A firm has the following balance sheet:
Cash:$ 10
Accounts payable:$ 10
Accounts receivable:10
Notes payable:20
Inventories:10
Long-term debt:40
Fixed assets:90
Common stock:40
Retained earnings:10
Total assets:$120
Total liabilities and equity:$120
Fixed assets are being used at 80 percent of capacity;sales for the year just ended were $200;sales will increase $10 per year for the next 4 years;the profit margin is 5 percent;and the dividend payout ratio is 60 percent.Assume that fixed assets cannot be sold.What are the total external financing requirements for the entire 4 years,i.e. ,the total AFN for the 4-year period?
A) $4.00
B) $2.00
C) −$0.80 (Surplus)
D) −$14.00 (Surplus)
E) $0

Question

Quizplus · Accepted Answer

First, we need to calculate the projected total assets (TA), total liabilities and equity (TE), and profit (NI) for each of the next four years:

Year 1: 
TA = $120 + ($200 × 5%) = $130 
TE = $130 
NI = $130 × 5% × (1 - 60%) = $2.08

Year 2: 
TA = $130 + (($200 + $10) × 5%) = $141.50 
TE = $141.50 
NI = $141.50 × 5% × (1 - 60%) = $2.26

Year 3: 
TA = $141.50 + (($200 + $10 × 2) × 5%) = $153 
TE = $153 
NI = $153 × 5% × (1 - 60%) = $2.45

Year 4: 
TA = $153 + (($200 + $10 × 3) × 5%) = $164.50 
TE = $164.50 
NI = $164.50 × 5% × (1 - 60%) = $2.63

Next, we need to calculate the additional funds needed (AFN) for each year using the AFN equation:

AFN = (A*/S0)ΔS - (L*/S0)ΔS - MS1b(1 - d)

Where:
A* = assets that vary directly with sales (inventories and accounts receivable) 
S0 = last year's sales ($200) 
ΔS = increase in sales ($10) 
L* = spontaneous liabilities (accounts payable) 
MS1 = additional required assets (80% of fixed assets - already in place) 
b = retention ratio (1 - dividend payout ratio = 40%) 
d = dividend payout ratio (60%)

Year 1: 
AFN = (($10 + $10)/$200)×$10 - ($10/$200)×$10 - (0.8×$90×(1 - 0.6)) = -$14

Year 2: 
AFN = (($10 + $10.50)/$210)×$10 - ($10/$200)×$10 - (0.8×$90×(1 - 0.6)) = -$9.40

Year 3: 
AFN = (($10 + $11)/$220)×$10 - ($10/$200)×$10 - (0.8×$90×(1 - 0.6)) = -$4.80

Year 4: 
AFN = (($10 + $11.50)/$230)×$10 - ($10/$200)×$10 - (0.8×$90×(1 - 0.6)) = -$0.20

Finally, we sum up the AFN for each year to get the total external financing requirement for the entire 4-year period:

Total AFN = -$14 - $9.40 - $4.80 - $0.20 = -$28.40

Since the total AFN is negative, it means that the firm will have a surplus of funds over the next four years and will not need any external financing. Therefore, the correct answer is D: $-14.00 (Surplus).

A Firm Has the Following Balance Sheet