Sales increase Pierce Furnishings generated $4 million in sales during 2012, and

Question

Sales increase

Pierce Furnishings generated $4 million in sales during 2012, and its year-end total assets were $3.2 million. Also, at year-end 2012, current liabilities were $500,000, consisting of $200,000 of notes payable, $200,000 of accounts payable, and $100,000 of accrued liabilities. Looking ahead to 2013, the company estimates that its assets must increase by $0.80 for every $1.00 increase in sales. Pierce's profit margin is 3%, and its retention ratio is 40%. How large of a sales increase can the company achieve without having to raise funds externally? Write out your answer completely. For example, 25 million should be entered as 25,000,000. Round your answer to the nearest cent.

$ _____

Explanation / Answer

Sales for 2012 S0= $ 4,000,000

Profit Margin PM = 3% = 0.03

Total Assets A = 3,200,000

Assets / Sales Ratio (A/S0) = (3,200,000/4,000,000) = 0.80

Current Liabilities L = 500,000

Spontaneous Liabilities which are linked to sales = Accounts payable L = 200,000

Spotaneous liabilities / Total Sales ratio (L/S0) = 200,000/4,000,000 = 0.05

Retention ratio RR = 40% = 0.40

If g is the growth rate which needs to be achieved for 2013, then sales for 2013 (S1) can be calculated using the formula

S1 = S0(1+g)

The External Fund requirement is calculated using the below formuala

EFR = (A/S0)*(S1-S0) - (L/S0)*(S1-S0) - PM * S1 * RR

Substituting S0(1+g) in place of S1, The formula can be rewritten as

EFR = (A/S0) * (S0(1+g) - S0) - (L/S0) * (S0(1+g) - S0) - PM * S0(1+g) * RR

EFR = (A/S0) * (S0 + S0g - S0) - (L/S0) * (S0 + S0g - S0) - PM* S0(1+g)* RR

EFR = (A/S0) * S0g - (L/S0) * S0g - PM *S0(1+g) * RR

Substituting the values and taking External Fund requirment as Zero the formula will be

0 = 0.8 * 4000000*g - 0.05*4000000*g - 0.03 * 4000000(1+g) * 0.40

0 = 3200000g - 200000g - (0.012)(4000000 + 4000000g)

0 = 3200000g - 200000g - 48000 - 48000g

48000 = 2952000g

g = 48000/2952000 = 0.0162602

That is the growth rate which can be supported without any fund requirement will be 1.62602%

Sales for year 2013 without External Fund Requirement = 4,000,000 (1+0.0162602)
= 4000000*1.0162602
= $ 4,065,040.80

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