The following will help you understand the process of calculating a cost of capital rate, using Peter's Shortline Rail Company as an example. The steps refer to those shown in Appendix A.

Step 1: Determine the Net Rail Investment

The net rail investment can be determined by examining the balance sheet of the railway company. Net rail investment is simply the sum of the company's net assets (book value less accumulated depreciation) and working capital (the cash and materials needed to support day-to-day operations). For example, Peter's Shortline Rail Company has a gross investment of $4,300,000 and accumulated depreciation of $500,000 resulting in $3,800,000 in net assets. Add to this $200,000 in working capital and the company's net rail investment is $4,000,000.

Step 2: Determine the Capital Structure

The capital structure of the firm is determined by identifying the capital instruments used by the railway company to fund its investments and calculating what percentage of the total investment each instrument contributes. In Appendix A, for example, Peter's Shortline Rail Company uses long-term debt, deferred income taxes and common equity to fund its $4,000,000 net rail investment. Deferred income taxes are included here because they are available to finance investment until the time they are due to government.

Step 3: Determine the Cost of Financing

Each component of the firm's capital structure has a different cost rate. Determining the cost of long-term debt is relatively straightforward as this cost is simply the weighted rates of interest or premia paid by the company on its debt instruments. Deferred income taxes do not have an associated cost, as the firm does not have to pay an interest premium or compensate any party to use them.

Determining the cost of common equity is somewhat more complex. The cost of common equity is a projection or informed estimate of a reasonable rate of return on the shareholders' investment. It can be estimated by using one of several market driven models commonly used to calculate the required rate of return, or, as in this example, by taking an average of two of these models.

The first model is the Capital Asset Pricing Model (CAPM), which attempts to measure the relationship between the risk of a share of stock and the return the stock provides at that level of risk. When applying the CAPM formula for Peter's Shortline Rail Company, the return on common equity is calculated, as shown in Appendix B, to be 12.81%.

The required rate of return on equity can also be estimated using a second model, called Discounted Cash Flow (DCF). This model implies that the rate of return is a function of the growth of expected cash flows from dividends, which are considered to have a constant rate of growth. Applying the DCF formula, as shown in Appendix C, the return on common equity for Peter's Shortline Rail Company is calculated to be 9.79%.

Averaging the required rates of return under each model establishes a cost of equity of 11.3 percent.

The cost of equity rate is then adjusted to reflect its gross pre-tax value, by dividing the cost of equity by a figure equal to one minus the corporate income tax rate. This adjusted rate of 18.83% takes into account the greater earnings that Peter's Shortline Rail Company needs to achieve, in order to deliver the expected rate of return to its investors, after satisfying the corporate income tax liability on those earnings. A similar adjustment for taxes is not required for the cost of debt rate because these costs are tax deductible.

Step 4: Determine the Cost of Capital

In the previous step, the cost of financing each component of the capital structure of Peter's Shortline Rail Company was determined. In this step, the cost of financing each component is weighted according to its proportion of the firm's total capital structure.

To finish the calculation, the weighted cost of equity adjusted for income tax is added to the weighted cost of debt and deferred taxes, with the total being the weighted average cost of capital rate (WACC). As shown in Appendix A, Step 4, the final WACC determined for Peter's Shortline Rail Company in this exercise is 10.04 per cent.

Appendix A

Development of a Cost of Capital Rate for Peter's Shortline Rail Company

Step 1: Net Rail Investment

Step 2: Capital Structure

Step 3: Cost of Financing

Step 4: Cost of Capital

Notes:

1. The cost of common equity is the average of the rate of return estimated by the CAPM and DCF methods, adjusted to reflect its pre-tax value (see Appendix B and C for calculations).

2. Equity adjusted for Income Tax Allowance was calculated by dividing the cost of common equity rate of 11.3% by 1 minus the corporate income tax rate of 40%.

Appendix B

Capital Asset Pricing Model (CAPM)

The equation to determine the required rate of return (k) under the CAPM is as follows:

where

R_f is the rate of return on a risk-free investment (ie: Government of Canada bonds),

ß is the beta, a measurement of the relative risk of a specific share to the market as a whole. (A beta share greater than 1 is considered to have greater risk than the market, and a beta share less than 1 is considered to have less risk than the market.)

R_m is the average rate of return on the market as a whole over the period being analysed.

(R_m - R_f) represents the market risk premium, or the difference in rates of return between investments that are considered risk-free, such as government bonds, and those investments that are market driven, over the period being analysed.

Now we apply the formula to Peter's Shortline Rail Company:

R_f = 3.50%
ß = 1.45
R_m = 9.92%

Therefore,

k = 0.0350 + 1.45(0.0992-0.0350)
k = 0.0350 + 0.0931
k = 0.1281
k = 12.81%

Appendix C

Discounted Cash Flow Model (DCF)

The required rate of return (k) under the DCF model is calculated as follows:

where

D is the dividend paid in the current year
P is the current share price
g is the expected dividend growth rate

Now we apply the formula to Peter's Shortline Rail Company:

D = $1.96
P = $29.75
g = 3.00%

Therefore,

k = (1.96/29.75)*(1+0.0300) + 0.0300
k = 0.0679 + 0.0300
k = 0.0979
k = 9.79%