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IFT Notes for Level I CFA® Program
IFT Notes for Level I CFA® Program

R33 Cost of Capital

Part 4


 

4.3.     Marginal Cost of Capital Schedule         

Marginal cost of capital schedule is a graph that plots the cost of raising additional capital. MCC schedule plots the weighted average cost of each dollar of additional capital on the y-axis to the amount of new capital raised on the x-axis. As a company raises more funds, the costs of capital from different sources change.

The marginal cost of capital is upward sloping because when a greater amount of capital is raised, the cost of equity and debt financing increase. We calculate a break point using information on when the different sources’ costs change and the proportions that the company uses when it raises additional capital:

Break\ point\ =\ \frac{amount\ of\ capital\ at\ which\ the\ source's cost\ of\ capital\ changes}{proportion\ of\ new\ capital\ raised\ from\ the\ source}

Let us understand this concept through an example.

Example

A company’s target capital structure is 60 percent equity and 40 percent debt. The cost and availability of raising various amounts of debt and equity capital is shown below:

Amount of new debt

(in millions)

Cost of debt
(after tax)
Amount of new equity
(in millions)
Cost of equity
≤ 4 14% ≤ 9.0 20%
> 4.0 16% > 9.0 22%

What is the WACC for raising the following amounts of capital: 5, 10, 15, and 20?

Solution:

  • If the company raises debt less than or equal to 4 million, then the cost is 14%. But if it is more than that, the cost goes up to 16%. Similarly, in the case of equity, if it is less than 9 million, then the cost is 20%. If the amount of equity is greater than 9 million, the cost goes up to 22%. After-tax cost of debt is given, so do not calculate the cost as (1-t) * cost of debt in WACC.

Steps:

  1. Calculate the proportion of debt and equity for each amount of capital raised.
Amount of capital Debt (40%) Equity (60%) Cost of debt (in %) Cost of equity (in %) WACC
(in %)
5 0.4 * 5 = 2 0.6 * 5 = 3 0.4 * 14 = 5.6 0.6 * 20 = 12 17.6
10 0.4 * 10 = 4 0.6 * 10 = 6 0.4 * 14 = 5.6 0.6 * 20 = 12 17.6
15 0.4 * 15 = 6 0.6 * 15 = 9 0.4 * 16 = 6.4 0.6 * 20 = 12 18.4
20 0.4 * 20 = 8 0.6 * 20 = 12 0.4 * 16 = 6.4 0.6 * 22 = 13.2 19.6

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  1. Note that the cost of capital changes when the amount of capital is greater than 10 million and 15 million.
  2. There are two break points – at 10 million and at 15 million because the cost of debt and cost of equity change at these points for any new amount of capital.
  3. You can calculate the break points using Equation 13 as 4/0.4 = 10 and 9/0.6 = 15.

4.4.     Flotation Costs

Floatation costs are the fees charged by investment bankers when a company raises external capital. There are two approaches to deal with floatation costs:

Approach 1: Incorporate flotation costs into the cost of capital. This will increase the cost of capital.
r_e=\frac{D_i}{{(P}_0-F)}+g

For example, consider a company that has a current dividend of $5 per share, a current price of $100 per share and an expected growth rate of 10%. The cost of equity without considering floatation costs would be:
r_e=\frac{\$5\times 1.1}{\$100}+0.1=0.155\ or\ 15.5\%

If the floatation costs are 3% of the issuance, the cost of equity considering the floatation costs would be:
r_e=\frac{\$5\times 1.1}{\$100-\$3}+0.1=0.1567\ or\ 15.67\%

However, the problem with this approach is that floatation costs are not an ongoing expense, they are a cost that the firm incurs at the start of the project. Hence, we should not be discounting all future cash flows at a higher cost of capital. The correct way to treat floatation costs is to use approach 2.

Approach 2: We adjust the initial cash flow by the amount of floatation costs. We do not adjust the discount rate.

Let’s say in the above example, the company raised $100,000 for a project by issuing new shares. The floatation costs would be 3% of $100,000 i.e. $3,000. In this approach we increase the initial cash outlay of the project to $103,000. The cost of equity, however, remains unchanged at 15.5%.

4.5.     What do CFOs do?

In this reading, we saw several methods to estimate the cost of capital for a company or project. A survey of a large number of US company CFOs to understand the methods they use to estimate the cost of capital revealed the following:

  • The capital asset pricing model is the commonly used model. The single-factor capital asset pricing model is the most popular one.
  • Few companies use the dividend cash flow model.
  • Publicly traded companies were more likely to use the capital asset pricing model than private companies.
  • Most companies used a single cost of capital across projects, while some used risk adjustments for individual projects.


Corporate Finance Cost of Capital Part 4