Ratios and Fixed Assets The Le Bleu Company has a ratio of long-term debt to total assets of .35 and a current ratio of 1.25. Current liabilities are $950, sales are $5,780, profit margin is 9.4 percent, and ROE is 18.2 percent. What is the amount of the firm’s net fixed assets?
The solution to this problem requires a number of steps. First, remember that CA + NFA = TA. So, if we find the CA and the TA, we can solve for NFA. Using the numbers given for the current ratio and the current liabilities, we solve for CA:
CR = CA / CL
CA = CR(CL) = 1.25($950) = $1,187.50
To find the total assets, we must first find the total debt and equity from the information given. So, we find the net income using the profit margin:
PM = NI / Sales
NI = Profit margin × Sales = .094($5,780) = $543.32
We now use the net income figure as an input into ROE to find the total equity:
ROE = NI / TE
TE = NI / ROE = $543.32 / .182 = $2,985.27
Next, we need to find the long-term debt. The long-term debt ratio is:
Long-term debt ratio = 0.35 = LTD / (LTD + TE)
Inverting both sides gives:
1 / 0.35 = (LTD + TE) / LTD = 1 + (TE / LTD)
Substituting the total equity into the equation and solving for long-term debt gives the following:
1 + $2,985.27 / LTD = 2.86
LTD = $2,985.27 / 1.86 = $1,607.46
Now, we can find the total debt of the company:
TD = CL + LTD = $950 + 1,607.46 = $2,557.46
And, with the total debt, we can find the TD&E, which is equal to TA:
TA = TD + TE = $2,557.46 + 2,985.27 = $5,542.73
And finally, we are ready to solve the balance sheet identity as:
NFA = TA – CA = $5,542.73 – 1,187.50 = $4,355.23
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