This is the Team Assignement. This Portion of the assignement is mine. Please do in Excel and must be complete by Sunday 11.00PM (Due in 45 hours. I will also post what other member of the team has done… Tomorrow I will be on a flight all day. So cannot respond to email till Sunday morning(24hours from now)
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Resource: Principles of Managerial Finance Ch. 9
Complete the Spreadsheet Exercise on p. 390 and The Interactive Case 4 Eco Plastics in Ch 9.
Create a spreadsheet with two tabs. Use one tab for the Spreadsheet Exercise on p. 390 and the other tab for The Interactive Case 4 Eco Plastics.
MY PORTION OF THE ASSIGNMENT:
f.
CHAPTER 9
In your professional life
ACCOUNTING You need to understand the various sources of capital and how their costs are calculated to provide the data necessary to determine the firms overall cost of capital.
INFORMATION SYSTEMS You need to understand the various sources of capital and how their costs are calculated to develop systems that will estimate the costs of those sources of capital as well as the overall cost of capital.
MANAGEMENT You need to understand the cost of capital to select long-term investments after assessing their acceptability and relative rankings.
MARKETING You need to understand the firms cost of capital because proposed projects must earn returns in excess of it to be acceptable.
OPERATIONS You need to understand the firms cost of capital to assess the economic viability of investments in plant and equipment needed to improve or grow the firms capacity.
In your personal life
Knowing your personal cost of capital will allow you to make informed decisions about your personal consuming borrowing and investing. Managing your personal wealth is a lot like managing the wealth of a business in that you need to understand the trade-offs between consuming wealth and growing wealth and how growing wealth can be accomplished by investing your own monies or borrowed monies. Understanding the cost of capital concepts will allow you to make better long-term decisions and maximize the value of your personal wealth.
Often listed among Americas most admired corporations Alcoa Inc. is the worlds largest producer of aluminum with more than 61000 employees in 30 countries. A quick glance at its financial statements might suggest that the company has been doing very well in recent years. Alcoa increased its total sales from $18.4 billion in 2009 to $23.7 billion in 2012 an annual growth rate of almost 9 percent far exceeding overall economic growth over the same period. In each of those years Alcoa spent more than $1 billion on capital expenditures expanding and upgrading its manufacturing facilities entering new joint ventures and making strategic acquisitions.
During that span however Alcoas stock underperformed. During the 5-year period ending in May 2013 Alcoa common stock lost almost 80 percent of its value while the broader stock market (as measured by the Standard & Poors 500 Stock Composite Index) rose by about 20 percent. Why did Alcoa perform so poorly? A simple answer is that its business investments failed to earn a return sufficient to meet the expectations of investors. Despite Alcoas continued growth the rate of return that it earned on the assets that it had invested was not sufficient to satisfy investors. When a firms operating results disappoint investors its stock price will fall as investors sell their shares and move to a more attractive investment. According to some estimates Alcoas cost of capital exceeded 12 percent but its investments were consistently earning returns below 5 percent. That is a recipe for a declining stock price which is precisely what Alcoa had been experiencing for several years.
For companies to succeed their investments have to earn a rate of return that exceeds investors expectations. How though do companies know what investors expect? The answer is that companies have to measure their cost of capital. Read on to learn how firms do that.
LG 1
LG 2
My Finance Lab Video
Chapter 1 established that the goal of the firm is to maximize shareholder wealth. To do so managers must make investments that are worth more than they cost. In this chapter you will learn about the cost of capital which is the rate of return that financial managers use to evaluate all possible investment opportunities to determine which ones add value to the firm. The cost of capital represents the firms cost of financing and is the minimum rate of return that a project must earn to increase firm value. In particular the cost of capital refers to the cost of the next dollar of financing necessary to finance a new investment opportunity. Investments with a rate of return above the cost of capital will increase the value of the firm because these investments are worth more than they cost. In contrast projects with a rate of return below the cost of capital will decrease firm value.
cost of capital
Represents the firms cost of financing and is the minimum rate of return that a project must earn to increase firm value.
The cost of capital is an extremely important financial concept. It acts as a major link between the firms long-term investment decisions and the wealth of the firms owners as determined by the market value of their shares. Financial managers are ethically bound to invest only in projects that they expect to exceed the cost of capital; see the Focus on Ethics box for more discussion of this responsibility.
Business Week once referred to Peter Drucker as The Man Who Invented Management. In his role as writer and management consultant Drucker stressed the importance of ethics to business leaders. He believed that it was the ethical responsibility of a business to earn a profit. In his mind profitable businesses create opportunities whereas unprofitable ones waste societys resources. Drucker once said Profit is not the explanation cause or rationale of business behavior and business decisions but rather the test of their validity. If archangels instead of businessmen sat in directors chairs they would still have to be concerned with profitability despite their total lack of personal interest in making profits.a
But what happens when businesses abandon ethics for profits? Consider Mercks experience with the drug Vioxx. Introduced in 1999 Vioxx was an immediate success quickly reaching $2.5 billion in annual sales. However a Merck study launched in 1999 eventually found that patients who took Vioxx suffered from an increased risk of heart attacks and strokes. Despite the risks Merck continued to market and sell Vioxx. By the time Vioxx was withdrawn from the market an estimated 20 million Americans had taken the drug 88000 had suffered Vioxxrelated heart attacks and 38000 had died.
News of the 2004 Vioxx withdrawal hit Mercks stock hard. The companys shares fell 27 percent on the day of the announcement slashing $27 billion off the firms market capitalization. Moodys Standard & Poors and Fitch cut Mercks credit ratings costing the firm its coveted AAA rating. The companys bottom line also suffered as its net income fell 21 percent in the final three months of 2004.
The recall dealt a major blow to Mercks reputation. The company was criticized for aggressively marketing Vioxx despite the drugs serious side effects. Questions were also raised about the research reports Merck had submitted in support of the drug. Lawsuits followed. In 2008 Merck agreed to fund a $4.85 billion settlement to resolve approximately 50000 Vioxxrelated lawsuits. The company had also incurred $1.53 billion in legal costs by the time of the settlement.
The Vioxx recall increased Mercks cost of capital. What effect would an increased cost of capital have on a firms future investments?
aPeter F. Drucker The Essential Drucker (New York: Collins Business Essentials 2001).
A firms cost of capital reflects the expected average future cost of funds over the long run and it reflects the entirety of the firms financing activities. For example a firm may raise the money it needs to build a new manufacturing facility by borrowing money (debt) by selling common stock (equity) or by doing both. Managers must take into account respective costs of both forms of capital when they estimate a firms cost of capital. In fact most firms do finance their activities with a blend of equity and debt. In Chapter 13 we will explore the factors that determine what mix of debt and equity is optimal for any particular firm. For now we will simply say that most firms have a desired mix of financing and the cost of capital must reflect the cost of each type of financing that a firm uses. To capture all the relevant financing costs assuming some desired mix of financing we need to look at the overall cost of capital rather than just the cost of any single source of financing.
My Finance Lab Solution Video
A firm is currently considering two investment opportunities. Two financial analysts working independently of each other are evaluating these opportunities. Assume the following information about investments A and B.
Investment A
The analyst studying this investment recalls that the company recently issued bonds paying a 6% rate of return. He reasons that because the investment project earns 7% while the firm can issue debt at 6% the project must be worth doing so he recommends that the company undertake this investment.
Investment B
Least costly financing source available
Equity = 14%
The analyst assigned to this project knows that the firm has common stock outstanding and that investors who hold the companys stock expect a 14% return on their investment. The analyst decides that the firm should not undertake this investment because it only produces a 12% return while the companys shareholders expect a 14% return.
In this example each analyst is making a mistake by focusing on one source of financing rather than on the overall financing mix. What if instead the analysts used a combined cost of financing? By weighting the cost of each source of financing by its relative proportion in the firms target capital structure the firm can obtain a weighted average cost of capital. Assuming that this firm desires a 5050 mix of debt and equity the weighted average cost here would be 10%[(0.50 6% debt) + (0.50 14% equity)]. With this average cost of financing the firm should reject the first opportunity (7% expected return < 10% weighted average cost) and accept the second (12% expected return > 10% weighted average cost).
In this chapter our concern is only with the long-term sources of capital available to a firm because they are the sources that supply the financing necessary to support the firms capital budgeting activities. Capital budgeting is the process of evaluating and selecting long-term investments. This process is intended to achieve the firms goal of maximizing shareholders wealth. Although the entire capital budgeting process is discussed throughout Part 5 at this point it is sufficient to say that capital budgeting activities are chief among the responsibilities of financial managers and that they cannot be carried out without knowing the appropriate cost of capital with which to judge the firms investment opportunities.
There are four basic sources of long-term capital for firms: long-term debt preferred stock common stock and retained earnings. All entries on the right-hand side of the balance sheet other than current liabilities represent these sources:
Not every firm will use all of these sources of financing. In particular preferred stock is relatively uncommon. Even so most firms will have some mix of funds from these sources in their capital structures. Although a firms existing mix of financing sources may reflect its target capital structure it is ultimately the marginal cost of capital necessary to raise the next marginal dollar of financing that is relevant for evaluating the firms future investment opportunities.
What is the cost of capital?
What role does the cost of capital play in the firms long-term investment decisions? How does it relate to the firms ability to maximize shareholder wealth?
What does the firms capital structure represent?
What are the typical sources of long-term capital available to the firm?
LG 3
The cost of long-term debt is the financing cost associated with new funds raised through long-term borrowing. Typically the funds are raised through the sale of corporate bonds.
cost of long-term debt
The financing cost associated with new funds raised through long-term borrowing.
The net proceeds from the sale of a bond or any security are the funds that the firm receives from the sale. The total proceeds are reduced by the flotation costs which represent the total costs of issuing and selling securities. These costs apply to all public offerings of securities: debt preferred stock and common stock. They include two components: (1) underwriting costs or compensation earned by investment bankers for selling the security; and (2) administrative costs or issuer expenses such as legal and accounting costs.
net proceeds
Funds actually received by the firm from the sale of a security.
flotation costs
The total costs of issuing and selling a security.
Duchess Corporation a major hardware manufacturer is contemplating selling $10 million worth of 20-year 9% coupon (stated annual interest rate) bonds each with a par value of $1000. Because bonds with similar risk earn returns greater than 9% the firm must sell the bonds for $980 to compensate for the lower coupon interest rate. The flotation costs are 2% of the par value of the bond (0.02 $1000) or $20. The net proceeds to the firm from the sale of each bond are therefore $960 ($980 minus $20).
The before-tax cost of debt rd is simply the rate of return the firm must pay on new borrowing. A firms before-tax cost of debt for bonds can be found in any of three ways: quotation calculation or approximation.
A relatively quick method for finding the before-tax cost of debt is to observe the yield to maturity (YTM) on the firms existing bonds or bonds of similar risk issued by other companies. The YTM of existing bonds reflects the rate of return required by the market. For example if the market requires a YTM of 9.7 percent for a similar-risk bond this value can be used as the before-tax cost of debt rd for new bonds. Bond yields are widely reported by sources such as the Wall Street Journal.
This approach finds the before-tax cost of debt by calculating the YTM generated by the bonds cash flows given the net proceeds that the firm receives when it issues the bonds. From the issuers point of view this value is the cost to maturity of the cash flows associated with the debt. The YTM can be calculated by using a financial calculator or an electronic spreadsheet. It represents the annual before-tax percentage cost of the debt.
In the preceding example $960 were the net proceeds of a 20-year bond with a $1000 par value and 9% coupon interest rate. The calculation of the annual cost is quite simple. The cash flow pattern associated with this bonds sales consists of an initial inflow (the net proceeds) followed by a series of annual outlays (the interest payments). In the final year when the debt is retired an outlay representing the repayment of the principal also occurs. The cash flows associated with Duchess Corporations bond issue are as follows:
End of year(s)
Cash flow
0
$960
120
$90
20
$1000
The initial $960 inflow is followed by annual interest outflows of $90 (9% coupon interest rate $1000 par value) over the 20-year life of the bond. In year 20 an outflow of $1000 (the repayment of the principal) occurs. We can determine the cost of debt by finding the YTM which is the discount rate that equates the present value of the bond outflows to the initial inflow.
My Finance Lab Financial Calculator
Calculator use (Note: Most calculators require either the present value [net proceeds] or the future value [annual interest payments and repayment of principal] to be input as negative numbers when we calculate yield to maturity. That approach is used here.) Using the calculator and the inputs shown at the left you should find the before-tax cost of debt (yield to maturity) to be 9.452%.
Spreadsheet use The before-tax cost of debt on the Duchess Corporation bond can be calculated using an Excel spreadsheet. The following Excel spreadsheet shows that by referencing the cells containing the bonds net proceeds coupon payment years to maturity and par value as part of Excels RATE function you can quickly determine that the appropriate before-tax cost of debt for Duchess Corporations bond is 9.452%.
Although you may not recognize it both the calculator and the Excel function are using trial-and-error to find the bonds YTM they just do it faster than you can.
Although not as precise as using a calculator there is a method for quickly approximating the before-tax cost of debt. The before-tax cost of debt rd for a bond with a $1000 par value can be approximated by
(9.1)
Where
Substituting the appropriate values from the Duchess Corporation example into the approximation formula given in Equation 9.1 we get
This approximate value of before-tax cost of debt is close to the 9.452% but it lacks the precision of the value derived using the calculator or spreadsheet.
Unlike the dividends paid to equityholders the interest payments paid to bond-holders are tax deductable for the firm so the interest expense on debt reduces the firms taxable income and therefore the firms tax liability. To find the firms net cost of debt we must account for the tax savings created by debt and solve for the cost of long-term debt on an after-tax basis. The after-tax cost of debt ri can be found by multiplying the before-tax cost rd by 1 minus the tax rate T:
ri = rd (1 T)
(9.2)
My Finance Lab Solution Video
Duchess Corporation has a 40% tax rate. Using the 9.452% before-tax debt cost calculated above and applying Equation 9.2 we find an after-tax cost of debt of 5.67%[9.452% (1 0.40)]. Typically the cost of long-term debt for a given firm is less than the cost of preferred or common stock partly because of the tax deductibility of interest.
My Finance Lab Solution Video
Kait and Kasim Sullivan a married couple in the 28% federal income-tax bracket wish to borrow $60000 to pay for a new luxury car. To finance the purchase they can either borrow the $60000 through the auto dealer at an annual interest rate of 6.0% or they can take a $60000 second mortgage on their home. The best annual rate they can get on the second mortgage is 7.2%. They already have qualified for both of the loans being considered.
If they borrow from the auto dealer the interest on this consumer loan will not be deductible for federal tax purposes. However the interest on the second mortgage would be tax deductible because the tax law allows individuals to deduct interest paid on a home mortgage. To choose the least-cost financing the Sullivans calculated the after-tax cost of both sources of long-term debt. Because interest on the auto loan is not tax deductible its after-tax cost equals its stated cost of 6.0%. Because the interest on the second mortgage is tax deductible its after-tax cost can be found using Equation 9.2:
Because the 5.2% after-tax cost of the second mortgage is less than the 6.0% cost of the auto loan the Sullivans may decide to use the second mortgage to finance the auto purchase.
What are the net proceeds from the sale of a bond? What are flotation costs and how do they affect a bonds net proceeds?
What methods can be used to find the before-tax cost of debt?
How is the before-tax cost of debt converted into the after-tax cost?
My Finance Lab
The interest expense on debt provides a tax deduction for the issuer so any calculation of a firms net cost of debt should reflect this benefit. Based on the information provided at MFL compute a firms after-tax cost of debt using a spreadsheet model.
LG 4
Preferred stock represents a special type of ownership interest in the firm. It gives preferred stockholders the right to receive their stated dividends before the firm can distribute any earnings to common stockholders. The key characteristics of preferred stock were described in Chapter 7. However the one aspect of preferred stock that requires review is dividends.
When dividends are stated as preferred stock dividends the stock is often referred to as x-dollar preferred stock. Thus a $4 preferred stock is expected to pay preferred stockholders $4 in dividends each year on each share of preferred stock owned.
Sometimes preferred stock dividends are stated as an annual percentage rate. This rate represents the percentage of the stocks par or face value that equals the annual dividend. For instance an 8 percent preferred stock with a $50 par value would be expected to pay an annual dividend of $4 per share (0.08 $50 par = $4). Before the cost of preferred stock is calculated any dividends stated as percentages should be converted to annual dollar dividends.
The cost of preferred stock rp is the ratio of the preferred stock dividend to the firms net proceeds from the sale of the preferred stock. The net proceeds represent the amount of money to be received minus any flotation costs. The following equation gives the cost of preferred stock rp in terms of the annual dollar dividend Dp and the net proceeds from the sale of the stock Np:
cost of preferred stock rp
The ratio of the preferred stock dividend to the firms net proceeds from the sale of preferred stock.
(9.3)
Duchess Corporation is contemplating issuance of a 10% preferred stock that they expect to sell for $87 per share. The cost of issuing and selling the stock will be $5 per share. The first step in finding the cost of the stock is to calculate the dollar amount of the annual preferred dividend which is $8.70 (0.10 $87). The net proceeds per share from the proposed sale of stock equals the sale price minus the flotation costs ($87 $5 = $82). Substituting the annual dividend Dp of $8.70 and the net proceeds Np of $82 into Equation 9.3 gives the cost of preferred stock 10.6% ($8.70 $82).
The cost of Duchesss preferred stock (10.6%) is much greater than the cost of its long-term debt (5.67%). This difference exists both because the cost of long-term debt (the interest) is tax deductible and because preferred stock is riskier than long-term debt.
How would you calculate the cost of preferred stock?
LG 5
The cost of common stock is the return required on the stock by investors in the marketplace. There are two forms of common stock financing: (1) retained earnings and (2) new issues of common stock. As a first step in finding each of these costs we must estimate the cost of common stock equity.
The cost of common stock equity rs is the rate at which investors discount the expected common stock dividends of the firm to determine its share value. Two techniques are used to measure the cost of common stock equity. One relies on the constant-growth valuation model the other on the capital asset pricing model (CAPM).
cost of common stock equity rs
The rate at which investors discount the expected dividends of the firm to determine its share value.
In Chapter 7 we found the value of a share of stock to be equal to the present value of all future dividends which in one model are assumed to grow at a constant annual rate over an infinite time horizon. This model the constant-growth valuation model is also known as the Gordon growth model. The key expression derived for this model first presented as Equation 7.4 is
constant-growth valuation (Gordon growth) model
Assumes that the value of a share of stock equals the present value of all future dividends (assumed to grow at a constant rate) that it is expected to provide over an infinite time horizon.
(9.4)
where
Solving Equation 9.4 for rs results in the following expression for the cost of common stock equity:
(9.5)
Equation 9.5 indicates that the cost of common stock equity can be found by dividing the dividend expected at the end of year 1 by the current market price of the stock (the dividend yield) and adding the expected growth rate (the capital gains yield).
Duchess Corporation wishes to determine its cost of common stock equity rs. The market price P0 of its common stock is $50 per share. The firm expects to pay a dividend D1 of $4 at the end of the coming year 2016. The dividends paid on the outstanding stock over the past 6 years (2010 through 2015) were as follows:
Year
Dividend
2015
$3.80
2014
3.62
2013
3.47
2012
3.33
2011
3.12
2010
2.97
Using a financial calculator or electronic spreadsheet in conjunction with the technique described for finding growth rates in Chapter 5 we can calculate the annual rate at which dividends have grown g from 2010 to 2015. It turns out to be approximately 5% (more precisely it is 5.05%). Substituting D1 = $4 P0 = $50 and g = 5% into Equation 9.5 yields the cost of common stock equity:
The 13.0% cost of common stock equity represents the return required by existing shareholders on their investment. If the actual return is less than that shareholders are likely to begin selling their stock.
Recall from Chapter 8 that the capital asset pricing model (CAPM) describes the relationship between the required return rs and the nondiversifiable risk of the firm as measured by the beta coefficient . The basic CAPM is
capital asset pricing model (CAPM)
Describes the relationship between the required return rs and the nondiversifiable risk of the firm as measured by the beta coefficient .
rs = RF + [ (rm RF)]
(9.6)
where
Using the CAPM indicates that the cost of common stock equity is the return required by investors as compensation for the firms nondiversifiable risk measured by beta.
Duchess Corporation now wishes to calculate its cost of common stock equity rs by using the CAPM. The firms investment advisors and its own analysts indicate that the risk-free rate RF equals 7%; the firms beta equals 1.5; and the market return rm equals 11%. Substituting these values into Equation 9.6 the company estimates the cost of common stock equity rs to be
rs = 7.0% + [1.5 (11.0% 7.0%)] = 7.0% + 6.0% = 13.0%
The 13.0% cost of common stock equity represents the required return of investors in Duchess Corporation common stock. It is the same as that found by using the constant-growth valuation model.
The CAPM technique differs from the constant-growth valuation model in that it directly considers the firms risk as reflected by beta in determining the required return or cost of common stock equity. The constant-growth model does not look at risk; it uses the market price P0 as a reflection of the expected riskreturn preference of investors in the marketplace. The constant-growth valuation and CAPM techniques for finding rs are theoretically equivalent although in practice estimates from the two methods do not always agree. The two methods can produce different estimates because they require (as inputs) estimates of other quantities such as the expected dividend growth rate or the firms beta.
Another difference is that when the constant-growth valuation model is used to find the cost of common stock equity it can easily be adjusted for flotation costs to find the cost of new common stock; the CAPM does not provide a simple adjustment mechanism. The difficulty in adjusting the cost of common stock equity calculated by using the CAPM occurs because in its common form the model does not include the market price P0 a variable needed to make such an adjustment. Although the CAPM has a stronger theoretical foundation the computational appeal of the traditional constant-growth valuation model justifies its use throughout this text to measure financing costs of common stock. As a practical matter analysts might want to estimate the cost of equity using both approaches and then take an average of the results to arrive at a final estimate of the cost of equity.
As you know dividends are paid out of a firms earnings. Their payment made in cash to common stockholders reduces the firms retained earnings. Suppose that a firm needs common stock equity financing of a certain amount. It has two choices relative to retained earnings: It can issue additional common stock in that amount and still pay dividends to stockholders out of retained earnings or it can increase common stock equity by retaining the earnings (not paying the cash dividends) in the needed amount. In a strict accounting sense the retention of earnings increases common stock equity in the same way that the sale of additional shares of common stock does. Thus the cost of retained earnings rr to the firm is the same as the cost of an equivalent fully subscribed issue of additional common stock. Stockholders find the firms retention of earnings acceptable only if they expect that it will earn at least their required return on the reinvested funds.
cost of retained earnings rr
The same as the cost of an equivalent fully subscribed issue of additional common stock which is equal to the cost of common stock equity rs.
Viewing retained earnings as a fully subscribed issue of additional common stock we can set the firms cost of retained earnings rr equal to the cost of common stock equity as given by Equations 9.5 and 9.6.
rr = rs
(9.7)
Thus it is not necessary to adjust the cost of retained earnings for flotation costs because by retaining earnings the firm raises equity capital without incurring these costs.
The cost of retained earnings for Duchess Corporation was actually calculated in the preceding examples: It is equal to the cost of common stock equity. Thus rr equals 13.0%. As we will show in the next section the cost of retained earnings is always lower than the cost of a new issue of common stock because it entails no flotation costs.
Retained Earnings the Preferred Source of Financing
In the United States and most other countries firms rely more heavily on retained earnings than any other financing source. For example a 2013 survey of Chinese firms found that 64% of the companies surveyed listed retained earnings as one of their primary sources of funds. Bank loans were a distant second choice mentioned as a primary source of funds by just 44% of the companies.1
Our purpose in finding the firms overall cost of capital is to determine the after-tax cost of new funds required for financing projects. The cost of a new issue of common stock rn is determined by calculating the cost of common stock net of underpricing and associated flotation costs. Normally when new shares are issued they are underpriced meaning that they are sold at a discount relative to the current market price P0. Underpricing is the difference between the market price and the issue price which is the price paid by the primary markt investors discussed in Chapter 2.
cost of a new issue of common stock rn
The cost of common stock net of underpricing and associated flotation costs.
underpriced
Stock sold at a price below its current market price P0.
1. Business in China Survey 2013 China Europe International Business School.
We can use the constant-growth valuation model expression for the cost of existing common stock rs as a starting point. If we let Nn represent the net proceeds from the sale of new common stock after subtracting underpricing and flotation costs the cost of the new issue rn can be expressed as2
(9.8)
The net proceeds from sale of new common stock Nn will be less than the current market price P0. Therefore the cost of new issues rn will always be greater than the cost of existing issues rs which is equal to the cost of retained earnings rr. The cost of new common stock is normally greater than any other long-term financing cost.
In the constant-growth valuation example we found Duchess Corporations cost of common stock equity rs to be 13% using the following values: an expected dividend D1 of $4; a current market price P0 of $50; and an expected growth rate of dividends g of 5%.
To determine its cost of new common stock rn Duchess Corporation has estimated that on average new shares can be sold for $47. The $3-per-share underpricing is due to the competitive nature of the market. A second cost associated with a new issue is flotation costs of $2.50 per share that would be paid to issue and sell the new shares. The total underpricing and