,000 / (1+IRR)4 IRR = 25.91% The IRR decision rule implies we accept project M because the IRR for M is greater than the IRR for N. (b) The NPV for each project is: M: NPV = -$125,000 + $57,000 / 1.15 + $64,000 / 1.152 + $59,000 / 1.153 + $34,000 / 1.154 NPV = $31,191.48 N: NPV = -$310,000 + $135,000 / 1.15 + $161,000 / 1.152 + $129,000 / 1.153 + $92,000 / 1.154 NPV = $66,551.33 The NPV criterion implies we accept N because N has a higher NPV than M. (c) Accept N since the NPV is higher. IRR cannot be used to rank mutually exclusive projects. |
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Handy Enterprises has gathered projected cash flows for two projects. Year Project I Project J Requirement 1: |
CFo $0 C01 $29,000 F01 1 C02 $7,000 F02 1 C03 -$17,000 F03 1 C04 -$33,000 F04 1 CPT IRR 14.28% 1: To find the crossover rate, we subtract the cash flows from one project from the cash flows of the other project, and find the IRR of the differential cash flows. We will subtract the cash flows from Project J from the cash flows from Project I. It is irrelevant which cash flows we subtract from the other. Subtracting the cash flows, the equation to calculate the IRR for these differential cash flows is: Crossover rate: 0 = $29,000 / (1+R) + $7,000 / (1+R)2 – $17,000 / (1+R)3 – $33,000 / (1+R)4 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: R = 14.28% 2: At a lower interest rate, project J is more valuable because of the higher total cash flows. At a higher interest rate, 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. |
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CHAPTER 8 SUMMARY |
5 Criteria used to evaluate proposed investments: 1. NPV 2. Payback period 3. Average accounting return 4. IRR 5, MIRR 6. Profitability Index Ultimately, a good capital budgeting criterion must tell two things: a) is a particular project and good investment? and b) if we have more than one good project, which one should we take? The main point of the chapter is that only NPV can always provide the correct answer to both questions. 1. NPV is always the difference between the market value of an asset or project and it’s cost 2. The financial manager acts in the shareholders’ best interests by identifying and taking positive NPV projects NPV can’t normally be observed in the market; instead they are estimated. |
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Incremental Cash Flows |
the difference between a firm’s future cash flows with a project and those without the project |
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Relevant Cash Flow |
a change in the firm’s overall future cash flow that comes about as a direct consequence |
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Incremental Cash Flow Evaluation |
consists of any and all changes in the firm’s future cash flows that are a direct consequence of taking the project |
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Stand-alone principle |
The assumption that evaluation of a project’s incremental cash flows. |
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Sunk Cost |
a cost that has already been incurred and cannot be recouped and therefore should not be considered in an investment decision |
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Opportunity Costs |
the most valuable alternative that is given up if a particular investment is undertaken |
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Erosion |
The cash flows of a new project that come at the expense of a firm’s existing projects. |
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A cost that should be ignored when evaluating a project because that cost has already been incurred and cannot be recouped is referred to as which type of cost? |
Sunk |
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Which one of the following terms is most commonly used to describe the cash flows of a new project that are simply an offset of reduced cash flows for a current project? |
Erosion |
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Pro Forma Financial Statements |
financial statements projecting future years’ operations Sales -VC =Gross Profit -Fixed Costs -Depreciation =NOI x Tax Rate =Net Income |
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Project Cash Flow |
=Project Operating Cash Flow- Project Change in Net working capital -Project capital spending |
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Project operating cash flow |
Operating Cash Flow=NOI (EBIT)+Depreciation-Taxes |
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The amount by which a firm’s tax bill is reduced as a result of the depreciation expense is referred to as the depreciation: |
tax shield. |
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The Shoe Box is considering adding a new line of winter footwear to its product lineup. Which of the following are relevant cash flows for this project? I. Decreased revenue from products currently being offered if this new footwear is added to the lineup |
I, II, and IV only |
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The Corner Market has decided to expand its retail store by building on a vacant lot it currently owns. This lot was purchased four years ago at a cost of $299,000, which the firm paid in cash. To date, the firm has spent another $38,000 on land improvements, all of which was also paid in cash. Today, the lot has a market value of $329,000. What value should be included in the analysis of the expansion project for the cost of the land? |
The current market value of the land-$329,000 |
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Steve owns a store that caters primarily to men and their hobbies. He is contemplating greatly expanding the hunting and fishing section of the store. If he does this, he expects his fishing and hunting sales will increase, his camping gear sales will increase, and his model train sales will decrease. Which of the following should Steve include in his revenue projection for the expansion project? I. Increase in fishing and hunting sales |
I, II, and III |
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The net working capital invested in a project is generally: |
recouped at the end of the project. |
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Tax Shield Approach |
Operating Cash Flow= (Sales-Costs)X(1-T) + Depreciation x T This approach shows: 1. What the project’s cash flow would be if there were no depreciation expense 2. The depreciation deduction multiplied by tax rate (depreciation tax shield) |
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Deprecation Tax Shield |
the tax saving that results from the depreciation deduction, calculated as depreciation multiplied by the corporate tax rate Depreciation x Tax Rate |
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The tax shield approach to computing the operating cash flow, given a tax-paying firm: |
recognizes that depreciation creates a cash inflow. |
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Networking Capital |
Accounts Receivable – Accounts Payable |
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Total Cash Flow |
OCF – Change in NWC – Capital Spending Cash inflow – Cash outflow |
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Accelerated Cost Recovery System (ACRS) |
depreciation method under US tax law allowing for the accelerated write-off of property under various classifications |
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A project has sales of $462,000, costs of $274,000, depreciation of $26,000, interest expense of $3,400, and a tax rate of 35 percent. What is the value of the depreciation tax shield? |
Depreciation tax shield = $26,000 × 0.35 = $9,100 |
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A project will reduce costs by $34,000 but increase depreciation by $16,500. What is the operating cash flow of this project based on the tax shield approach if the tax rate is 40 percent? |
Operating cash flow = [$34,000 × (1 – 0.40)] + [$16,500 × 0.40] = $27,000 |
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Forecasting Risk |
the possibility that errors in projected cash flows |
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Scenario Analysis |
The determination of what happens to NPV estimates when we ask what if questions |
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Sensitivity Analysis |
investigation of what happens to NPV when only one variable is changed |
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Managerial Options |
opportunities that managers can exploit if certain things happen in the future. "Real" options. |
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Contingency Planning |
taking into account the managerial options implicit in a project. 1. Option to expand-Can we expand the project or repeat it to get an even larger NPV? Underestimate NPV when ignored 2. Option to abandon-Underestimate NPV if we assume that the project must last for some fixed number of years no matter what happens in the future 3. Option to wait- As long as there is some possible future scenario under which a project has a positive NPC, then the option to wait is valuable |
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Strategic Options |
Options for future, related business products or strategies |
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Capital Rationing |
exists when we have profitable (positive NPV) investments available but we can’t get the needed funds to undertake them. |
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Soft Rationing |
occurs when units in a business are allocated a certain amount of financing for capital budgeting |
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Hard Rationing |
when a business cannot raise capital for a project under any circumstances. |
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Winnebagel Corp. currently sells 28,000 motor homes per year at $73,000 each and 7,000 luxury motor coaches per year at $115,000 each. The company wants to introduce a new portable camper to fill out its product line; it hopes to sell 29,000 of these campers per year at $18,500 each. An independent consultant has determined that if Winnebagel introduces the new campers, it should boost the sales of its existing motor homes by 2,500 units per year and reduce the sales of its motor coaches by 750 units per year. |
Sales due solely to the new product line are: 29,000($18,500) = $536,500,000 Increased sales of the motor home line occur because of the new product line introduction; thus: 2,500($73,000) = $182,500,000 in new sales is relevant. Erosion of luxury motor coach sales is also due to the new mid-size campers; thus: 750($115,000) = $86,250,000 loss in sales is relevant. The net sales figure to use in evaluating the new line is thus: Net sales = $536,500,000 + 182,500,000 – 86,250,000 Net sales = $632,750,000 |
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Sales $657,900 Requirement 2: |
OCF = EBIT + Depreciation – Taxes OCF = $207,500 + 97,500 – 72,625 OCF = $232,375 The depreciation tax shield is the depreciation times the tax rate, so: Depreciation tax shield = Depreciation(TC) Depreciation tax shield = .35($97,500) Depreciation tax shield = $34,125 The depreciation tax shield shows us the increase in OCF by being able to expense depreciation. |
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Consider an asset that costs $635,000 and is depreciated straight-line to zero over its eight-year tax life. The asset is to be used in a five-year project; at the end of the project, the asset can be sold for $125,000. |
The asset has a useful life of 8 years and we want to find the book value of the asset after 5 years. With straight-line depreciation, the depreciation each year will be: Annual depreciation = $635,000 / 8 Annual depreciation = $79,375 So, after 5 years, the accumulated depreciation will be: Accumulated depreciation = 5($79,375) Accumulated depreciation = $396,875 The book value at the end of Year 5 is thus: BV5 = $635,000 – 396,875 BV5 = $238,125 The asset is sold at a loss to book value, so the depreciation tax shield of the loss is recaptured. Aftertax salvage value = $125,000 + ($238,125 – 125,000)(.35) Aftertax salvage value = $164,593.75 To find the taxes on salvage value, remember to use the equation: Taxes on salvage value = (BV – MV)TC This equation will always give the correct sign for a tax inflow (refund) or outflow (payment). |
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Book Value |
Sales- accumulated depreciation Sales- (Depreciation x #years of project) Sales- ((Cost/useful life)x#years of project)) |
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Aftertax salvage value |
=What asset can be sold for+ (Book Value-what asset is sold for) x Tax Rate |
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Cochrane, Inc., is considering a new three-year expansion project that requires an initial fixed asset investment of $1,860,000. The fixed asset will be depreciated straight-line to zero over its three-year tax life, after which time it will be worthless. The project is estimated to generate $1,950,000 in annual sales, with costs of $1,060,000. Required: |
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.), we get: OCF = (Sales – Costs)(1 – TC) + Depreciation(TC) OCF = ($1,950,000 – 1,060,000)(1 – .35) + .35($1,860,000 / 3) OCF = $795,500 |
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Cochrane, Inc., is considering a new three-year expansion project that requires an initial fixed asset investment of $1,860,000. The fixed asset will be depreciated straight-line to zero over its three-year tax life, after which time it will be worthless. The project is estimated to generate $1,950,000 in annual sales, with costs of $1,060,000. Assume the tax rate is 35 percent and the required return on the project is 14 percent. Required: |
OCF = $795,500 Since we have the OCF, we can find the NPV as the initial cash outlay, plus the PV of the OCFs, which are an annuity, so the NPV is: NPV = −$1,860,000 + $795,500(PVIFA14%,3) NPV = −$13,141.72 [(1 – (1 / (1 + i)^n)) / i]…where i = discount rate(14%) and n=number of periods being discounted(3) |
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Your firm is contemplating the purchase of a new $480,000 computer-based order entry system. The system will be depreciated straight-line to zero over its five-year life. It will be worth $30,000 at the end of that time. You will save $145,000 before taxes per year in order processing costs, and you will be able to reduce working capital by $35,000 at the beginning of the project. Working capital will revert back to normal at the end of the project. |
First, we will calculate the annual depreciation of the new equipment. It will be: Annual depreciation charge = $480,000 / 5 Annual depreciation charge = $96,000 The aftertax salvage value of the equipment is: Aftertax salvage value = $30,000(1 – .35) Aftertax salvage value = $19,500 Using the tax shield approach, the OCF is: OCF = $145,000(1 – .35) + .35($96,000) OCF = $127,850 Now we can find the project IRR. There is an unusual feature that is a part of this project. Accepting this project means that we will reduce NWC. This reduction in NWC is a cash inflow at Year 0. This reduction in NWC implies that when the project ends, we will have to increase NWC. So, at the end of the project, we will have a cash outflow to restore the NWC to its level before the project. We must also include the aftertax salvage value at the end of the project. The IRR of the project is: NPV = 0 = -$480,000 + 35,000 + $127,850(PVIFAIRR%,5) + [($19,500 – 35,000) / (1 + IRR)5] IRR = 12.65% |
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Which one of the following is defined as a bell-shaped frequency distribution that is defined by its average and its standard deviation? |
Normal distribution |
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When, if ever, will the geometric average return exceed the arithmetic average return for a given set of returns? |
Never |
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Over the past five years, a stock returned 8.3 percent, -32.5 percent, -2.2 percent, 46.9 percent, and 11.8 percent, respectively. What is the variance of these returns? |
Average return = (0.083 – 0.325 – 0.022 + 0.469 + 0.118)/5 = 0.0646 σ2 = [(0.083 – 0.0646)2 + (-0.325 – 0.0646)2 + (-0.022 – 0.0646)2 + (0.469 – 0.0646)2 + (0.118 – 0.0646)2]/(5 – 1) = 0.081504 |
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One year ago, Peyton purchased 3,600 shares of Broncos stock for $101,124. Today, he sold those shares for $26.60 a share. What is the total return on this investment if the dividend yield is 1.9 percent? |
Purchase price = $101,124/3,600 shares = $28.09 a share Total return = [($26.60 – $28.09)/$28.09] + 0.019 = -3.40 percent |
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Total Dollar Return |
=dividend income + capital gain (or loss) |
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Total cash if stock sold |
=initial investment + Total return |
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You bought a share of 8.5 percent preferred stock for $87.40 last year. The market price for your stock is now $88.10. What is your total return for last year? |
Total return = ($88.10 – $87.40 + $8.50)/$87.40 = 10.53 percent |
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Capital Gains Yield |
(Pt+1 – Pt)/Pt |
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Suppose a stock had an initial price of $61 per share, paid a dividend of $1.40 per share during the year, and had an ending share price of $69. Requirement 1: |
1: The return of any asset is the increase in price, plus any dividends or cash flows, all divided by the initial price. The return of this stock is: R = [($69 – 61) + 1.40] / $61 R = .1541, or 15.41% 2: The dividend yield is the dividend divided by price at the initial price, so: Dividend yield = $1.40 / $61 Dividend yield = .0230, or 2.30% 3: And the capital gains yield is the increase in price divided by the initial price, so: Capital gains yield = ($69 – 61) / $61 Capital gains yield = .1311, or 13.11% |
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Suppose a stock had an initial price of $61 per share, paid a dividend of $1.40 per share during the year, and had an ending share price of $54. Requirement 1: |
1: Using the equation for total return, we find: R = [($54 – 61) + 1.40] / $61 R = -.0918, or -9.18% 2: And the dividend yield and capital gains yield are: Dividend yield = $1.40 / $61 Dividend yield = .0230, or 2.30% 3: Capital gains yield = ($54 – 61) / $61 Capital gains yield = -.1148, or -11.48% |
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Use the following returns for X and Y. Returns
Requirement 1: |
Add all up and divide by 5 =8.4% and 15.4% Var= (Return-E(x))^2+….. =.029580 and 058030 The standard deviation is the square root of the variance, so the standard deviation of each stock is: σX = (.029580)1/2 σsX = .1720, or 17.20% σY = (.058030)1/2 σY = .2409, or 24.09% |
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Consider the following table for a period of six years. Returns 7.99 37.23 5.87 23.93 5.07 5.45 6.57 7.64 Requirement 1: Requirement 2: (a) |
1: The average return for large company stocks over this period was: Large company stock average return = 19.41% / 6 Large company stock average return = 3.24% And the average return for T-bills over this period was: T-bills average return = 39.31% /6 T-bills average return = 6.55% 2: Using the equation for variance, we find the variance for large company stocks over this period was: Variance = 1/5[(-.1469 – .0324)2 + (-.2647 – .0324)2 + (.3723 – .0324)2 + (.2393 – .0324)2 + (-.0716 – .0324)2 + (.0657 – .0324)2] Variance = .058136 And the standard deviation for large company stocks over this period was: Standard deviation = (.058136)1/2 Standard deviation = .2411, or 24.11% Using the equation for variance, we find the variance for T-bills over this period was: Variance = 1/5[(.0729 – .0655)2 + (.0799 – .0655)2 + (.0587 – .0655)2 + (.0507 – .0655)2 + (.0545 – .0655)2 + (.0764 – .0655)2] Variance = .000153 And the standard deviation for T-bills over this period was: Standard deviation = (.000153)1/2 Standard deviation = .0124, or 1.24% 3: (a) The average observed risk premium over this period was: Average observed risk premium = -19.90% / 6 Average observed risk premium = -3.32% (b) The variance of the observed risk premium was: Variance = 1/5[(-.2198 – (-.0332))2 + (-.3446 – (-.0332))2 + (.3136 – (-.0332))2 + (.1886 – (-.0332))2 + (-.1261 – (-.0332))2 + (-.0107 – (-.0332))2] Variance = .062078 And the standard deviation of the observed risk premium was: Standard deviation = (.062078)1/2 Standard deviation = .2492, or 24.92% |
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You bought a stock three months ago for $34.18 per share. The stock paid no dividends. The current share price is $35.07. |
The return of any asset is the increase in price, plus any dividends or cash flows, all divided by the initial price. This stock paid no dividend, so the return was: R = ($35.07 – 34.18) / $34.18 R = .0260, or 2.60% This is the return for three months, so the APR is: APR = 4(2.60%) APR = 10.42% And the EAR is: EAR = (1 + .0260)4 – 1 EAR = .1083, or 10.83% |
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onsider the following table for different assets for 1926 through 2011. Series Requirement 1: Requirement 2: |
Looking at the long-term corporate bond return history, we see that the mean return was 6.4 percent, with a standard deviation of 8.4 percent. The range of returns you would expect to see 68 percent of the time is the mean plus or minus 1 standard deviation, or: R∈ μ ± 1σ = 6.4% ± 8.4% = -2.00% to 14.80% The range of returns you would expect to see 95 percent of the time is the mean plus or minus 2 standard deviations, or: R∈ μ ± 2σ = 6.4% ± 2(8.4%) = -10.40% to 23.20% |
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A stock has had returns of −26 percent, 6 percent, 34 percent, −5 percent, 28 percent, and 19 percent over the last six years. Required: |
The arithmetic average return is the sum of the known returns divided by the number of returns, so: Arithmetic average return = (-.26 + .06 + .34 -.05 + .28 +.19) / 6 Arithmetic average return = .0933, or 9.33% Using the equation for the geometric return, we find: Geometric average return = [(1 + R1) × (1 + R2) × … × (1 + RT)]1/T – 1 Geometric average return = [(1 – .26)(1 + .06)(1 + .34)(1 – .05)(1 + .28)(1 + .19)](1/6) – 1 Geometric average return = .0724, or 7.24% Remember, the geometric average return will always be less than the arithmetic average return if the returns have any variation. |
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Expected Return |
return on a risky asset expected in the future =the sum of the possible returns multiplied by their probabilities |
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Risk Premium |
Expected return – risk free rate |
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Variance |
determine the squared deviations from the expected returns, then multiply by the probabilities |
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Portfolio |
a group of assets such as stocks and bonds held by investors |
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Portfolio weights |
Percentage of a portions total value in a particular asset Asset $ 1/Total $ Asset amount |
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Total Return |
=expected return + unexpected Return |
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Announcement |
=expected part + surprise =expected +systematic portion +unsystematic portion |
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Systematic Risk |
a risk that influences a large number of assets. market risk. GSP, interest rates, inflation |
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Unsystematic Risk |
a risk that affects at most a small number of assets. Also unique or asset-specific risk. Afffects single or small group of assets Oil strike |
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Principle of Diversification |
spreading an investment across a number of assets will eliminate some but not all of the risk |
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Important diversification point |
unsystematic risk is essentially eliminated by diversification, so a relatively large portfolio has almost no unsystematic risk |
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Systematic risk principle |
the expected return on a risky assets depends only on that asset’s systematic risk the expected return on an assets depends only on that assets systematic risk |
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Beta coefficient |
measures how much systematic risk a articular asset has relative to an average asset. 1 is average |
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Reward to risk ratio |
E(Ra)-Rf/beta A = E(Rb)-Rf/beta B must be the same for all assets in the market |
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Security Market Line |
positively sloped straight line displaying the relationship between expected return and beta |
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market risk premium |
Slope of the SML, the difference between the expected return on a market portfolio and the risk-free rate =E(Rm)-Rf |
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Capital Asset pricing model |
shows relationship between expected return and beta What CAPM shows is that the expected return fora a particular asset depends on three things: 1. The pure time value of money- the reward for waiting for your money without taking any risks 2. The reward for bearing systematic risk- reward the market offers for bearing an average amount of systematic risk in addition to waiting 3. The amount of systematic risk- the amount of systematic risk present in a particular asset |
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Cost of Capital |
the minimum required return on a new investment. What firm must earn to break even. Opportunity cost associated with the investment |
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The systematic risk principle states that the expected return on a risky asset depends only on which one of the following? |
Market risk |
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Which one of the following measures the amount of systematic risk present in a particular risky asset relative to that in an average risky asset? |
Beta coefficient |
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If a security plots to the right and below the security market line, then the security has ____ systematic risk than the market and is ____. |
more; overpriced |
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Which one of the following portfolios will have a beta of zero? |
A portfolio comprised solely of U. S. Treasury bills |
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The stock of Wiley United has a beta of 0.92. The market risk premium is 8.6 percent and the risk-free rate is 3.2 percent. What is the expected return on this stock? |
E(R) = 0.032 + 0.92(0.086) = 11.11 percent risk free rate + beta(market risk premium) |
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You own a portfolio that has $1,300 invested in Stock A and $2,100 invested in Stock B. Assume the expected returns on these stocks are 10 percent and 16 percent, respectively. Required: |
The expected return of a portfolio is the sum of the weight of each asset times the expected return of each asset. The total value of the portfolio is: Total value = $1,300 + 2,100 Total value = $3,400 So, the expected return of this portfolio is: E(Rp) = ($1,300 / $3,400)(.10) + ($2,100 / $3,400)(.16) E(Rp) = .1371, or 13.71% |
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Consider the following information: State of Required: |
E(R) = .30(-.08) + .70(.19) E(R) = .1090, or 10.90% |
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Rate of Return if State Occurs Requirement 1: |
1. E(RA) = .15(.02) + .55(.10) + .30(.15) E(RA) = .1030, or 10.30% E(RB) = .15(-.30) + .55(.18) + .30(.31) E(RB) = .1470, or 14.70% 2: To calculate the standard deviation, we first need to calculate the variance. To find the variance, we find the squared deviations from the expected return. We then multiply each possible squared deviation by its probability, and then sum. The result is the variance. So, the variance and standard deviation of each stock is: σA2 = .15(.02 – .1030)2 + .55(.10 – .1030)2 + .30(.15 – .1030)2 σA2 = .00170 σA = (.00170)1/2 σA = .0412, or 4.12% σB2 = .15(-.30 – .1470)2 + .55(.18 – .1470)2 + .30(.31 – .1470)2 σB2 = .03854 σB = (.03854)1/2 σB = .1963, or 19.63% |
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A stock has a beta of 1.15, the expected return on the market is 10.9 percent, and the risk-free rate is 3.8 percent. Required: |
The CAPM states the relationship between the risk of an asset and its expected return. The CAPM is: E(Ri) = Rf + [E(RM) – Rf] × βi Substituting the values we are given, we find: E(Ri) = .038 + (.109 – .038)(1.15) E(Ri) = .1197, or 11.97% |
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You own a stock portfolio invested 15 percent in Stock Q, 25 percent in Stock R, 40 percent in Stock S, and 20 percent in Stock T. The betas for these four stocks are .85, .91, 1.31, and 1.76, respectively. Required: |
The beta of a portfolio is the sum of the weight of each asset times the beta of each asset. So, the beta of the portfolio is: βp = .15(.85) + .25(.91) + .40(1.31) + .20(1.76) βp = 1.23 |
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CHAPTER 11 SUMMARY |
SML is important because it tells us the reward offered un financial markets for bearing risk. Once we know this,we have a benchmark against which we compare the returns expected from real asset investments to determine if they are desirable Basic logic underlying the SML: 1. Based on capital market history, there is a reward for bearing risk. The reward is the risk premium on an asset. 2. The total risk associated with an asset has two parts: systematic risk and unsystematic risk. Unsystematic Risk can be freely eliminated by diversification, so only systematic risk is rewarded. The risk premium on an asset is determined by it’s systematic risk (systematic risk principle) 3. An assets’ systematic risk can be measured by it’s beta coefficient. The risk premium on an asset is then given by it’s beta coefficient multiplied by the market risk premium [E(R,)-Rf] x beta 4. The expected return on an asset is equal to the risk-free rate plus the risk premium E(Ri)= Rf + [E(Rm)-Rf] x beta –> called capital asset pricing model |
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One of the most important lessons in finance lol |
The Cost of Capital depends primarily on the use of the funds, NOT the source doesn’t depend on how and where capital is raised |
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Cost of Equity |
the return that equity investors require on their investment in the firm |
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Katie owns 100 shares of ABC stock. Which one of the following terms is used to refer to the return that Katie and the other shareholders require on their investment in ABC? |
Cost of equity |
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Dividend Growth Model |
P0=D1/(R-g) R=D1/P0 + g where R is the return that the shareholders require on the stock => it is the firms cost of equity capital |
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The weighted average cost of capital is defined as the weighted average of a firm’s: |
cost of equity and its aftertax cost of debt. |
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Required/Expected Return on a risky asset depends on three things |
1. Risk free rate (Rf) 2. Market risk premium (E(Rm)-Rf) 3. Systematic risk of the asset relative to average or it’s BETA COEFFICIENT |
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Advantage of Dividend growth model |
Simplicity. it is easy to understandd and easy to use |
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Disadvantages of Dividend growth model |
only applicable to companies that pay dividends. The key to the underlying assumption is that the dividend grows at a constant rate, which is not always the case. Estimated cost of equity is very sensitive to the estimated growth rate. Does not consider risk. |
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Advantages of SML approach |
1. It explicitly adjusts for risk 2. It is applicable to other companies other than just those with steady dividend growth. |
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Disadvantages of SML |
Requires that market risk premium and beta be estimated, which makes cost of equity inaccurate. Relis on past to predict future since economic conditions can change very quickly |
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Costof debt |
the return that lenders require on the firms debt. Interest rate the firm must ay on new borrowing |
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The cost of preferred stock |
R=D/Po |
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Farmer’s Supply, Inc. is considering opening a clothing store, which would be a new line of business for the firm. Management has decided to use the cost of capital of a similar clothing store as the discount rate that should be used to evaluate this proposed expansion. Which one of the following terms is used to describe the approach Farmer’s Supply is taking to establish an appropriate discount rate for the project? |
Pure play approach |
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Ted is trying to decide what cost of capital he should assign to a project. Which one of the following should be his primary consideration in this decision? |
Risk level of the project |
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Which of the following features are advantages of the dividend growth model? |
I and II only |
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In an efficient market, the cost of equity for a risky firm does which one of the following according to the security market line? |
Increases in direct relation to the stock’s systematic risk |
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Combined market value of the debt and equity |
V=E+D 100%=E/V + D/V which is called the capital structure weights |
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Weighted Average Cost of Capital (WACC) |
the weighted average of the cost of equity and the aftertax cost of debt. =(E/V) x Re + (D/V) x Rd x (1-Tc) the overall return the firm must earn on it’s existing assets to maintain the value of it’s stock. |
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The Lo Tech Co. just issued a dividend of $1.80 per share on its common stock. The company is expected to maintain a constant 6 percent growth rate in its dividends indefinitely. |
With the information given, we can find the cost of equity using the dividend growth model. Using this model, the cost of equity is: RE = [$1.80(1.06) / $41] + .06 RE = .1065, or 10.65% D(1+g)/P0 |
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ICU Window, Inc., is trying to determine its cost of debt. The firm has a debt issue outstanding with seven years to maturity that is quoted at 108 percent of face value. The issue makes semiannual payments and has an embedded cost of 6.1 percent annually. Requirement 1: |
1: CALCULATOR The pretax cost of debt is the YTM of the company’s bonds, so: P0 = $1,080 = $30.50(PVIFAR%,14) + $1,000(PVIFR%,14) R = 2.371% YTM = 2 × 2.371% YTM = 4.74% 2: And the aftertax cost of debt is: RD= .0474(1 – .38) RD = .0294, or 2.94% |
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Aftertax cost of debt |
YTM*(1-T) |
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Mullineaux Corporation has a target capital structure of 75 percent common stock, 5 percent preferred stock, and 20 percent debt. Its cost of equity is 11.25 percent, the cost of preferred stock is 5.5 percent, and the cost of debt is 6.1 percent. The relevant tax rate is 35 percent. Required: |
WACC = .75(.1125) + .05(.055) + .20(.0610)(1 – .35) WACC = .0951, or 9.51% COMMON x it’s Cost of Equity + Preferred x it’s Cost of equity + Debt x cost of equity x 1-Tax Rate Since interest is tax deductible and dividends are not, we must look at the aftertax cost of debt, which is: RD = .061(1 – .35) RD = .0397, or 3.97% |
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Information on Janicek Power Co., is shown below. Assume the company’s tax rate is 35 percent. Debt: Common stock: 225,000 shares outstanding, selling for $87 per share; beta is 1.15. Preferred stock: Market: 7 percent market risk premium and 3.1 percent risk-free rate. Calculate the company’s WACC |
We will begin by finding the market value of each type of financing. We find: MVD = 8,500($1,000)(1.18) = $10,030,000 MVE = 225,000($87) = $19,575,000 MVP = 15,000($98) = $1,470,000 And the total market value of the firm is: V = $10,030,000 + 19,575,000 + 1,470,000 V = $31,075,000 Now, we can find the cost of equity using the CAPM. The cost of equity is: RE = .031 + 1.15(.07) RE = .1115, or 11.15% The cost of debt is the YTM of the bonds, so: P0 = $1,180 = $36(PVIFAR%,50) + $1,000(PVIFR%,50) R = 2.91% YTM = 2.91% × 2 YTM = 5.82% And the aftertax cost of debt is: RD = (1 – .35)(.0582) RD = .0379, or 3.79% The cost of preferred stock is: RP = $4.80 / $98 RP = .0490, or 4.90% Now we have all of the components to calculate the WACC. The WACC is: WACC = .0379($10,030,000 / $31,075,000) + .1115($19,575,000 / $31,075,000) + .0490($1,470,000 / $31,075,000) WACC = .0848, or 8.48% Notice that we didn’t include the (1 – TC) term in the WACC equation. We used the aftertax cost of debt in the equation, so the term is not needed here. |
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Summary of Capital Cost Calculations |
1. The cost of equity, Rf a) Dividend growth model approach Re=D1/(P0+g) where D1 is the divided in one period, g is the dividend growth rate, and P0 is the current stock price b) SML Approach Rd= Rf + Beta e x (Rm-Rf) where Rf is the risk-free rate, Rm is the expected return on the overall market, and Beta e is the systematic risk of the equity. 2. The Cost of Debt a) For a firm with publicly held debt, the cost of debt can be measured as the yield to maturity on the outstanding debt. The coupon rate is irrelevant. b) if the firm has no publicly traded debt, then the cost of debt can be measured as the yield to maturity on similarly rated bonds 3. The weighted average cost of capital WACC a) The firm’s WACC is the overall required return on the firm as a whole. It is the appropriate discount rate to use for cash flows similar in risk to the overall firm b) WACC= (E/V) x Re+ (D/V)x Rd x (1-T) where T is the corporate tax rate, E is the market value of the firm’s equity, D is the market value of the firm’s debt, and V=E+D. Note that E.V is the percentage of the firms financing that is equity, and D/V is the percentage that is debt. |
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Pure Play approach |
use of a WACC that is unique to a particular project, based on companies in similar lines of business. |
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Organic Produce Corporation has 6.3 million shares of common stock outstanding, 350,000 shares of 5.8 preferred stock outstanding, and 150,000 of 7.1 percent semiannual bonds outstanding, par value $1,000 each. The common stock currently sells for $74 per share and has a beta of 1.09, the preferred stock currently sells for $107 per share, and the bonds have 20 years to maturity and sell for 109 percent of par. The market risk premium is 6.8 percent, T-bills are yielding 4.3 percent, and the firm’s tax rate is 34 percent. Required: |
(a) We will begin by finding the market value of each type of financing. We find: MVD = 150,000($1,000)(1.09) = $163,500,000 MVE = 6,300,000($74) = $466,200,000 MVP = 350,000($107) = $37,450,000 And the total market value of the firm is: V = $163,500,000 + 466,200,000 + 37,450,000 V = $667,150,000 So, the market value weights of the company’s financing is: D/V = $163,500,000 / $667,150,000 = .2451 P/V = $37,450,000 / $667,150,000 = .0561 E/V = $466,200,000 / $667,150,000 = .6988 (b) For projects equally as risky as the firm itself, the WACC should be used as the discount rate. First, we can find the cost of equity using the CAPM. The cost of equity is: RE = .043 + 1.09(.068) RE = .1171, or 11.71% The cost of debt is the YTM of the bonds, so: P0 = $1,090 = $35.50(PVIFAR%,40) + $1,000(PVIFR%,40) R = 3.151% YTM = 3.151% × 2 YTM = 6.30% And the aftertax cost of debt is: RD = (1 – .34)(.0630) RD = .0416, or 4.16% The cost of preferred stock is: RP = $5.80 / $107 RP = .0542, or 5.42% Now, we can calculate the WACC as: WACC = .2451(.0416) + .0561(.0542) + .6988(.1171) WACC = .0951, or 9.51% |
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Gnomes R Us is considering a new project. The company has a debt-equity ratio of .65. The company’s cost of equity is 13.2 percent, and the aftertax cost of debt is 5.1 percent. The firm feels that the project is riskier than the company as a whole and that it should use an adjustment factor of +3 percent. Requirement 1: |
To find the required return for the project, we need to adjust the company’s WACC for the level of risk in the project. A debt-equity ratio of .65 implies a weight of debt of .65/1.65 and a weight of equity of 1/1.65, so the company’s WACC is: WACC = (.65/1.65)(.0510) + (1/1.65)(.1320) WACC = .1021, or 10.21% Adjusting for risk, the project discount rate is: Project discount rate = .1021 + .03 Project discount rate = .1321, or 13.21% |
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WACC is used to discount |
Cash flows |
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What will happen over time if a firm uses it’s overall WACC to evaluate all projects, regardless of each projects risk level? |
the firm will become riskier, it will accept projects it should have rejected, ansi t will reject projects it should have accepted |
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What is tax deductible to the firm? |
coupon interest paid on bonds |
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What is true about a firms cost of debt? |
it is easier to estimate than cost of equity, and yields can be calculated from observable data |
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The return an investor in a security receives is _____ the cost of the security to the company that it issued |
equal to |
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To estimate a firms equity cost of Capital using CAPM we need to know |
the stocks beta, market risk premium, and the risk free rate |
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WHEN CALCULATING WACC |
ALWAYS MULTIPLY 1-T BY THE DEBT (or bonds) NOT PREFERRED STOCK OR EQUITY |
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The rate used to discount project cash flows is known as |
the discount rate or cost of capital or required return |
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