Carter Corporation\'s sales are expected to increase from $X in 2012 to $10 mill

Question

Carter Corporation's sales are expected to increase from $X in 2012 to $10 million in 2013. Its assets totaled $5 million at the end of 2012. Carter is at full capacity, so its assets must grow in proportion to projected sales. At the end of 2012, current liabilities are $1.8 million, consisting of $500,000 of account payable, $800,000 of notes payable, and $500,000 of accruals. Its profit margin is forecasted to be 8%, and the forecasted retention ratio is 40%. If the firm can achieve this increase in sales without raising funds externally, what was the firm's sales ($X) during 2012? Show your work.

Explanation / Answer

Using the AFN equation, the value of 'x' can be obtained as follows:

AFN = (A/S0) x Increase in Sales - (L/S0)x increase in Sales - MS1 x RR
(10 m - 'x') = 'x' * (10.0m - 'x') / 'x' - (0.8 x (10.0m - 'x') / 'x' - [0.08 x 10m x 0.40]
(10 m - 'x') + 0.32 = (10 m - 'x') - 0.8 * (10.0m - 'x') / 'x'   

(10 m - 'x') - (10 m - 'x') + 0.32 = - 0.8 * (10.0m-'x') / 'x'

- 0.32 / 0.8 = (10.0 m - 'x') / 'x'

0..4 'x' = 10.0 m - 'x'

1.4 'x' = 10 m

'x' = 10 m / 1.4

'x' = 7.143 m

Therefore, the firm's sales during 2012 is $7.143 m.

S0 = Sales for 2012 = 'x'
S1 = Sales for 2013 = 10.0m
MS1 = After tax profit margin rate x S1 = 10.0m x 8% = 0.8
L = accounts payables + accruals. Spontaneous liabilities that will be affected by sales = 1 m

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