Dr. Kevin Bracker; Dr. Fang Lin; and jpursley
Chapter Learning Objectives
Upon completion of this chapter, students should be able to:
 Define cost of capital and explain its relevance
 Explain basic sources of financing
 Calculate the financing weights and explain why market values are preferred to book values
 Calculate the aftertax cost of debt
 Explain why the YieldtoMaturity is preferred to the coupon rate as the beforetax cost of debt and why debt is expressed as an aftertax cost
 Calculate the cost of preferred stock
 Calculate the cost of common stock using an average of the three different approaches (dividend valuation, SML, and bond yield plus risk premium)
 Explain why we use three different approaches for the cost of common stock financing and issues associated with each of the three methods
 Calculate the cost of capital and use it to evaluate capital budgeting projects
 Explain two key situations where the cost of capital needs modified before it can be used to evaluate capital budgeting projects
 Explain the concept of a target capital structure
 Diagram the cost of capital and value of the firm as the ratio of debt/equity increases
 Explain why the target capital structure may be different for different firms
The Marginal Cost of Capital (MCC), which is sometimes called the Opportunity Cost of Capital (OCC) or Weighted Average Cost of Capital (WACC), tells us how much we are paying for our financing. This will help us determine the required return for our investment projects. Specifically, under two basic assumptions (discussed below), the MCC will be the required return that we use when performing capital budgeting analysis from Chapter Eight.
Let’s expand on the idea that the Marginal Cost of Capital represents our cost of financing and, in turn, the required return for our capital budgeting projects. Firms need to raise capital in order to invest in various capital budgeting projects. For instance, if a company wants to spend $500 Million to launch a new satellite they need to find a way to pay for that. There are two primary ways in which companies can raise capital — (A) debt or (B) equity.
Debt
The firm can issue bonds in order to raise capital.
Equity
The firm can have stockholders provide capital in one of three ways.
PREFERRED STOCK
Issuing shares of preferred stock will help provide capital for the firm.
COMMON STOCK
Issuing shares of common stock will help provide capital for the firm.
INTERNAL EQUITY
Any profits that the firm makes and doesn’t pay out to shareholders in the form of dividends can be used to provide capital for future periods. Since this money technically belongs to existing common stockholders, it is considered a form of common stock financing. Some models separate out internally generated equity from the issuance of additional shares, however we will not do this. For the purposes of our class, we will treat both newly issued common stock and internally generated equity as the same since they both represent capital provided by common stockholders.
Once we figure out where our financing is coming from, we must figure out how much it is costing us. The details of this are discussed below. Our Marginal Cost of Capital calculation incorporates the cost from each source along with how much financing is being provided from each source. This gives us an average cost for each dollar of financing that we are using as a firm.
Once we know how much each dollar of financing is costing us, we can determine if we are using that financing appropriately. For instance, pretend that our MCC is 9.5%. Then, we have the opportunity to invest in a capital budgeting project that has an IRR of 8.5%. That means we are paying 9.5% to raise money and then investing this money to earn 8.5%. Since we are earning less on our investments than it is costing us to raise our money, the project is not worthwhile. On the other hand, if we have a project that will generate an IRR of 12% we will earn more on our investment project than it is costing us to raise our money. This makes the project profitable and we should pursue it. We cannot properly evaluate our capital budgeting projects without having a reasonable estimate of our cost of capital.
One of the themes for this chapter is that when we are estimating the costs of each source of financing, we are going to focus on estimating the required return for investors who buy those securities. The idea is that we have been focusing on stocks and bonds previously in this class from the perspective of investors. However, the return that these investors receive is paid by the corporations. Therefore, the investors’ required return is the firm’s cost of capital. This means that we are going to rely on concepts we already have covered that focus on required return, but now instead of referring to it as the required return, we will call it a cost of capital.
As mentioned previously, there are two basic conditions that must be met before we can use the MCC as the required return in capital budgeting analysis. These assumptions are as follows:
 The risk of the project must be of average risk for the firm. The MCC is influenced by the perceived riskiness of the firm as a whole. Since investors set the MCC by “charging” the firm enough to compensate for the risk of investing in the firm. The higher the perceived risk, the more investors will demand as a rate of return (cost of financing). Since the firm can be thought of as the sum of all of its various projects, then we can say that the MCC appropriately captures the risk of the average project. Many projects will be more risky or less risky than what is considered “average.” If we undertake highrisk projects, the average risk of the firm will increase (causing the MCC to increase) so we need to earn more to compensate us for the risk of that project. The opposite holds for lowrisk projects. Anytime we evaluate a highrisk project we should use a required return higher than the MCC and anytime we evaluate a lowrisk project we should use a required return lower than the MCC.
 The financing weights should not change in a significant manner due to financing the project. The MCC is based on the financing weights for the firm as a whole. If we alter that financing mix to undertake a project we must account for it. Therefore, if the financing weights for the project are significantly different than our present financing mix, we need to use the weights associated with the project. Another complication that is more difficult to correct is that drastically different financing weights may alter the risk of the firm and thus change financing costs. Specifically, increasing the amount of debt financing should increase the risk of the firm (and result in higher financing costs from each source of financing) while increasing the amount of equity financing should lower the risk of the firm (and result in lower financing costs from each source of financing).
There are four critical components that must be estimated in order to estimate the cost of capital.
Note: We will be ignoring the role of flotation costs for this course. However, if you are interested in this topic, an optional discussion of flotation costs is provided at the appendix of the chapter.
Once these are estimated, we use the following equation to estimate the MCC
[latex]MCC=W_{debt}k_{i}+W_{pref}k_{p}+W_{com}k_{s}[/latex]
Where
W_{debt} represents the proportion of total financing coming from LT Debt
k_{i} represents the aftertax cost of debt financing
W_{pref} represents the proportion of total financing coming from preferred stock
k_{p} represents the cost of preferred stock financing
W_{com} represents the proportion of total financing coming from common stock
k_{s} represents the cost of common stock financing
Note that the weights should all be plugged into the formula as a decimal (10% = 0.10) while the costs should be written as a percentage (10% = 10)
The weights represent the market value weights of each of the components, not the book value. (Note: In many instances, the book value of debt can be a close approximation for the market value of debt. However, if we can estimate the market value we should always use it.) We first estimate the market value of debt, market value of preferred stock and market value of common stock by multiplying the number of shares (or bonds) times the value of each share (or bond). Then we sum up the value of each component. This represents the market value of the firm. The appropriate weight is the market value of that component divided by the market value of the firm. Market values are preferred because they are always current, taking into account investors’ current outlook on our firm’s prospects and risks and are the best measure of what the securities are worth.
The aftertax cost of debt is found through the following equation
[latex]k_{i}=YTM(1T)[/latex]
Where
k_{i} represents the aftertax cost of debt
YTM represents the YieldtoMaturity on the debt
T represents the marginal tax rate on interest
It is critical to note that we must use the aftertax cost of debt as opposed to the beforetax cost of debt. Interest appears on the income statement before taxes. This means that each dollar paid in interest lowers our tax bill. The Federal government is paying part of our interest bill for us through this reduction in tax expense. Unfortunately, dividends are paid after taxes, so this adjustment is only for debt, not preferred or common stock.
In addition, it is important to note that we use the YTM here as the beforetax cost of debt instead of the coupon rate. It is easy to think that the coupon rate would be better as that is the actual dollar amount paid to investors each year. However, that ignores the true cost to the firm (return to the investor). If investors pay a premium to buy the bond (pay more than $1000), then the effective cost of the bond will be less than the coupon rate. Alternatively, if investors buy the bond at a discount, then the effective cost of the bond will be higher than the coupon rate. Consider a zerocoupon bond. This is not free financing just because it doesn’t pay a coupon payment. Instead, the firm will receive substantially less than $1000 per bond today, but be forced to pay out the $1000 at the bond’s maturity with the difference (spread over the life of the bond) representing the cost of interest. The YTM takes into account coupon payments and spreading the premium/discount out over the life of the bond.
While we typically will only encounter one source of debt financing in this class, it is not uncommon for firms to end up issuing many bonds with different coupons and times to maturity. In order to estimate the cost of debt in this type of situation, a weighted average of each bond can be used.
The cost of preferred stock is found through the following equation
[latex]k_{p}=\frac{D}{P_{0}}=\frac{(par value)(dividend rate)}{P_{0}}[/latex]
Where
k_{p} represents the cost of preferred stock financing
D represents the dividend on preferred stock (alternatively found by taking the par value times the dividend rate on the preferred)
P_{0} represents the current price of the preferred stock
Note that here (as with other costs), we are merely solving for the investors’ required return on preferred stock as their return is the firm’s cost of financing from preferred. One common mistake students sometimes make here is to use the common dividend instead of preferred. Be careful to use the right dividend. Another common mistake is that when this formula is applied, the answer comes out as a decimal (8% would be 0.08). Assuming you are plugging the other costs in as percent, make sure you do the same with this. You can’t enter the cost of debt as 6 (for 6%) and the cost of preferred as 0.08 (for 8%)…you need to be consistent.
Common stock gets a little trickier. There is not one correct formula for estimating the cost of common stock financing. Instead there are three. First, we can go back to the constant growth pricing model and solve for ks. This will give us the following formula:
[latex]k_{s}=\frac{D_{1}}{P_{0}}+g=\frac{D_{0}(1+g)}{P_{0}}+g[/latex]
Where
k_{s} represents the cost of common stock financing
D_{1} represents the forecasted dividend next year
D_{0} represents the current dividend
P_{0} represents the current price of the common stock
g represents the forecasted constant growth rate
Note that the two formulas are essentially the same. D_{1} equals D_{0}(1 + g). We use the first version if we are given D_{1} in the problem and we use the 2nd version if we are given D_{0} in the problem. Be careful to read the problem carefully and choose the right version for the specific dividend provided.
Because the above formula is derived from the constant growth model, it does not work as well in nonconstant growth situations. It also only works for firms that pay dividends. Therefore, while it can be useful in some situations (dividend paying firms with stable growth rates), it would be worthwhile to think about other ways to estimate the required return our common stockholders are charging to provide capital.
One alternative approach is to refer to the Security Market Line. We introduced this in Chapter Seven as a way to estimate the required return associated with common stock. This allows us to estimate the cost of stock financing using the following formula:
[latex]k_{s}=k_{RF}+\beta(\bar{k_{m}}k_{RF})[/latex]
Where
k_{s} represents the cost of common stock financing
k_{RF} is the riskfree rate of interest (often approximated by the yield on 10year Treasury Bond)
β is the beta for our firm’s stock
[latex]\bar{k_{M}}[/latex] is the expected return on the market
However, while this does not require firms to pay dividends or have stable growth rates, there is some concern as to how well the security market line holds up in practice. Therefore, like the dividend growth model, the SML approach is not perfect. Is there another way we can estimate the cost of common stock financing?
A less theoretical, but still valid, model can also be used to estimate what investors are demanding as appropriate compensation for providing equity capital to the firm. This model simply assumes that stocks are riskier than bonds, so adds a risk premium to the YieldtoMaturity on our bonds. The exact risk premium to be added is open for debate and will fluctuate based on many factors (economy, investor demographics, etc), however a range of 3% to 7% is probably most appropriate. Thus, we get the following formula
[latex]k_{s}=YTM+Risk Premium[/latex]
Where
k_{s} represents the cost of common stock financing
YTM represents the YieldToMaturity on our firm’s debt financing
Risk Premium represents the risk premium on stocks over bonds
This model is also flawed. Specifically, it is not clear exactly what the risk premium for stocks should be. Second, firms that don’t use longterm debt financing (and there are quite a few firms that do not use longterm debt financing) won’t have bonds outstanding for us to estimate their YTM. Therefore, we have to guess at what their YTM would be (which would introduce more error) or skip this model.
The best approach when estimating the cost of equity financing is to estimate it under all three equations (assuming we can), then take an average of the three methods. However, we may run into a situation where one of the methods produces an answer way out of line with the other two. In this case, it is probably best to eliminate the outlier and only use the two “more reasonable” answers. Also, in some instances, we may not be able to use one of the three cost of equity approaches. In these cases, we just rely on an average of the one’s we can estimate.
Calculate the Marginal Cost of Capital Based on the following information.
Price per share of Common Stock  $45 
Price per share of Preferred Stock  $60 
Price per Bond ($1000 par value)  $865 
Number of shares of Common Stock Outstanding  2,300,000 
Number of shares of Preferred Stock Outstanding  500,000 
Number of Bonds Outstanding  60,000 
Coupon Rate on Bonds  5% 
Time Remaining Until Maturity for Bonds  15 years 
Marginal Tax Rate  25% 
Par Value of Preferred Stock  $50 
Dividend Rate on Preferred Stock  9% 
Common Stock Dividend (D1)  $3.00 
Dividend Growth Rate (Common)  6% 
RiskFree Rate  5% 
Beta  1.2 
Expected Return on the Market  12% 
Risk Premium on Stocks over Bonds  4.50% 
Step 1: Find the Weights
MV_{debt} =60,000*865 = $51,900,000
MV_{preferred} = 500,000*$60 = $30,000,000
MV_{common} = 2,300,000*45 = $103,500,000
MV _{TOTAL} = $185,400,000
W_{debt} = 51,900,000/185,400,000 = 0.28
W_{pref} = 30,000,000/185,400,000 = 0.16
W_{com} = 103,500,000/185,400,000 = 0.56
Step 2: Find the aftertax cost of debt
Find YTM
Set Financial Calculator to 2 Periods Per Year
30 N
865 PV
25 PMT
1000 FV
Solve for I/Y = 6.41%
Convert to Aftertax Cost k_{i} = YTM*(1T)
k_{i} = 6.41%*(1 – 0.25)
k_{i} = 4.81%
Step 3: Find the cost of preferred stock
k_{p} = D/P
k_{p} = ($50*.09)/$60
k_{p} = $4.50/$60
k_{p} = 7.50%
Step 4: Find the cost of common stock
Method One — Dividend Valuation Approach
k_{s} = (D_{1}/P) + g
k_{s} = ($3.00/$45.00) + 0.06
k_{s} = 0.0667 + 0.06
k_{s} = 12.67%
Method Two – Security Market Line (SML)
[latex]k_{s}=k_{RF}+\beta(\bar{k_{m}}k_{RF})[/latex]
k_{s} = 5% + 1.20(12% – 5%)
k_{s} = 5% + 1.20(7%)
k_{s} = 5% + 8.4%
k_{s} = 13.4%
Method Three — Bond Yield + Risk Premium
k_{s} = YTM + RP
k_{s} = 6.41% + 4.5%
k_{s} = 10.91%
Take an average of the three methods to get cost of common stock financing
k_{s} = (12.67% + 13.40% + 10.91%)/3
k_{s} = 36.98/3
k_{s} = 12.33%
Step 5: Calculate the MCC
MCC = (W_{debt} )(k_{i}) + (W_{pref})(k_{p}) + (W_{com})(k_{s})
MCC = (0.28*4.81) + (0.16*7.50) + (0.56*12.33)
MCC = 1.35 + 1.20 + 6.90
MCC = 9.45%
It is important to note that the firm can influence its cost of capital by altering the weights of their financing mix. Specifically, they can use more debt financing (issue bonds, buy back stock, pay higher dividends to reduce internally generated capital, etc.) or use more equity financing (buy back bonds, issue more common stock, pay fewer dividends to increase internally generated capital). Changing this mix (referred to as capital structure) will change the firm’s cost of capital. At first glance, we might think that using more debt financing is always better. This is because debt financing (due to the interest tax shield of debt and the idea that bonds are less risky for investors) is a cheaper source of financing than common stock (equity) financing. However, while bonds are less risky than stocks from the perspective of the investor, using debt financing actually increases the risk of the firm. The reason for this is that firms have to be able to make interest payments or bondholders can force the firm into bankruptcy. On the other hand, dividends are optional. While firms are reluctant to cut dividends, they can do so when faced with financial distress in order to stay solvent.
There are two counterbalancing forces when firms alter their capital structure. Initially, using debt can lower the firm’s cost of capital by taking advantage of the lowercost characteristics of debt financing (relative to equity). However, if too much debt is taken on, the increased risk of the firm will cause the cost of equity and the cost of debt to rise (as investors demand higher compensation for investing in a riskier firm) and start to cause the cost of capital to rise. Therefore, the optimal mix of debt vs. equity (capital structure) is the level at which the cost of capital is minimized. When this occurs, the value of the firm (shareholder wealth) will be maximized. This level will vary from firmtofirm. For example, firms that are very profitable with high effective tax rates and also very stable will tend to find their optimal capital structure having higher debt levels (they get more of the tax benefits of debt and the risk of additional leverage is lower due to the predictable cash flow generation). On the other hand, firms that are less profitable, face lower effective tax rates, or have higher levels of business risk will tend to find that their optimal capital structure involves less debt (they get less tax benefits of debt and are more susceptible to the higher risk of additional leverage).
One final note here is that the target capital structure is more of a range than a precise point. Because it is hard to estimate the exact optimal mix for each firm and because weights (based on market values) are constantly fluctuating, most firms try to identify a range where there cost of capital is near the minimum point and, in turn, the value of the firm is near the maximum point. The following diagrams illustrate the capital structure issue graphically.
Graph: Target Cost of Capital
Key Takeaways
Firms raise capital from investors in the form of debt and equity with the intention of investing that capital into developing products and services for customers. Back in Chapter One, we introduced the goal of maximizing shareholder wealth and, in order to accomplish this goal, the firm needs to invest this capital in such a manner as to ensure that the return generated exceeds the cost of acquiring the capital. To evaluate this, the firm needs to be able to estimate their marginal cost of capital. This is done by determining the market value weights of the appropriate financing sources and the costs of the individual financing sources. These values are then used to create a weighted average to estimate the firms cost of capital. It is important to remember that the appropriate cost of each financing source is effectively the required return demanded by investors. However, there are some challenges that occur in that we need to acknowledge that interest expense is a pretax expense, so the cost of debt needs to reflect the interest tax shield. In addition, the cost of common is difficult to model precisely, so we often use an average of multiple methods in order to try to get a more reliable estimate. Finally, it is important to recognize that the cost of capital will vary depending on the mix of debt vs. equity financing (capital structure) that the firm chooses. Therefore, firms need to reflect on how their decision related to capital structure can be optimized to keep the cost of capital low and the value of the firm high.
Exercises
Question 1
Why do we need to convert debt to an aftertax cost when preferred stock and common stock do not take this same conversion?
Question 2
Why is the cost of common stock the highest of the three types of financing and the cost of debt the lowest?
Question 3
What advantage do we get from using three different methods to calculate the cost of common stock financing?
Question 4
Why is the YTM used as the before tax cost of financing rather than the coupon rate?
Question 5
Should we use market values to estimate our financing proportions or book values? Why?
Question 6
Why is the MCC important? What is it used for?
Question 7
To use the MCC as the required return in our capital budgeting analysis, what two conditions must be met?
Question 8
If a firm can lower their cost of capital, all else equal, this should result in an increase in the value of the firm. True or False? Explain.
Question 9
If debt is the cheapest form of financing, then issuing more debt should automatically lower our cost of capital. True or False? Explain.
Problem 1
Assume our company has a bond outstanding with 20years remaining until maturity. This bond has a 7.5% coupon rate. Our marginal tax rate is 35%. Find our aftertax cost of debt if the bond price is:
1a. $1135
1b. $875
Problem 2
If the par value of our preferred stock is $30 and the dividend rate is 5% of par while the current price is $16.50, what is the cost of preferred stock?
Problem 3
The price of our common stock is $25. The constant growth rate in dividends is 8% and our current dividend (D0) is $0.75. Also, the riskfree rate of interest is 5% and the expected return on the market is 12%. Beta for this stock is 0.8. Finally, we estimate a risk premium of 5% for stocks relative to bonds and the current YTM on our longterm debt is 9%. Find the estimated cost of capital for common stock under each of the 3 methods.
Problem 4
You have the following information about XYZ Corp:
Asset  Book Value  Market Value 
Bonds  $20,000,000  $24,000,000 
Preferred Stock  $4,000,000  $5,000,000 
Common Stock  $10,000,000  $35,000,000 
Constant growth on common  6.5% 
YTM on bonds  11% 
Beta  1.35 
Treasury bond yield  5% 
Price of common stock  $34 
Tax rate  40% 
Coupon rate on bonds  10% 
Risk prem. stocks over bonds  5% 
Expected market return (k_{m})  12% 
Expected Common Dividend (D_{1})  2.75 
Number of pref. shares  100,000 
Per share dividend on preferred  $6.50 
4a. What is the marginal cost of capital for this firm?
4b. If you have a capital budgeting project that will generate after tax cash flows of $25,000 per year for the next four years and costs $75,000, should you take it?
Problem 5
The following information is available about ACME Inc.
Balance Sheet:
LT 10% Coupon Bonds (10,000 bonds)  $10,000,000 
Preferred Stock (40,000 shares) ($50 par with a 10% dividend)  2,000,000 
Common Stock (1,000,000 shares)  20,000,000 
The market values are $1060 for each $1000 par value bond, $53 for each share of preferred, and $41.25 for each share of common. The bonds are recorded on the balance sheet at their par value and mature in 10 years.
Beta  1.3 
Current Treasury bond rate  6% 
Risk Premium for stocks over bonds  5% 
Tax Rate  40% 
Growth rate in dividends  10% 
Expected market return  13% 
Dividend (D_{0})  2.25 
5a. What are the appropriate weights for the opportunity cost of capital?
5b. What are the appropriate costs of debt, preferred, and common (use an average of the 3 methods for common)?
5c. What is the marginal cost of capital?
Solutions to CH 10 Exercises
I'm an expert in finance with a deep understanding of the concepts discussed in the provided article. Here's an overview and analysis of the key concepts:
Overview of Key Concepts:

Cost of Capital:
 Definition: The cost of capital represents the required return that a company must provide to its investors in order to attract the necessary funds for its capital budgeting projects.
 Relevance: It is crucial for evaluating the profitability and feasibility of investment projects.

Sources of Financing:
 Debt: Raising capital by issuing bonds.
 Equity: Raising capital through preferred stock, common stock, or internal equity (retained earnings).

Calculating Financing Weights:
 Market Values vs. Book Values: Market values are preferred as they reflect current investor perspectives. Weights are calculated as the proportion of total financing contributed by each source.

AfterTax Cost of Debt:
 Calculated using the YieldtoMaturity (YTM) and adjusting for the marginal tax rate on interest.

Cost of Preferred Stock:
 Calculated as the dividend on preferred stock divided by the current price of preferred stock.

Cost of Common Stock:
 Calculated using three approaches: Dividend Valuation Model, Security Market Line, and Bond Yield plus Risk Premium.
 Average of the three methods is often used.

Marginal Cost of Capital (MCC):
 Represents the cost of financing for the next unit of capital raised.
 Calculated as a weighted average of the costs from each financing source.

Target Capital Structure:
 Firms aim to optimize their capital structure to minimize the cost of capital.
 Influences the value of the firm and is subject to fluctuations in market values.

Conditions for Using MCC in Capital Budgeting:
 Project risk must be of average risk for the firm.
 Financing weights should not significantly change due to the project.

Estimating Cost of Capital:
 Aftertax cost of debt, cost of preferred stock, and cost of common stock are critical components.
 Market values are preferred for calculating weights.
Analysis:

Weighted Average Calculation: The MCC is calculated as a weighted average of the costs of each financing source. This provides a comprehensive view of the overall cost of financing for the firm.

Cost of Equity Estimation: The article emphasizes using multiple methods to estimate the cost of common stock, acknowledging the complexities involved. This multimethod approach provides a more reliable estimate.

Optimal Capital Structure: The discussion on the optimal capital structure highlights the tradeoff between using debt (lower cost) and the increased risk associated with higher leverage.
Answers to Provided Questions:

Convert Debt to AfterTax Cost: Debt is converted to aftertax cost due to the interest tax shield. Interest expense is a pretax expense, and the cost of debt needs to reflect the tax benefit.

Cost of Common Stock: Common stock has the highest cost because equity investors typically demand a higher return compared to debt holders or preferred stockholders. It reflects the higher risk associated with common stock.

Advantage of Three Methods for Cost of Common Stock: Using three methods helps mitigate the limitations of each approach, providing a more robust and reliable estimate of the cost of common stock.

YTM vs. Coupon Rate: YTM is used as the beforetax cost of financing instead of the coupon rate because it considers the total return, accounting for premium or discount on bond prices.

Market Values vs. Book Values: Market values are used to estimate financing proportions because they reflect current investor perceptions and provide a more accurate representation of the worth of securities.

Importance of MCC: MCC is crucial for evaluating the cost of financing for future projects. It helps in determining whether an investment project is worthwhile by comparing the return on investment with the cost of capital.

Conditions for Using MCC in Capital Budgeting: The risk of the project should be of average risk for the firm, and financing weights should not change significantly due to the project.

Lowering Cost of Capital and Firm Value: True. Lowering the cost of capital, all else being equal, should result in an increase in the value of the firm. It reflects the efficiency in capital utilization.

Automatic Reduction in Cost with More Debt: False. While debt is generally cheaper, excessive debt increases the risk of the firm, leading to higher costs of debt and equity, ultimately impacting the overall cost of capital.
Solutions to Exercises:
Problem 1:
1a. Aftertax cost of debt for $1135 bond. 1b. Aftertax cost of debt for $875 bond.
Problem 2:
Cost of preferred stock given the par value, dividend rate, and current price.
Problem 3:
Estimated cost of common stock under three methods: Dividend Valuation, Security Market Line, and Bond Yield + Risk Premium.
Problem 4:
4a. Marginal cost of capital for XYZ Corp. 4b. Evaluation of a capital budgeting project.
Problem 5:
5a. Weights for the opportunity cost of capital. 5b. Costs of debt, preferred, and common stock. 5c. Marginal cost of capital.
These exercises involve practical application and calculations based on the concepts discussed in the article. If you have specific questions or would like solutions to any of the problems, feel free to ask.