cost of capital question

Which if the following statement is correct? A. the appropriate tax rate to use in the adjustment of the before-tax cost of debt to determine the after-tax cost of debt is the average tax rate because interest is deductible against the company’s entire taxable income B.For a given company, the after-tax cost of debt is less than both the cost of preferred equity and the cost of common equity C for a given company, the investment opportunity schedule is upward sloping because as a company invests more is capital projects, the returns from investing increase D the target capital structure is the average ratio of debt to equity for the most recent fiscal year. answer is B. anyone can explain?

It’s because of the tax treatment of interest expense on corporate debt. If a company has interest costs of debt of 8% and a 40% tax rate the after tax cost of debt is 4.8% = 0.08(1-0.40) because that income would have otherwise flowed to EBT. I think the statement is attempting to be overly complicated as well; consider the nature of corporate financing and the ownership rights of lenders and shareholders debt will be the “cheapest” financing, then preferred, then equity. But since preferred equity and common equity will cost more then 8%, it will certainly cost more then the after tax equivalent 4.8%

I think the question is badly worded. Consider the following capital structure: 40% Debt @ 15% - Tax rate 50% 30% Pref. Equity @ 7% 30% Common Equity @ 7% The after-tax cost of debt is 7.5%, higher than both cost of preferred equity and common equity. I think the answer should read “Given equivalent costs for all sources of financing, the after-tax cost of debt is less than both the cost of preferred equity and the cost of common equity.” In this case the question is fairly elementary, and this is the only way I can get it to make sense. As a sidenote, while this is not mentioned, reading 45 has a considerable amount of errors in it and you might want to take a look at the errata:

Sharpshooter, I can’t think of a case were the cost of common equity would be ever be less then debt though, so i think your example is not valid. Even the strongest balance sheet and earnings wouldn’t account for a situation where unsecured capital (i.e. equity) would cost less then secured debt… I just can’t plausible conceive such a scenario.

Hmm interesting. I have a fairly limited background in finance (math major) so I simply tried to refute the answer with a contradicting capital structure. I am wondering why the information you are bringing up, which is required to solve this problem, was not mentioned during the reading (Cost of common equity > cost of preferred shares > cost of debt.)

“Cost of common equity > cost of preferred shares > cost of debt” This is the only reason , I thought of . I haven’t relevant content in CFAi books or Schweser Notes. I agree on this with my common sense. Image company bankrupt, the priority of capital type, debt credior>preferred share owner> common share owner. the junior one desire higher reurn, i.e. cost of capital for a given firm. just my 2 cents.

I agree that this answer is found by intuitiveness, but worded very poorly because it is possible that the after tax cost of debt could be higher than preferred or equity. It is extremely unlikely, but not completely out of the question.

If a company’s cost of debt is higher than a company’s cost of equity, it means that investor’s require a higher expected rate of return for owning a comapny’s debt than owning its equity (assuming the tax shield can only lower cost of debt but not equity). That makes no sense as a debt holder has a better claim on assets than equity holders and thus it is a less risky investment.

That makes a lot of sense, thanks everyone.

found this in notes: Kce=bond yield + risk preium this may prove cost of capital of Equity is higher than Bond at least.