Calculate cost of capital?

Your firm is planning to invest in a new electrostatic power generation system. Electrostat Inc is a firm that specializes in this business. Electrostat has a stock price of $25 per share with 16 million shares outstanding. Electrostat's equity beta is 1.18. It also has $220 million in debt outstanding with a debt beta of 0.08. If the risk-free rate is 3%, and the market risk premium is 6%, then your estimate of your cost of capital for electrostatic power generators is closest to:
A) 7.50%
B) 7.75%
C) 9.50%
D) 10.10%

 
Not not a boutique:
Look up CAPM to calculate cost of equity - should be in your textbook For cost of debt, should be immediately before of after the section on CAPM

I got the cost of equity. Not sure how to get the cost of debt... textbook says I need the yield to maturity rate & probability of default?

 

You don't need the cost of debt. You can get to the firm's cost of capital by calculating the unlevered beta. The formula for calculating unlevered beta is: Equity Beta / [1 + (1 - Tax Rate) * (Debt/Equity)]. You aren't given a corporate tax rate, and in a world of no taxes, the unlevered beta would simply be the weighted average of the debt and equity betas.

Your firm is capitalized with 64.5% equity and 35.5% debt; its weighted average beta (ignoring taxes) is 0.79. If you run that through the CAPM, your firm cost of capital is 3% + 0.79 * (3% + 6%) = 10.1% (Answer D).

If you assume a 35% tax rate, then your tax-effected firm beta becomes 0.87 and the cost of capital rises to 10.8% (not an option).

 
re-ib-ny:
You don't need the cost of debt. You can get to the firm's cost of capital by calculating the unlevered beta. The formula for calculating unlevered beta is: Equity Beta / [1 + (1 - Tax Rate) * (Debt/Equity)]. You aren't given a corporate tax rate, and in a world of no taxes, the unlevered beta would simply be the weighted average of the debt and equity betas.

Your firm is capitalized with 64.5% equity and 35.5% debt; its weighted average beta (ignoring taxes) is 0.79. If you run that through the CAPM, your firm cost of capital is 3% + 0.79 * (3% + 6%) = 10.1% (Answer D).

If you assume a 35% tax rate, then your tax-effected firm beta becomes 0.87 and the cost of capital rises to 10.8% (not an option).

How did you calculate the 0.79? Also, the link to the CAPM formula subtracts the risk free rate from the market risk rate, whereas you added the two. Can you please clarify? Thanks!

 

Here is the CAPM Formula:

Expected Return = Risk Free + Asset Beta * Market Risk Premium

Market Risk Premium = Expected Market Return - Risk Free Rate

In your example, they gave you 6% as the Market RISK PREMIUM, not the Market Return. So that number already has the Risk Free subtracted. This makes sense, since a market return is probably somewhere around a 9%, give or take, so with a risk free at 3% the 6% risk premium is sensible. Subtracting 3% from 6% would give you a 3% market risk premium, which is ridiculously low.

0.79 is the weighted average beta. You have $220MM of debt and $400MM of equity. So your firm is 35.5% debt and 64.5% equity. Your debt beta is 0.08 and your equity beta is 1.18. The weighted average formula says Weighted Average Beta = Debt Beta * Percent Debt + Equity Beta * Percent Equity = 0.08 * 35.5% + 1.18 * 64.5% = 0.79.

 

Pretty easy.. There's only a few steps you have to take to figure it out. First, figure out the cost of equity (risk-free rate + beta * (market rate of return - risk-free rate)). Second, figure out the Weight of debt (amount of debt / (amount of debt + amount of equity)). Third, figure out the Weight of equity (amount of equity / (amount of debt + amount of equity)). Finally you incorporate your answers into the cost of capital formula (Weighted average cost of capital = cost of debt * weight of debt * (1 - tax rate) + cost of equity * weight of equity). Like I said, easy stuff.

Good luck.

 

Why do you think it is strange that the tax-advantaged status of debt results in higher PV of cash flows? Keep in mind the WACC represents your opportunity cost of making that investment. The cash flows in the future are certain, but their value depends on what your opportunity cost is. If you have to give up a lot in order to receive those cash flows (i.e. WACC is high), they're less valuable (i.e. PV is smaller). If you don't have to give up much to receive them (i.e. WACC is low), the cash flows are more valuable (i.e. PV is higher).

The fact that debt is tax-advantaged means that you do not have to give up as much as you otherwise would have if debt were NOT tax-advantaged; i.e. WACC is lower than it would otherwise be. As I noted above, a lower WACC causes higher PV's.

 

When there is no debt in the capital structure, WACC is equal to the cost of equity. As the proportion of debt in the capital structure increases, WACC gradually decreases due to the tax deductibility of interest expense. WACC continues to decrease up to the point where the optimal capital structure is reached. Once this threshold is surpassed, the cost of potential financial distress - namely, the negative effects of an over-leveraged capital structure, including the increased probability of insolvency - begins to override the tax advantages of debt. As a result, both debt and equity investors demand a higher yield for their increased risk, thereby driving WACC upward beyond the optimal capital structure threshold.

Capitalist
 

@esbanker

Thanks for that insightful commentary on the movement of cost of capital.

@MFFL

Thanks I think you have helped in my understanding of this issue. I think maybe I'm thinking of it in the wrong way. I'm guessing for a particular company then, cost of capital is going to be the same among any projects that they are doing as it's based on the cost of their equity and debt? Or would it change in any case depending on the project. Sorry, I'm a really noob, but just still trying to understand exactly the purpose of cost of capital. I get the concept of 'cash today is more valuable than cash in 5 years time', so there should be some discounting, but just unsure about exactly how this cost of capital is calculated which is of course important if you are doing multiple DCFs in order to compare an investment.

Thanks.

 

The actual cost of capital for a given project depends on the type of capital they use. When using WACC you're basically operating under the assumption that they're going to finance this specific project with the same capital mix as their current capital structure. The purpose of this kind of analysis is to determine if the project is worth doing it not, so you want to compare the benefits of the project (the revenue streams in the future) with the costs of the project (the cost of capital used to finance the project).

Think of it this way: let's just hypothetically assume your cost of capital is 10%. That is what it costs you to use capital. You are evaluating a project that costs $100 now, and pays you $110 exactly one year from now. From discounting that cash flow at the cost of capital, you get a NPV for the project of $0. The project does not gain anything and it doesn't cost anything, since the return on the capital is equal to the cost of the capital.

Now let's assume that form of capital suddenly becomes tax deductible (regardless of whether its debt, equity, etc, just assume its all tax deductible). So your true cost of capital is no longer 10%, it is now 6% (assuming 40% tax rate). Under the same scenario as before (spending $100 now to receive $110 in one year), your NPV comes out to $3.77. That different can be attributed completely to the fact that your source of capital is now tax deductible.

That example assumes your entire source of capital is tax deductible. But chances are only the debt portion of your cost of capital is tax deductible, so imagine you have a capital structure that is 50% stock and 50% equity. The cost of each is 10% (also unrealistic, but go with it), and the debt is tax advantaged. So after accounting for the tax shield provided by the debt, the true cost of the debt is 6%. The WACC just averages the 10% cost of equity with the 6% tax advantaged cost of debt, to give you an 8% WACC.

This type of analysis basically just answers the question of whether or not you would undertake an investment, or a project. It sets a minimum hurdle for what kind of return you need to acquire to make the investment worthwhile. For comparing multiple investments you could do the same thing, just choosing the one that has the higher NPV. More common when comparing multiple investments is looking at IRR, although the same information is contained in both

 
  1. CAPM and risk free rate: Academic purists say that risk free rate should equal the life time of a company, but 10 year is a good approximation based on past estimates as normally in 10 years there are very large changes to companies thus the current capital structure becomes irrelevant

  2. Terminal growth rate: Get equity reports of all companies in that industry, look at their DCF and see what rates they are projecting for various companies and take mean/median. Look at their explanation for using these numbers

  3. I am not sure what "(1+r)^n" is?

  4. Cost of debt, i would beinterested in knowing that as well

 

Risk-free rate:

There is no one theoretically correct "risk-free rate" to use, we just use t-bill/bonds/LIBOR/Euribor rates to make things easy.. The 10 year rate is not necessarily the theoretically correct rate to use as the above post suggests. Whilst a company may change over 10 years, an investor may only have holdings in a stock for a couple of months/weeks/days/minutes. Nevertheless, it doesn't matter too much which maturity you pick - it won't have too much impact on the final valuation, you should be more worried about errors in your cash flow forecasts. It wouldn't be criminal to just arbitrarily use e.g. 3%

And as for "the (1+r)^n thing" rates are quoted on an annual basis, so the calculation is still valid.


Cost of Debt:

Why not just calculate the cost of debt from the financial statements? interest expense/debt... makes things easier... Like you said, because of different debt issues there won't be one correct cost of debt to use but this will give you a approximate average cost of debt, and works around all the problems you've encountered.


Terminal Growth Rate:

Once again there is no one theoretically correct terminal value... If you want to make the most sensible assumption, maybe find some academic research which provides the long-term growth rate of your industry or something...Check out Damodarans site... you'll find some stuff there... Why your school thinks taking an average of 3 arbitrarily assigned rates is better than just using 1 is beyond me...

I think you're missing the point with the whole thing... There is no one correct anything when your predicting the future, you have to just think everything through thoroughly and make the most logical assumptions you can based on convincing reasoning

 

You use the levered beta when calculating cost of equity. If you're calculating the beta from comps, you would unlever those, take the the average and the relever at the company's capital structure

 

Hi Maria-Lopez, whoops, looks like nobody chimed in here.... maybe one of these discussions below is relevant:

Calling relevant pros to the rescue! xiaotian.d.zhao David-Gutiérrez courtneyland

You're welcome.

I'm an AI bot trained on the most helpful WSO content across 17+ years.
 
Best Response

in general, short-term debt (i.e. commercial paper) is cheaper than long-term debt (i.e. 5-year term loan bs or bonds).

the answer you gave is right in the sense that short term debt is cheaper, but wrong in the sense that it would increase your cost of capital.

i realize that other posters might chime in with additional insights, but if i was to answer your question exactly in the way it was asked based on the scenario you repsonded with, i would reply with the following:

  • assuming that equity remains constant, more short term debt increases the firm's debt capitalization and decreases the firm's equity capitalization.

  • since debt is cheaper than equity, increasing the weighting of a "cheaper" financing means will decrease the overall weighted average.

  • since you're using more short term debt, you'll also be invariably reducing the "cost" of your debt (i.e. greater proportion of "cheaper" short term debt versus the existing "more expensive" long term debt already on the balance sheet).

  • thus, lowered cost of debt due to influx of new "cheaper" debt combined with a greater percentage of debt in the overall capital structure decreases the overall wacc.

hope this helps.

 
streetbuck:
I was asked a similar question, except, the interviewer asked about the effect of current assets and cash on the WACC calculation. I said I didn't think it wouldn't have any effect, but was unsure of my answer.

Anyone know what the correct answer is?

in general you're right.

cash on its own has no effect on wacc since it's not debt and not equity or preferred stock.

however, what the interviewer was probably hoping for was you reaching a little further and applying the concept.

for example, does the company plan to use the cash/short-term investments to pay down debt? if that's the case, then wacc should increase as cheaper financing is removed from the company's balance sheet and the company's overall capitalization becomes more weighted toward expensive equity.

 

i realize i may have talked over your head a little.

this basic formula (yes, i know there's other stuff that needs to be in there to make it more accurate like capm, preferred stock, country risk premiums, etc., but i'm trying to give an idea as opposed to a finance lecture) should help you out:

WACC = weighting of debt x cost of debt + weighting of equity x cost of equity

weighting of debt = debt / (debt+equity)

weighting of equity = equity / (debt+equity)

run through a simple example using some made up numbers and you'll understand what's going on.

 

Just to add to your WACC formula, on the debt component, tax has implications in that interest paid is deductible. If I remember correctly from my corporate finance class, WACC = weight of debt * cost of debt * (1-tax rate) + weighting of equity * cost of equity. With that said, the implications of taking on additional and similar debt interest is that it should lower your WACC because of the tax component.

Using simple numbers, lets say on the balance sheet there is $500 on both the debt and equity. This gives it an equal weighting of .5 Let's assume the cost of the debt is 7% and cost of equity is 10%, and the tax bracket is 30%.
WACC = (.5)(.07)(1-.3) + (.5) * (.1) = .0745 or 7.45%

If the company took on an additional $250 in debt at the same cost of 7%, the weighting would change to debt being $750/1250 or 60%, and equity at $500/1250 being 40%. New WACC = (.6)(.07)(1-.3) + (.4)*(.1) = .0694. A lower WACC.

That's one component and one particular aspect of what debt does to your WACC.

 

I am glad someone asked this question. I would have said that current liabilities, both long term and short term, have a negative impact on the cost of capital. When i looked back I saw that cost of capital however, is the weighted sum of cost of equity and cost of debt. Really though, when thinking about cost of capital as an opportunity cost, shouldn't it be the difference of the two, and not the sum?

 

it's the mimimum return that your investors and lenders need in order to keep on giving you the capital you need to run your business.

think about it this way. if you walk down the street to wamu and apply for a $10,000 5-year loan with a 10% interest rate, the bank expects you to pay $1,000 in interest a year for 5 years and then pay the principal back at the end of year 5. through it's internal models, the bank has determined that while you're risky as a potential borrower of money, being able to obtain 10% in interest a year would compensate them adequately for that risk.

now, with that in mind, let's say that your first year in business, you earn $10,000. however, because of high expenses, ect., your net income at the end of the year gives you only a 5% margin, or $500.

as a result, you're now $500 short of the $1,000 you need to service your debt.

well, guess what?

you're now not giving the bank the "minimum return" it needs and the bank's going to call its loan and foreclose.

thus, at the end of the day, it's not about opportunity cost.

what it is about is giving you "hurdle rate" upon which to evaluate projects.

in the example above in the case of a company with 100% debt and no equity, why would you choose to pursue a project with a return of only 5% if your "hurdle rate" or wacc is 10%?

the point of wacc is to give you a hurdle rate that tells you the minium acceptable return which you need to meet in order to satisfy your investors. for debt holders that rate is the interest rate of your financial instruments. for equity holders, it's more complicated, but based on the same principle.

however, the reason you ADD at the end of the day is because you're adding your debt holders' minimum acceptable return to the mimimum acceptable return of your equity holders.

 
Monkey_Island:
it's the mimimum return that your investors and lenders need in order to keep on giving you the capital you need to run your business.

I've always wondered this, but haven't been able to get a clear answer: In terms of the DCF, why is the WACC the discount rate?

Are you assuming that this is the minimum return your business will be generating (so its debt and equity holders are satisfied)? Wouldn't the actual return of the firm per year change?

 

On the other hand, the WACC says the debt side depends on the Debt/Equity ratio, the average LONG term debt rate, and if this is zero (no long term debt, but current liabilities) the debt side should be zero.

Recall,

WACC= (E/E+D)(Rel) + (D/D+E)*(1-t)(Rd)

Where Rd is the avg. interest rate on LONG term debt or the yield to maturity (IRR) for the companies outstanding bonds, so "technically" if a firm carried no long term debt debt, shouldn't we make the LONG term debt rate Rd=0, and eliminate the debt side completely, weighting the WACC based on equity alone?

And doesn't the WACC assume a historical leveraged firm that carries long term debt?

+++++++++++++++++++++++++++++++++++++++++++++++++

Well current liabilities or short term debt will affect the cost of capital, but debt carries less weight than equity in the WACC, but it ultimately depends on the ratio of debt to equity and equity to debt; IMO it's a totally relative concept.

And while you are correct that short term debt should be cheaper than long term debt (however with an inverted bond yield curve right now this is certainly not the case!), nonetheless if your short term debt is way higher than your equity, then you will have a much lower cost of capital than if you had much more equity than debt, but its all very relative.

A similar question is if company-A had an equity to debt ratio of 40% and company-B had a debt to equity ratio of 40%, with all things even, which has a higher cost of capital?

ANSWER: Because the cost of equity is more expensive than the cost of debt, (equity more risky than debt, and thus more cost) company B which has a equity to debt ratio of 60% is more expensive and will have a higher cost of capital.

 

I don't want to confuse the issue, but surely there comes a point where after adding an additional dollar of debt the required return on the equity increases by enough to actually increase the wacc. don't you think?

say a company has 50/50 debt/equity. increasing it to 60/40 debt/equity probably won't increase your required rate of return onthe equity by much, but consider a ratio of 85/15 debt to equity? would you still require the same rate fo return on your equity? what effect would that have on the wacc.

[don't think about this unless you have already conseptualized monkey islands posts]

 
relinquo:
I don't want to confuse the issue, but surely there comes a point where after adding an additional dollar of debt the required return on the equity increases by enough to actually increase the wacc. don't you think?

say a company has 50/50 debt/equity. increasing it to 60/40 debt/equity probably won't increase your required rate of return onthe equity by much, but consider a ratio of 85/15 debt to equity? would you still require the same rate fo return on your equity? what effect would that have on the wacc.

[don't think about this unless you have already conseptualized monkey islands posts]

I agree...was trying to keep it simple to illustrate one aspect without having to go too deeply, but given that you leverage absurdly, the total risk of the firm goes up, increasing the required rate of return on equity after a certain point. I believe this does go into the topic of optimal capital budgeting and there is a financial technique that can be used to determine that threshold or breakeven point. This was from my school days and forget how to determine the optimal debt and equity mix to achieve the lowest WACC, but I'm sure one of the bankers or finance gurus can answer that.

 

At high levels of levaerage, the risk of bankrupcy raises the after-tax cost of debt and the cost of financial distress. Therefore, after a certain point, raising the debt/market capitalization actually increases the total cost of capital.

Picture a graph with the y-axis the weighted-average cost of capital, and an x-axis labeled debt/market capitalization rate. If plotted, the line looks kind of like a candy cane or hockey stick. As debt approached 100% of Debt/Market capitalization rate the line is very steep...much steeper than when debt/market capitalization is closer to zero.

Hope that helps.

 

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