Question

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?

Answer 1

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