### Capitalization

# More Advance with Cost of Capital Analysis

**The cost of capital is defined as the rate of return that is necessary to maintain the market value of the firm (or price of the firm’s stock). Financial managers must know the cost of capital (the minimum required rate of return) in (1) making capital budgeting decisions, (2) helping to establish the optimal capital structure, and (3) making decisions such as leasing, bond refunding, and working capital management. The cost of capital has been used either as a discount rate under the NPV method or as a hurdle (cutoff) rate under the IRR method**.

This post discusses cost of capital in greater detail, yet more rich in techniques with simple examples. Enjoy!Advertisement

### Who Uses The “Cost of Capital” Analysis and When?

**Financial Managers**– Cost of capita] is a very important concept within financial management, because it is the rate of return that must be achieved in order for the price of the stock to remain unchanged. Therefore, the cost of capital is the minimum acceptable rate of return for the company’s new investments. Financial officers should be thoroughly familiar with the ways to compute the costs of various sources of financing for financial, capital budgeting, and capital structure decisions. A comparison should be made of the cost of capital rates under alternative financing strategies (e.g., mix of debt, preferred stock, and common stock). The financial manager should typically issue the financing instrument that results in the lowest overall cost of capital.**Top Management and Corporate Strategists**– Top managers must have a good understanding of the cost of capital before making important strategic decisions such as mergers, acquisitions, and buyouts.**Investment and Credit Analysts**– An increase in a company’s cost of capital relative to competing companies in the industry means that it is viewed as being more risky in the eyes of the investment and credit community.

### How Is Cost of Capital Computed?

**The cost of capital is computed as a weighted average of the various capital components, which are items on the right-hand side of the balance sheet, such as debt, preferred stock, common stock, and retained earnings**. Each element of capital has a component cost that is identified by the following:

**ki**= before-tax cost of debt**kd**= ki(1 – t) = after-tax cost of debt, where t = tax rate**kp**= cost of preferred stock**ks**= cost of retained earnings (or internal equity)**ke**= cost of external equity, or cost of issuing new common stock**ko**= firm’s overall cost of capital, or a weighted average cost of capital

**I am going to describe each of these calculations in this post, as well as the determination of historical, target, and marginal weights**. Read on…

**1. Cost of Debt** – The before-tax cost of debt can be found by determining the internal rate of return (or yield to maturity) on bond cash flows. However, the following short-cut formula may be used for approximating the yield to maturity on a bond:

ki = [I + (M-V)/n]/[(M+V)/2]

where:

**I** = annual interest payments

**M** = par or face value, usually $1000 per bond

**V** = market value or net proceeds from the sale of a bond

**n** = term of the bond in n years

**Note**: Since the interest payments are tax-deductible, the cost of debt must be stated on an after-tax basis.

**Example-1**

Assume that the Carter Company issues a $1000, 8 percent, 20-year bond whose net proceeds are $940. The tax rate is 40 percent. **Then, the before-tax cost of debt, **“**ki**“** is**:

Ki = [I + (M-V)/n]/[(M+V)/2]

Ki = [$80 + (1000 – 940)/20]/[(1000 + 940)/2]

Ki = 83/970

ki = 8.56%

Therefore, the after-tax cost of debt is:

kd = ki (1-t)

kd = 8.56% (1-0.4)

kd = 5.14%

**2. Cost of Preferred Stock** – The cost of preferred stock (**kp**) is found by dividing the annual preferred stock dividend, dp, by the net proceeds from the sale of the preferred stock “**p**” as follows:

kp = dp/p

**Note**: Since preferred stock dividends are not a tax-deductible expense, these dividends are paid out after taxes. Consequently, no tax adjustment is required.

**Example-2**

Suppose that the Carter Company has preferred stock that pays a $13 dividend per share and sells for $100 per share in the market. The flotation (or underwriting) cost is 3 percent, or $3 per share. Then the cost of preferred stock is:

kp = dp/p

kp = $13/$97 = 13.4%

**3. Cost of Equity Capital** – The cost of common stock, ke, is generally viewed as the rate of return that investors require on a firm’s common stock. Two techniques for measuring the cost of common stock equity capital are widely used: **(a) Gordon’s growth model** and **(b) the capital-asset pricing model (CAPM)** approach.

Let’s have a look at each of the approach. Read on…

**(a). Gordon’s Growth Model** – Gordon’s model is:

P0 = D1/r-g

where:

**P0** = value (or market price) of common stock

**D1** = dividend to be received in 1 year

**r** = investor’s required rate of return

**g** = rate of growth (assumed to be constant over time)

Solving the model for r yields a formula for the cost of common stock:

r = D1/P0 + g or ke = D1/P0 + g

**Note**: that r is changed to ke to show that it is used for the computation of cost of capital.

**Example-3**

Assume that the market price of the Carter Company’s stock is $40. The dividend to be paid at the end of the coming year is $4 per share and is expected to grow at a constant annual rate of 6 percent. Then the cost of this common stock is:

**ke** = D1/P0 + g = $4/$40 + 6% = 16%

The cost of new common stock, or external equity capital, is higher than the cost of existing common stock because of the flotation costs involved in selling the new common stock. Flotation costs, sometimes called issuance costs, are the total costs of issuing and selling a security, including printing and engraving, legal fees, and accounting fees.

If “**f**” is flotation cost in percent, the formula for the cost of new common stock is:

ke = [D1/[P0 (1-f)]] + g

**Example-4**

Assume the same data as in Example-3, except that the firm is trying to sell new issues of stock A and its flotation cost is 10 percent. Then:

ke = [D1/[P0 (1-f)]] + g

ke = [4/[$40 (1-0.1)] + 6%

ke = $4/36 + 6% = 11.11% + 6% = 17.11%

**(b). Capital-Asset Pricing Model (Capm) Approach** – An alternative approach to measuring the cost of common stock is to use the CAPM, which involves the following steps:

- Estimate the risk-free rate, rf, generally taken to be the U.S. Treasury bill rate.
- Estimate the stock’s beta coefficient, b, which is an index of systematic (or non-diversifiable market) risk.
- Estimate the rate of return on the market portfolio, rm, such as the Standard & Poor’s 500 Stock Composite Index or Dow Jones 30 Industrials.

Estimate the required rate of return on the firm’s stock, using the CAPM equation:

ke = rf + b(rm – rf)

Again, note that the symbol rj has been changed to ke.

**Example-5**

Assuming that rf is 7 percent, b is 1.5, and rm is 13 percent, then:

**ke** = rf + b(rm – rf) = 7% + 1.5% (13% – 7%) = 16%

This 16 percent cost of common stock can be viewed as consisting of a 7 percent risk-free rate plus a 9 percent risk premium, which reflects that the firm’s stock price is 1.5 times more volatile than the market portfolio to the factors affecting nondiversifiable, or systematic, risk. (See also No. 26, Capital-Asset Pricing Model).

**4. Cost of Retained Earnings** – The cost of retained earnings, ks, is closely related to the cost of existing common stock, since the cost of equity obtained by retained earnings is the same as the rate of return that investors require on the firm’s common stock. Therefore:

ke = ks

### Measuring the Overall Cost of Capital

**A firm’s overall cost of capital is the weighted average of the individual capital costs, with the weights being the proportions of each type of capital used. Let ko be the overall cost of capital**:

ko = wd*kd + wp*kp + we*ke + ws*ks

where:

**wd**= percent of total capital supplied by debts**wp**= percent of total capital supplied by preferred stock**we**= percent of total capital supplied by external equity**ws**= percent of total capital supplied by retained earnings (or internal equity)

**Weights Average Capital Cost**

**The weights used in this analysis can be**: **historical, target, or marginal**.

**(a). Historical Weights** – Historical weights are based on a firm’s existing capital structure. The use of these weights is based on the assumption that the firm’s existing capital structure is optimal and therefore should be maintained in the future. Two types of historical weights can be used: book-value weights and market-value weights.

**(b). Book-value weights** – The use of book-value weights in calculating the firm’s weighted cost of capital assumes that new financing will be raised using the same method the firm used for its present capital structure. The weights are determined by dividing the book value of each capital component by the sum of the book values of all the long-term capital sources. The computation of overall cost of capital is illustrated in the following example.

**Example-6**

Assume the following capital structure and cost of each source of financing for the Carter Company:

Capital asset Cost

Mortgage bonds ($1000 par) $20,000,000 –> 5.14% (from Example 1)

Preferred stock ($100 par) $5,000,000 –> 13.40% (from Example 2)

Common stock ($40 par) $20,000,000 –> 17.11% (from Example 4)

Retained earnings $5,000,000 –> 16.00% (from Example 3)

Total $50,000,000

**The book-value weights and the overall cost of capital are computed as follows**:

Source Book value Weight Cost Weighted cost

Debt $20,000,000 40%(a) 5.14% 2.06%(b)

Preferred stock $5,000,000 10 13.40% 1.34

Common stock $20,000,000 40 17.11% 6.84

Retained

Earnings $5,000,0000 10 16.00% 1.60

Total $50,000,000 100% 11.84%

**Overall cost of capital** = **ko** = 11.84%

- $20,000,000/$50,000,000 = 0.40 = 40%
- 5.14% × 40% = 2.06%

**(c). Market-value weights** – Market-value weights are determined by dividing the market value of each source by the sum of the market values of all sources. The use of market-value weights for computing a firm’s weighted-average cost of capital is theoretically more appealing than the use of book-value weights, because the market values of the securities closely approximate the actual dollars to be received from their sale.

**Example-7**

In addition to the data from Example-6, assume that the security market prices are as follows:

**Mortgage bonds**= $20,000,000 per bond**Preferred stock**= $90 per share**Common stock**= $80 per share

The firm’s number of securities in each category is:

**Mortgage bonds**= $20,000,000 / $1,000,000 = 20,000**Preferred stock**= $5,000,000/$100 = 50,000**Common stock**= $20,000,000/$40 = 500,000

Therefore, the market value weights are:

Source Number of securities Price Market value

Debt 20,000 $1,100 $22,000,000

Preferred stock 50,000 $ 90 $4,500,000

Common stock 500,000 $ 80 $40,000,000

Total $66,500,000

The $40 million common-stock value must be split in the ratio of 4 to 1 (the $20 million common stock versus the $5 million retained earnings in the original capital structure), since the market value of the retained earnings has been impounded into the common stock.

The firm’s cost of capital is as follows:

Source Market value Weight Cost Weighted average

Debt $22,000,000 33.08% 5.14% 1.70%

Preferred

Stock $4,500,000 6.77 13.40% 0.91

Common

Stock 32,000,000 48.12 17.11% 8.23

Retained

Earnings 8,000,000 12.03 16.00% 1.92

Total $66,500,000 100.00% 12.76%

**Overall cost of capital** = **ko** = 12.76%

**(d). Target weights** – If the firm has a target capital structure (desired debt-equity mix) that is maintained over the long term, then the use of that capital structure and associated weights can be used in calculating the firm’s weighted cost of capital.

**(f). Marginal weights** – Marginal weights involve the use of the actual financial mix used in financing the proposed investments. In using target weights, the firm is concerned with what it believes to be the optimal capital structure or target percentage. In using marginal weights, the firm is concerned with the actual dollar amounts of each type of financing needed for a given investment project. This approach, while attractive, presents a problem: The cost of capital for the individual sources depends on the firm’s financial risk, which is affected by the firm’s financial mix. If the company alters its present capital structure, the individual costs will change, which makes it more difficult to compute the weighted cost of capital. The important assumption needed is that the firm’s financial mix is relatively stable and that these weights will closely approximate future financing practice.

**Example-8**

The Carter Company is considering raising $8 million for plant expansion. Management estimates using the following mix to finance this project:

Debt $4,000,000 50%

Common stock 2,000,000 25

Retained earnings 2,000,000 25

Total $8,000,000 100%

The company’s cost of capital is computed as follows:

Source Marginal Weights Cost Weighted Cost

Debt 50% 5.14% 2.57%

Common stock 25 17.11% 4.28

Retained earnings 25 16.00% 4.00

100% 10.85%

**Overall cost of capital** = **ko** = 10.85%