 Hi all,

I encountered this question in Schweser on end of chapter…after studying free cash flow I do not remember if involving debt to asset ratio changes how you approach the question but here it is:

The Gray Furniture Company. earned 3.50 per share last year. Investment in fixed capital was 2.00 per share, depreciation was 1.6 and the investment in working capital was .50 per share. Gray is currently operating at its target debt to asset ratio of 40%, thus 40% of annual investments in working capital and fixed capital will be financed with new borrowings. Share holders require a return of 14% on their investment, and the growth rate is expected to be 4%. The value of Gray’s stock is closest to:

A.27.04

B.29,9

C.30.78

I used FCFE = NI+NCC-WCinv - FC inv +Net borrowing and got 3.5+1.6-2-.5+.1 … I got Net borrowing by multiplaying 40% by FCinv and WCinv… then divided that by rquired return - expected growth rate, and got A. 27.04… however the naswer in the back of the book showed differently and the formula was completely different. Can anyone explain or advise, thanks so much!

[(3.5+1.6-2-.5+1)(1+.04)]/(.14-.04) = 37.44

[(3.5+1.6-2-.5)(1.04)]/(.14-.04)= 27.04

NI - (1-DR)[(FC - Dep) - WC) = 3.5 - (1-0.4)[(2-1.6) + 0.5) = 2.96

Stock value = 2.96(1 + 0.4)/(0.14-0.04) = 30.78

There are lot of variations in FCFE equations.

FCFE = NI - (1-DR)(FCINV - DEP) - (1-DR)(WCInv)

V0 = FCFE x (1+g) / (r-g)

This yields to C 30.78

Thanks guys. I really need to go review all the FCFE and FCFF stuff.

Same here phew

Thanks all for the help. Do you use that formula when they give you debt to equity ratio? I cannot find much reading on that formula itself… I have 5 FCFE formulas and that one would make six… Just want to make sure im not missing anything

Thanks again! Jason

It’s there… It’s actually the most basic formula. FCFE = NI + D - FCINV - WC + Net borrowing. Since they fund the purchases of fix asset and working capital with 40% debt, your net borrowing just increased.

NC = WC*.4

-WC (1-.4) = -WC + NC

-WC (1-.4) = -WC + .4*WC

But why does this happen? I am not following as this forces us to take Fixed capital, subtract NCC from it and then multiply by the 1-debt ratio. And where does net borrowing go that it increased? I am a bit confused by this concept and don’t follow your explanation kys but appreciate any clarity you can lend.

Ok let break it down.

NI = 3.5, Depreciration = 1.6, Fixed Investment = 2, net WC = .5, netborrowing = .36

How did I get net borrowing you ask?

We know that the company borrowed .4 of WC and NET FC Investment. Depreciation is a non-cash expensive. Therefore just cause your fixed asset went down, it doesn’t mean you’re using cash. The increase in fixed investment is the net fixed investment.

.5*.4 [WC] + (2-1.6) [FC Investment - Depreciation = Net FC Investment] *.4

Now if you put it into the FCFE formula:

FCFE = 3.5 [Ni] + 1.6[Dep] - 2 [FC] -.5 [WC]+ .5*.4 [borrowed WC] + (2-1.6)*.4 [FC Investment - Depreciation = Net FC Investment].

Rearranging everything:

3.5 - (1-0.4)[(2-1.6) + 0.5) = 2.96

2.96(1.04)/(.14-.04) = 30.78.

Got it. Thanks so much for breaking it down like that!

They don’t really explain the concept very well, but that formula is just the mathematical result if you simply the longer FCFE formula. Same deal with that freaking swap formula they provide in the derivatives section… it is just a mathematical simplification and they don’t seem to explain how they arrived at it.