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Sagot :
Let's break down the cash receipts schedule and compute the monthly receipts step by step.
### Given Data:
1. Sales Projections:
- January: \[tex]$46,000 - February: \$[/tex]45,000
- March: \[tex]$43,000 - April: \$[/tex]49,000
- May: \[tex]$38,000 - June: \$[/tex]47,000
- July: \[tex]$55,000 - August: \$[/tex]57,000
2. Collection Percentages:
- 10% uncollectible
- 35% collected in the month of sale
- 45% collected one month after sale
- 10% collected two months after sale
### Step-by-Step Calculation:
#### Collections in the Month of Sale:
- For March: [tex]\( \$43,000 \times 0.35 = \$15,050 \)[/tex]
- For April: [tex]\( \$49,000 \times 0.35 = \$17,150 \)[/tex]
- For May: [tex]\( \$38,000 \times 0.35 = \$13,300 \)[/tex]
- For June: [tex]\( \$47,000 \times 0.35 = \$16,450 \)[/tex]
- For July: [tex]\( \$55,000 \times 0.35 = \$19,250 \)[/tex]
- For August: [tex]\( \$57,000 \times 0.35 = \$19,950 \)[/tex]
#### Collections One Month After Sale:
- For February (collected in March): [tex]\( \$45,000 \times 0.45 = \$20,250 \)[/tex]
- For March (collected in April): [tex]\( \$43,000 \times 0.45 = \$19,350 \)[/tex]
- For April (collected in May): [tex]\( \$49,000 \times 0.45 = \$22,050 \)[/tex]
- For May (collected in June): [tex]\( \$38,000 \times 0.45 = \$17,100 \)[/tex]
- For June (collected in July): [tex]\( \$47,000 \times 0.45 = \$21,150 \)[/tex]
- For July (collected in August): [tex]\( \$55,000 \times 0.45 = \$24,750 \)[/tex]
#### Collections Two Months After Sale:
- For January (collected in March): [tex]\( \$46,000 \times 0.10 = \$4,600 \)[/tex]
- For February (collected in April): [tex]\( \$45,000 \times 0.10 = \$4,500 \)[/tex]
- For March (collected in May): [tex]\( \$43,000 \times 0.10 = \$4,300 \)[/tex]
#### Total Monthly Cash Receipts:
- March:
[tex]\[ \$15,050 \quad (\text{in month collection}) \][/tex]
[tex]\[ + \$20,250 \quad (\text{one month after February}) \][/tex]
[tex]\[ + \$4,600 \quad (\text{two months after January}) \][/tex]
[tex]\[ = \$39,900 \][/tex]
- April:
[tex]\[ \$17,150 \quad (\text{in month collection}) \][/tex]
[tex]\[ + \$19,350 \quad (\text{one month after March}) \][/tex]
[tex]\[ + \$4,500 \quad (\text{two months after February}) \][/tex]
[tex]\[ = \$41,000 \][/tex]
- May:
[tex]\[ \$13,300 \quad (\text{in month collection}) \][/tex]
[tex]\[ + \$22,050 \quad (\text{one month after April}) \][/tex]
[tex]\[ + \$4,300 \quad (\text{two months after March}) \][/tex]
[tex]\[ = \$39,650 \][/tex]
- June:
[tex]\[ \$16,450 \quad (\text{in month collection}) \][/tex]
[tex]\[ + \$17,100 \quad (\text{one month after May}) \][/tex]
[tex]\[ = \$33,550 \][/tex]
- July:
[tex]\[ \$19,250 \quad (\text{in month collection}) \][/tex]
[tex]\[ + \$21,150 \quad (\text{one month after June}) \][/tex]
[tex]\[ = \$40,400 \][/tex]
- August:
[tex]\[ \$19,950 \quad (\text{in month collection}) \][/tex]
[tex]\[ + \$24,750 \quad (\text{one month after July}) \][/tex]
[tex]\[ = \$44,700 \][/tex]
### Final Cash Receipts Schedule:
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}
\hline \multicolumn{10}{|c|}{ Watt's Lighting Stores } \\
\hline \multicolumn{10}{|c|}{ Cash Receipts Schedule } \\
\hline & January & February & March & April & May & June & July & August & Total \\
\hline \multicolumn{10}{|l|}{ Credit sales } \\
\hline \multicolumn{10}{|l|}{ Collections: } \\
\hline In month of sale & & & \[tex]$15,050 & \$[/tex]17,150 & \[tex]$13,300 & \$[/tex]16,450 & \[tex]$19,250 & \$[/tex]19,950 & \[tex]$168,300 \\ \hline One month after sale & & & \$[/tex]20,250 & \[tex]$19,350 & \$[/tex]22,050 & \[tex]$17,100 & \$[/tex]21,150 & \[tex]$24,750 & \$[/tex]124,700 \\
\hline Two months after sale & & & \[tex]$4,600 & \$[/tex]4,500 & \[tex]$4,300 & & & & \$[/tex]13,400 \\
\hline Total cash receipts & & & \[tex]$39,900 & \$[/tex]41,000 & \[tex]$39,650 & \$[/tex]33,550 & \[tex]$40,400 & \$[/tex]44,700 & \$239,200 \\
\hline
\end{tabular}
### Given Data:
1. Sales Projections:
- January: \[tex]$46,000 - February: \$[/tex]45,000
- March: \[tex]$43,000 - April: \$[/tex]49,000
- May: \[tex]$38,000 - June: \$[/tex]47,000
- July: \[tex]$55,000 - August: \$[/tex]57,000
2. Collection Percentages:
- 10% uncollectible
- 35% collected in the month of sale
- 45% collected one month after sale
- 10% collected two months after sale
### Step-by-Step Calculation:
#### Collections in the Month of Sale:
- For March: [tex]\( \$43,000 \times 0.35 = \$15,050 \)[/tex]
- For April: [tex]\( \$49,000 \times 0.35 = \$17,150 \)[/tex]
- For May: [tex]\( \$38,000 \times 0.35 = \$13,300 \)[/tex]
- For June: [tex]\( \$47,000 \times 0.35 = \$16,450 \)[/tex]
- For July: [tex]\( \$55,000 \times 0.35 = \$19,250 \)[/tex]
- For August: [tex]\( \$57,000 \times 0.35 = \$19,950 \)[/tex]
#### Collections One Month After Sale:
- For February (collected in March): [tex]\( \$45,000 \times 0.45 = \$20,250 \)[/tex]
- For March (collected in April): [tex]\( \$43,000 \times 0.45 = \$19,350 \)[/tex]
- For April (collected in May): [tex]\( \$49,000 \times 0.45 = \$22,050 \)[/tex]
- For May (collected in June): [tex]\( \$38,000 \times 0.45 = \$17,100 \)[/tex]
- For June (collected in July): [tex]\( \$47,000 \times 0.45 = \$21,150 \)[/tex]
- For July (collected in August): [tex]\( \$55,000 \times 0.45 = \$24,750 \)[/tex]
#### Collections Two Months After Sale:
- For January (collected in March): [tex]\( \$46,000 \times 0.10 = \$4,600 \)[/tex]
- For February (collected in April): [tex]\( \$45,000 \times 0.10 = \$4,500 \)[/tex]
- For March (collected in May): [tex]\( \$43,000 \times 0.10 = \$4,300 \)[/tex]
#### Total Monthly Cash Receipts:
- March:
[tex]\[ \$15,050 \quad (\text{in month collection}) \][/tex]
[tex]\[ + \$20,250 \quad (\text{one month after February}) \][/tex]
[tex]\[ + \$4,600 \quad (\text{two months after January}) \][/tex]
[tex]\[ = \$39,900 \][/tex]
- April:
[tex]\[ \$17,150 \quad (\text{in month collection}) \][/tex]
[tex]\[ + \$19,350 \quad (\text{one month after March}) \][/tex]
[tex]\[ + \$4,500 \quad (\text{two months after February}) \][/tex]
[tex]\[ = \$41,000 \][/tex]
- May:
[tex]\[ \$13,300 \quad (\text{in month collection}) \][/tex]
[tex]\[ + \$22,050 \quad (\text{one month after April}) \][/tex]
[tex]\[ + \$4,300 \quad (\text{two months after March}) \][/tex]
[tex]\[ = \$39,650 \][/tex]
- June:
[tex]\[ \$16,450 \quad (\text{in month collection}) \][/tex]
[tex]\[ + \$17,100 \quad (\text{one month after May}) \][/tex]
[tex]\[ = \$33,550 \][/tex]
- July:
[tex]\[ \$19,250 \quad (\text{in month collection}) \][/tex]
[tex]\[ + \$21,150 \quad (\text{one month after June}) \][/tex]
[tex]\[ = \$40,400 \][/tex]
- August:
[tex]\[ \$19,950 \quad (\text{in month collection}) \][/tex]
[tex]\[ + \$24,750 \quad (\text{one month after July}) \][/tex]
[tex]\[ = \$44,700 \][/tex]
### Final Cash Receipts Schedule:
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}
\hline \multicolumn{10}{|c|}{ Watt's Lighting Stores } \\
\hline \multicolumn{10}{|c|}{ Cash Receipts Schedule } \\
\hline & January & February & March & April & May & June & July & August & Total \\
\hline \multicolumn{10}{|l|}{ Credit sales } \\
\hline \multicolumn{10}{|l|}{ Collections: } \\
\hline In month of sale & & & \[tex]$15,050 & \$[/tex]17,150 & \[tex]$13,300 & \$[/tex]16,450 & \[tex]$19,250 & \$[/tex]19,950 & \[tex]$168,300 \\ \hline One month after sale & & & \$[/tex]20,250 & \[tex]$19,350 & \$[/tex]22,050 & \[tex]$17,100 & \$[/tex]21,150 & \[tex]$24,750 & \$[/tex]124,700 \\
\hline Two months after sale & & & \[tex]$4,600 & \$[/tex]4,500 & \[tex]$4,300 & & & & \$[/tex]13,400 \\
\hline Total cash receipts & & & \[tex]$39,900 & \$[/tex]41,000 & \[tex]$39,650 & \$[/tex]33,550 & \[tex]$40,400 & \$[/tex]44,700 & \$239,200 \\
\hline
\end{tabular}
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