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to calculate the free cash flow to equity, should we deduct the interest.?
on my understanding, interest is part of the cost of debt. thus, interest should not be deducted.
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hmm
You are correct that interest is part of the cost of debt. However you are confusing two things.
If you are calculating a normal project NPV, then you do not deduct interest from the cash flows, and you discount at the WACC.
However, if you are using free cash flow to EQUITY, then you do deduct the interest (cos there is less left for equity) and you discount at the cost of equity.
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Neither should we deduct interest expenses from the FCFE because the cost of equity has taken account for the financing side-effect according to MM’s 2 propositions. We should not double count it.
@sosologos said:
Neither should we deduct interest expenses from the FCFE because the cost of equity has taken account for the financing side-effect according to MM’s 2 propositions. We should not double count it.No, that is not true. MM’s propositions are explaining how the risk and hence the cost of equity are affected by the level of gearing. However it is the free cash flow to equity and the shareholders required rate of return that can be used to determine the market value of the equity in a firm. The free cash flow to equity is effectively the cash available to shareholders after deducting interest payments and after adjusting for debt repayments.
Taking the cash flow after interest and discounting at the cost of equity is not double counting and is in line with MMs dividend irrelevancy work.Importantly for the exam, the examiner takes this view also.
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Hi John
Actually, I have deleted my posting. I don’t know why it appears again. After checking with the ACCA past papers, I know that ACCA take your view. CFA also takes your view. In order to avoid making the candidates confused, I chose to delete it. The candidates are busy enough to prepare the examination.
As my posting appears again, I would like to have an educated discussion with you on my points of double counting. I try to illustrate it with some simple data.
There is a newly startup firm with Ke and kd of 10% and 4% respectively. The gearing (D/E) ratio is 1. The invested capital is $200. Today, the firm announces its 2-year venture which can generate a FCFF of $119.05 p.a.. I assume no tax to make everything simple.Therefore, the WACC must be 7.0%.
Step 1: The firm value after the announcement should be as follows:
FCFF: $119.05(Y1), $119.05(Y2)
Discount at 7%
PV: $111.26(Y1) + $103.99(Y2) = $215.25Step 2: The equity value by deducting interest from FCFF (ACCA approach)
FCFF: $119.05(Y1), $119.05(Y2)
Less interest: $4.00(Y1), $4.00(Y2)
FCFE: $115.05(Y1), $115.05(Y2)
Discount at 10%
PV: $104.59 + $95.09 = $199.68 (firm value) – $100 (debt) = $99.68 (equity value)
The firm value is $15.57 (i.e. $215.25 – $199.68) below the one at Step 1.Step 3: The equity value without deducting interest from FCFF (my approach)
FCFE: $119.05(Y1), $119.05(Y2)
Discount at 10%
PV: $108.23(Y1) + $98.39(Y2) = $206.62 (firm value) – $100 (debt) = $106.62
The firm value is $8.63 (i.e. $215.25 – $206.62) below the one at Step 1.The smaller firm values at steps 1 and 2 must be explained by the payment of $8 of interest. We can see that step 3 (without deducting interest from FCFF for FCFE) should be more logical because the difference is only $8.63. The ACCA approach appears to doubly count the financing cost to make a difference of $15.57.
Hi
The flaw in your argument is this:
Discounting the before-interest flows at the WACC will give the value of the firm (equity + debt). However discounting the FCFE (after interest) at the cost of equity gives the value of the equity (not the value of the firm – for that you then have to add on the value of the debt).
It will obviously still not give the same result in your example, because MM assumptions are not holding.
Here is another example (assuming MM is working and without tax):
Suppose firstly that a company is all equity financed. Cost of equity is 10%. Earnings are $100 p.a. in perpetuity.
Market value of firm = market value of equity = $1000
Suppose same company now has $500 equity and $500 debt at 4% interest.
(total MV must still be $1000 according to MM without tax).
Also according to MM, cost of equity will rise to 16% (so WACC stays constant at 10%)
Obviously total value of the firm is still the pre-interest cash flows discounted at WACC. (100 / 10% )
Market value of equity is after-interest cash flows (100 – interest of 20 (4% x 500) = $80 p.a.) discounted at cost of equity (16%) = 80 / 16% = $500
This is MV equity, not MV firm. MV firm = equity (500) + debt (500)- Topics: 0
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John, I totally agree with your explanation assuming the investment as a perpetuity.
My purpose is to apply the FCFF and FCFE in a real world, that is, with limited investment time horizon and uneven annual cash flows. Therefore, my computation assumed a 2-year time frame.
After comparing your perpetuity illustration, I understand why getting the equity value through discounting FCFE is impractical in the real world. Therefore, I was forced to follow an approach of PV(FCFF) less Debt to derive the equity value. This is the strategy I used in Step 3.
In Step 2, I made a mistake by subtracting $100 debt straightly again without considering the inclusion in the cash flows of the two years interest payments. If I do so (i.e. $199.68 (firm value) – $100 (debt) + 7.94 (PV of interest payments) = $106.62 (equity value) ), Step 2 and Step 3 are identical.
This might be the reason some texts say that FCFE should not deduct interest but the others tell the opposite (applicable to finite investment time horizon only where we must use the FCFF- Debt approach, but not a problem for perpetuity). The crucial point is on adjusting the PV of debt correctly.
Thank you for letting me see it clearly.OK – thanks for your reply.
However, to avoid confusing the students – for the exam, the free cash flow to equity is the cash available for shareholders AFTER subtracting interest, and this is discounted at the cost of equity to get the value of equity.
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Thanks for the interesting debate. Could you pls clearify, which particular assumption of MM does not hold that we can not reconcile the Steps 1 and 2. That is – why do we not get the same equity value when we deduct cost of debt from the firm value using FCFF discounted on WACC and FCFE discounted on cost of equity? And secondly – which of them is more correct to value equity for finite investments horizons?
That is not to add to the confusion, but perhaps making things more clear in this troublsome issue. I understand the exam rule but the logic behind it is not clear at all.The real problem is that M&M assume that debt is risk free. i.e. that it is the risk free rate less tax relief. If this were the case then both approaches would lead to the same result.
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John, sorry but could you pls elaborate on this issue. Have 2 questions:
1. If the debt was risk free in the above example, what would change in the calcualtion of equity value? How would the both appraches reach the same result?
2. And in real life, which of the two methods is more correct (or used more often) for valuing finite projects?
Again sorry, but the issue is really confusing, hopefully not only for me.According to M&M, the cost of equity in a geared company is
Ke (ungeared) + (1-T)(ke-kd)Vd/Ve
Kd is the pre-tax cost of debt, which in a perfect world will be the risk free rate.In the real world, free cash flow to equity would be perhaps more correct.
Do not worry for the exam – the examiner will make it clear which approach he wants.
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