Question

Upton Computers makes bulk purchases of small computers, stocks them in conveniently located warehouses, ships them to its chain of retail stores, and has a staff to advise customers and help them set up their new computers. Upton's balance sheet as of December 31, 2019, is shown here (millions of dollars):

Cash	$   3.5		Accounts payable	$   9.0
Receivables	26.0		Notes payable	18.0
Inventories	58.0		Line of credit	0
Total current assets	$ 87.5		Accruals	8.5
Net fixed assets	35.0		Total current liabilities	$ 35.5
			Mortgage loan	6.0
			Common stock	15.0
			Retained earnings	66.0
Total assets	$122.5		Total liabilities and equity	$122.5

Sales for 2019 were $475 million and net income for the year was $14.25 million, so the firm's profit margin was 3.0%. Upton paid dividends of $5.7 million to common stockholders, so its payout ratio was 40%. Its tax rate was 25%, and it operated at full capacity. Assume that all assets/sales ratios, (spontaneous liabilities)/sales ratios, the profit margin, and the payout ratio remain constant in 2020. Do not round intermediate calculations.

1. If sales are projected to increase by $99.75 million, or 21%, during 2020, use the AFN equation to determine Upton's projected external capital requirements. Enter your answers in millions. For example, an answer of $10,550,000 should be entered as 10.55. Round your answer to two decimal places.

   $    million

2. Using the AFN equation, determine Upton's self-supporting growth rate. That is, what is the maximum growth rate the firm can achieve without having to employ nonspontaneous external funds? Round your answer to two decimal places.

     %

Answer 1

a). Additional Funds Needed = [A0 x (ΔS / S0)] - [L0 x (ΔS / S0)] - [S1 x PM x b]

Where,
A_o = current level of assets
L_o = current level of liabilities
ΔS/S_o = percentage increase in sales i.e. change in sales divided by current sales
S₁ = new level of sales
PM = profit margin
b = retention rate = 1 - payout rate

AFN = [122.5 x 0.21] - [(8.5 + 9) x 0.21] - [(475 + 99.75) x 0.03 x (1 - 0.40)]

= 25.725 - 3.675 - 10.3455 = 11.7045, or $11.70 million

b). AFN = {[(A*/S0) - (L*/S0)] - [M × RR ×(1+g)/g]} ×∆S

0 = {[(122.5/475) - (17.5/475) - [0.03 * 0.6 * (1 + g)/g]} * 99.75

0 / 99.75 = 0.2579 - 0.0368 - [0.018 * (1 + g) / g]

0 = 0.2211 - [0.018 + 0.018g] / g

0 = [0.2211g - 0.018 + 0.018g] / g

0 * g = 0.2391g - 0.018

0.2391g = 0.018

g = 0.018 / 0.2391 = 0.07530, or 7.53%