What is the Marginal Cost of Capital?

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.

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. Firm's need to raise capital in order to invest in various capital budgeting projects. For instance, if DirecTV 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 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 then 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 then it is costing us to raise our money. This makes the project profitable and we should pursue it. We can not properly evaluate our capital budgeting projects without having a reasonable estimate of our cost of capital.

When is the MCC appropriately used as the required return for capital budgeting?

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:

1. 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 high risk 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 low risk projects. Anytime we experience a high risk project we must use a required return higher than the MCC and anytime we experience a low risk project we must use a required return lower than the MCC.

2. 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).

The Key Components of the Cost of Capital

There are four critical components that must be estimated in order to estimate the cost of capital. These are:

• The Market Value Weights of the Financing Components
• The Cost of Debt
• The Cost of Preferred Stock
• The Cost of Common Stock (Equity)
• Note: We will be ignoring the role of flotation costs for this course.

Once these are estimated, we use the following equation to estimate the MCC

• Where Wdebt represents the proportion of total financing coming from LT Debt
• ki represents the after-tax cost of debt financing
• Wpref represents the proportion of total financing coming from preferred stock
• kp represents the cost of preferred stock financing
• Wcom represents the proportion of total financing coming from common stock
• ks 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 % (10% = 10)

Estimating the Market Value Weights of the Financing Components

The weights represent the market value weights of each of the components, not the book value. (Note: In some 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.

Estimating the After-Tax Cost of Debt

The after-tax cost of debt is found through the following equation

ki = YTM(1 - T)

It is critical to note that we must use the after-tax cost of debt as opposed to the before-tax cost of debt. Interest appears on the income statement BEFORE taxes. This means that each dollar paid in interest lowers our tax bill. The IRS is paying part of our interest bill for us. Unfortunately, dividends are paid after taxes, so this adjustment is only for debt, not preferred or common stock. 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 is used.

Estimating the Cost of Preferred Stock

The cost of preferred stock is found through the following equation

Estimating the Cost of Common Stock

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

Because the above formula is derived from the constant growth model, it does not work as well in non-constant growth situations. One alternative approach is to refer to the Security Market Line. This allows us to estimate the cost of stock financing using the following formula

However, there is some concern as to how well the security market line holds up in practice. Therefore, a less theoretical but still valid model can also be used. This model simply assumes that stocks are riskier than bonds, so adds a risk premium to the Yield-to-Maturity 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 6% is probably most appropriate. Thus, we get the following formula

ks = YTM + Risk Premium

The best approach when estimating the cost of equity financing is to estimate it under all three equations, 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. For instance, the dividend growth model requires firms to pay dividends. Alternatively, firms that do not have any long-term debt outstanding may not be able to use the bond-yield plus risk premium approach due to the inability to estimate the YTM.

Example

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%
Risk-Free Rate -- 5%
Beta -- 1.20
Expected Return on the Market -- 12%
Risk Premium on Stocks over Bonds -- 4.5%

STEP ONE -- FIND THE WEIGHTS

• MVdebt = 60,000*865 = $51,900,000
• MVpreferred = 500,000*$60 = $30,000,000
• MVcommon = 2,300,000*45 = $103,500,000
• MV TOTAL = $185,400,000

• Wdebt = 51,900,000/185,400,000 = 0.28
• Wpref = 30,000,000/185,400,000 = 0.16
• Wcom = 103,500,000/185,400,000 = 0.56

STEP TWO -- FIND THE AFTER-TAX 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 After-tax Cost
  • ki = YTM*(1-T)
  • ki = 6.41%*(1 - 0.25)
  • ki = 4.81%

STEP THREE -- FIND THE COST OF PREFERRED STOCK

• kp = D/P
• kp = ($50*.09)/$60
• kp = $4.50/$60
• kp = 7.50%

STEP FOUR -- FIND THE COST OF COMMON STOCK

Method One -- Dividend Valuation Approach

• ks = (D1/P) + g
• ks = ($3.00/$45.00) + 0.06
• ks = 0.0667 + 0.06
• ks = 12.67%

Method Two -- Security Market Line (SML)

• 
• ks = 5% + 1.20(12% - 5%)
• ks = 5% + 1.20(7%)
• ks = 5% + 8.4%
• ks = 13.4%

Method Three -- Bond Yield + Risk Premium

• ks = YTM + RP
• ks = 6.41% + 4.5%
• ks = 10.91%

Take an average of the three methods to get cost of common stock financing

• ks = (12.67% + 13.40% + 10.91%)/3
• ks = 36.98/3
• ks = 12.33%

STEP FOUR -- CALCULATE THE MCC

• 
• MCC = (0.28*4.81) + (0.16*7.50) + (0.56*12.33)
• MCC = 1.35 + 1.20 + 6.90
• MCC = 9.45%

Floatation Costs -- (This will not be part of FIN326 required material, but is available for those interested)

The calculations made above assume that there are no additional costs to raising money other than paying the investors' their required return. However, this is not the case. When issuing new debt or selling additional shares of stock, most firms use (and must pay for) the services of an investment banker. Their also may be some other additional costs of issuing new securities. The investment banking fees and other costs of issuing securities are referred to as FLOATATION COSTS. To accurately capture the cost of capital it would be appropriate to consider floatation costs when appropriate.

When are floatation costs appropriate? Well, any additional debt financing or preferred stock financing needs to be generated by issuing more bonds and preferred stock. Thus, debt financing and preferred stock financing should consider floatation costs. Common stock financing on the other hand can come from two sources -- (A) Retained Earnings and (B) Newly Issued Securities. If the firm can generate all of its equity financing from retained earnings, then it doesn't have to issue new stock and can avoid floatation costs. On the other hand, if the company needs more equity financing than can be supplied by retained earnings, then it must issue new stock and pay floatation costs. This leads to BREAKPOINTS in the firm's Cost of Capital.

Consider a firm that has market value weights of 40% debt, 10% preferred, and 50% common stock. Also, the firm has $1,000,000 in retained earnings being generated this year. Since 50% of the firm's financing is coming from common equity, it can spend $2,000,000 on capital budgeting projects before it runs out of retained earnings and must issue new shares of common stock. Thus, there will be a Cost of Capital Breakpoint at $2,000,000 where the Marginal Cost of Capital will increase to reflect the impact of floatation costs associated with issuing new common stock financing. Additional Breakpoints could also happen if the company issues so much debt that investors feel the firm has become more risky and increase their required return.

To include floatation costs in the cost of debt financing, we would re-estimate the Yield-to-Maturity on the bonds. Specifically, instead of using the market price of the bond we would replace it with the amount that would be received after floatation costs. For example, consider a situation where the firm estimates floatation costs on debt to be 3%. If we currently have bonds outstanding with a price of $888, 6% coupon rate and 12 years to maturity, then the current YTM would be 7.44%. However, with floatation costs, we would use a price of $861.36 [($888)*(1 - .03)] to calculate the YTM and instead have a before tax cost of 7.82%.

To include floatation costs in the cost of preferred stock, we would re-estimate the cost. Specifically, instead of using the market price of preferred stock, we would replace it with the amount that would be received after floatation costs. For example, consider a situation where the firm estimates floatation costs on preferred stock to be 4.5%. If we currently have preferred stock outstanding with a 9% dividend rate, a $50 par value and a $45 market price, then the current cost of preferred stock would be 10%. However, with floatation costs, we would use a price of $42.98 [($45)*(1 - .045)] to calculate the cost of preferred and would get kp to be 10.47%.

To include floatation costs in the cost of common stock, we would re-estimate the cost. Specifically, instead of using the market price of common stock, we would replace it with the amount that would be received after floatation costs. For example, consider a situation where the firm estimates floatation costs on common stock to be 7%. If we currently have common stock outstanding with a forecasted dividend (D1) of $2.50, a $25 market price and a 5% growth rate, then the current cost of common stock would be 15%. However, with floatation costs, we would use a price of $23.25 [($25)*(1 - .07)] to calculate the cost of common and would get ks to be 15.75%. Note that this only works with the dividend valuation approach. To adjust the cost of common stock financing using the SML or Bond Yield Plus Risk Premium approach would require a subjective adjustment. Also, remember that we would only include floatation costs in estimating the cost of common AFTER we have used up all of our retained earnings financing.