CFA CFA Level 2 FCFE Valuation Problem

# FCFE Valuation Problem

• Author
Posts
• 53

Hi all! Need some help understanding a FCF Valuation problem found in the Schweser study notes (Book 3, Page 137, Concept Checker #1):

1. The Gray Furniture Co. earned 3.50 per share last year. Investment in fixed capital was 2.00 per share, depreciation was 1.60, and the investment in working capital was 0.50 per share. Gray is currently operating at its target debt-to-assets ratio of 40%. Thus, 40% of annual investments in working capital and fixed capital will be financed with new borrowings. Shareholders require a return of 14% of their investment, and expected growth rate is 4%. The value of Gray’s stock is closest to:

A. 27.04

B. 29.90

C. 30.78

What confuses me is how they arrive at FCFE:

FCFE = NI – (1-DR)(FCInv-Dep) – (1-DR)(WCInv)

FCFE = 3.50 – [(1-.04)(2.00-1.60)] – [(1-.40)(0.50)] = 2.96

My train of thought brought me here:

FCFE = NI + Dep – WCInv – FCInv + Net Borrowings
FCFE = 3.50 + 1.60 – 0.50 – 2.00 + [(0.40)(2.00+0.50)]

Where did I go wrong??

• 8

To continue with my same logic, I just realized that I didn’t apply depreciation to FCInv which would give me the following:

FCFE = 3.50 + 1.60 – 0.50 – 2.00 + (0.40)(2.00-1.60+0.50) = 2.96

Which I think might make sense. If the structure is 40% debt, then that means 60% is equity. So I should have applied that 40% to the depreciation as well. Which would be a long way to do @vincentt ‘s formula:

FCFE = NI – (1-DR)(FCInv – Depr + WCInv)

• 5

@vincentt I will definitely keep that formula in my back pocket! But is there a reason why net borrowings is excluded from it?

And for your second formula shouldn’t that Int(1-T) be Net Borrowings?

• 5

@Sophie Not a problem at all! Thank you both so much for bearing with me as I try to understand this! I

I think I was partly getting tripped up on the algebra as well.

In the FCFE = NI – (1-DR)(FCInv-Dep) – (1-DR)(WCInv) formula, I couldn’t understand why they didn’t just break out the Depreciation term and multiply it by (1-DR) as well. I was fixating on why they chose to deduct it from FCInv when, algebraically, you could just as well apply it to WCInv or break it out on its own and multiply it by (1-DR).

@Vincentt
@Sophie Thank you again you two!!!! You have no idea how much I appreciate your help ðŸ˜€

• 4

Someone on analyst forum put it this way:

One more way to calculate this :

FCFE formula says NI + NCC – FCinv – WC Inv + Net Borrowigs.

if in the given question we consider only equity portion ( since debt to assets 0.4 is given ) as we need to arrive at FCFE then

NI – 3.5

+ NCC – 1.6 * 0.6

– FC inv – 2 * 0.6

– WC inv – 0.5 * 0.6

+ Net borrowings – 0 **( coz we are considering only equity portion here in the above analytics )

FCFE = 2.96

Hope this helpsâ€¦

I apologize for making this harder than it is but I just can’t wrap my mind around it. I suppose I just don’t understand why net borrowings is 0.

• vincentt
Participant
• CFA Level 3
4

@dollarstodonuts my pleasure! ðŸ˜‰

In fact, i was in the same situation as you couple of months ago, took me awhile to understand all the various FCFF/FCFE formulas and ‘refactor’ them to something I would remember better. At least, i that works better than memorising some formulas in their original form (given by CFAI or schweser).

• vincentt
Participant
• CFA Level 3
3

This is a less famous formula but you should know too and it’s not too hard to memorise it.

My take on this is whenever there’s a debt ratio and they are asking for FCFE use the following formula:

FCFE = NI – (1-DR)(FCInv – Depr + WCInv)

To remember this formula:
Just remember that since there’s a negative sign before the (1-DR), you have to inverse all the signs for the 3 items based on the original FCFE formula.

FCFE = NI + NCC WCInv FCInv + Int(1-T)

NI – (1-DR)(FCInv – Depr + WCInv) could be written as NI + (1-DR)(-FCInv + Depr – WCInv)

• 3

I’m glad we made sense! ðŸ˜‰ And we’re addicted to solving questions and helping you guys out in this silly time – so no worries @dollarstodonuts!

• 2

@Sophie ah nice catch on the typo!

The way I read the problem was that if 40% of FCInv and WCInv are to be financed with new borrowings, then wouldn’t that mean net borrowings is equal to 40% of their combined amounts (2.00 + 0.50)?

Ah yes, I did miss this part that mentions it explicitly in the question -_-. Sorry for that!

AF’s calculation although correct, explanations on net borrowing doesn’t make sense.

Ok, a rule of thumb – if ever a FCFE question gives information of target debt ratio (DR), it means they want you to use this specific formula FCFE = NI – (1-DR)(FCInv-Dep) – (1-DR)(WCInv), and you should.

The only difference of your usage of the other formula (FCFE = NI + Dep – WCInv – FCInv + Net Borrowings) with the answer is the treatment of depreciation. Technically you should add back the part of depreciation that is NON-debt financed, i.e. 0.6*1.6, as you’d mentioned as a long way to arrive to @Vincentt ‘s formula.

• 1

Hi @Dollarstodonuts, first of – a little typo in the first FCFE formula where DR should be 0.4 (not 0.04) in the first half of the calculation.

On your formula, the formula correct, but the part on net borrowing, I don’t fully understand how you got to that number as net borrowing = New Debt – Debt Repayment, and this info is not available in the question. Care to shed any light?

• 1

@Sophie ah nice catch on the typo!

The way I read the problem was that if 40% of FCInv and WCInv are to be financed with new borrowings, then wouldn’t that mean net borrowings is equal to 40% of their combined amounts (2.00 + 0.50)?

• 1

Ok, once again I apologize but please ignore all of my convoluting posts before hand.

After some digging, I finally understand that it is common to assume that the firm mantains a target debt-to-assets ratio for net new investment in fixed capital and working capital.

Thus, net borrowing may be expressed without having to specifically state debt issuance or repayments:

FCFE = NI – [(1-DR)(FCInv – Dep)] – [(1-DR)(WCInv)], which is the expanded form of @vincentt ‘s formula.

FCFE = 3.50 – 0.24 – 0.30 = 2.96.

Now I see that net borrowing is embedded into the formula through 1-DR.

Now my last question is, why is Depreciation subtracted from Fixed Capital Investments? @sophie @vincentt

• vincentt
Participant
• CFA Level 3
1

yes my bad.. clearly that formula was incorrect.

It should be
FCFE = NI + NCC – WCInv – FCInv + Net Borrowings

• 1

@vincentt I totally agree. It really is much better to truly understand the concept and not just memorizing formulas. Plus, I feel that the formulas are much easier to remember when you understand the reasoning behind each part of the formula.

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