Chapter 26, Problem 13QP

a.

Summary Introduction

To prepare: Cash budget of W Incorporation.

Cash Budget:

Cash budget is prepared to ascertain the amount of cash after a given period of time. Cash budget is a statement that contains the information of cash receipts and cash payments.

Closing balance of cash is calculated with the help of cash budget.

Explanation of Solution

Prepare cash budget.

W Incorporation
Cash budget
($ in millions)
Particulars	Q1 ($) millions	Q2 ($) millions	Q3 ($) millions	Q4 ($) millions
Beginning cash balance	32	37.50	13.1	16.7
Net cash inflows	5.5	(24.7)	3.6	25.4
Ending cash balance	37.5	12.8	16.7	42.1
Minimum cash balance	(15)	(15)	(15)	(15)
Cumulative surplus (deficit)	22.5	(2.2)	1.7	27.1

Table (1)

Working Note:

The average collection period is of 45 days, it means the cash collection is 50% of current and 50% of old balance of credit sales.

The average accounts payable period is of 36 days it means the firm has to pay 60% of current quarter purchase and 40% of previous quarter purchase in current quarter.

Table that shows calculation of cash inflow and outflow,

Particulars	Q1 ($) millions	Q2 ($) millions	Q3 ($) millions	Q4 ($) millions
Beginning receivables	34	52.50	45	61
Sales	105	90	122	140
Collection on account (A)	(86.5)	(97.50)	(106)	(131)
Ending receivables	52.5	45	61	70
Purchase	41	55	63	54
Payment of accounts	43.5	49.2	59.8	57.6
Wages, taxes and expenses $\left(\text{Sales}\times 30\%\right)$	31.5	27	36.60	42
Capital expenditure		40
Interest and dividend	6	6	6	6
Total cash disbursement (B)	81	122.2	102.4	105.6
Net cash inflows $\left(\text{A}-\text{B}\right)$	5.5	(24.7)	3.6	25.4

Table (2)

Calculate collection on account receivables in Q1,

$\begin{array}{c}\text{Cash collection}=\left(\text{Sales}\times \frac{45}{90}\right)+\text{Beginning receivables}\\ =\left(\$105\text{ million}\times \frac{45}{90}\right)+\$34\text{ million}\\ =\$52.5\text{ million}+\$34\text{ million}\\ =\$86.5\text{ million}\end{array}$

Calculation of ending receivable in Q1,

$\begin{array}{c}\text{Ending receivables}=\text{Sales}\times \frac{45}{90}\\ =\$105\text{ million}\times \frac{45}{90}\\ =\$52.5\text{ million}\end{array}$

Calculation of purchase of Q1,

$\begin{array}{c}\text{Purchase}=\text{Sales of Q2}\times 45\%\\ =\$90\text{ million}\times 45\%\\ =41\text{ million}\end{array}$

Calculation of payment to accounts payable in Q1,

$\begin{array}{c}\text{Payment to accounts}=\left[\left(\text{Purchase}\times \frac{\left(90-36\right)}{90}\right)+\left(\text{Q1 sales}\times 45\%\times \frac{36}{90}\right)\right]\\ =\left[\left(\$41\text{ million}\times \frac{54}{90}\right)+\left(\$105\text{ million}\times 45\%\times \frac{36}{90}\right)\right]\\ =\left[\left(\$24.6\text{ million}\right)+\left(\$18.9\text{ million}\right)\right]\\ =\$43.5\text{ million}\end{array}$

Calculate collection on account receivables in Q2,

$\begin{array}{c}\text{Cash collection}=\text{Sales}\times \frac{45}{90}+\text{Beginning receivables}\\ =\$90\text{ million}\times \frac{45}{90}+\$52.50\text{ million}\\ =\$45\text{ million}+\$52.50\text{ million}\\ =\$97.5\text{ million}\end{array}$

Calculation of ending receivable in Q2,

$\begin{array}{c}\text{Ending receivables}=\text{Sales}\times \frac{45}{90}\\ =\$90\text{ million}\times \frac{45}{90}\\ =\$45\text{ million}\end{array}$

Calculation of purchase of Q2,

$\begin{array}{c}\text{Purchase}=\text{Sales of Q3}\times 45\%\\ =\$122\text{ million}\times 45\%\\ =\$55\text{million}\end{array}$

Calculation of payment to accounts payable in Q2,

$\begin{array}{c}\text{Payment to accounts}=\left[\left(\text{Purchase}\times \frac{\left(90-36\right)}{90}\right)+\left(\text{Q2 sales}\times 45\%\times \frac{36}{90}\right)\right]\\ =\left[\left(\$55\text{ million}\times \frac{54}{90}\right)+\left(\$90\text{ million}\times 45\%\times \frac{36}{90}\right)\right]\\ =\left[\left(\$33\text{ million}\right)+\left(\$16.2\text{ million}\right)\right]\\ =\$49.2\text{ million}\end{array}$

Calculate collection on account receivables in Q3,

$\begin{array}{c}\text{Cash collection}=\text{Sales}\times \frac{45}{90}+\text{Beginning receivables}\\ =\$122\text{ million}\times \frac{45}{90}+\$45\text{ million}\\ =\$61\text{ million}+\$45\text{ million}\\ =\$106\text{ million}\end{array}$

Calculation of ending receivable in Q3,

$\begin{array}{c}\text{Ending receivables}=\text{Sales}\times \frac{45}{90}\\ =\$122\text{ million}\times \frac{45}{90}\\ =\$61\text{ million}\end{array}$

Calculation of purchase of Q3,

$\begin{array}{c}\text{Purchase}=\text{Sales of Q4}\times 45\%\\ =\$140\text{ million}\times 45\%\\ =\$63\text{million}\end{array}$

Calculation of payment to accounts payable in Q3,

$\begin{array}{c}\text{Payment to accounts}=\left[\left(\text{Purchase}\times \frac{\left(90-36\right)}{90}\right)+\left(\text{Q3 sales}\times 45\%\times \frac{36}{90}\right)\right]\\ =\left[\left(\$63\text{ million}\times \frac{54}{90}\right)+\left(\$122\text{ million}\times 45\%\times \frac{36}{90}\right)\right]\\ =\left[\left(\$37.8\text{ million}\right)+\left(\$22\text{ million}\right)\right]\\ =\$59.8\text{ million}\end{array}$

Calculate collection on account receivables in Q4,

$\begin{array}{c}\text{Cash collection}=\text{Sales}\times \frac{45}{90}+\text{Beginning receivables}\\ =\$140\text{ million}\times \frac{45}{90}+\$61\text{ million}\\ =\$70\text{ million}+\$61\text{ million}\\ =\$131\text{ million}\end{array}$

Calculation of ending receivable in Q4,

$\begin{array}{c}\text{Ending receivables}=\text{Sales}\times \frac{45}{90}\\ =\$140\text{ million}\times \frac{45}{90}\\ =\$70\text{ million}\end{array}$

Calculation of purchase of Q4,

$\begin{array}{c}\text{Purchase}=\text{Sales of next quarter}\times 45\%\\ =\$120\text{ million}\times 45\%\\ =\$54\text{million}\end{array}$

Calculation of payment to accounts payable in Q4,

$\begin{array}{c}\text{Payment to accounts}=\left[\left(\text{Purchase}\times \frac{\left(90-36\right)}{90}\right)+\left(\text{Q3 sales}\times 45\%\times \frac{36}{90}\right)\right]\\ =\left[\left(\$54\text{ million}\times \frac{54}{90}\right)+\left(\$140\text{ million}\times 45\%\times \frac{36}{90}\right)\right]\\ =\left[\left(\$32.4\text{ million}\right)+\left(\$25.2\text{ million}\right)\right]\\ =\$57.6\text{ million}\end{array}$

b.

Summary Introduction

To prepare: A statement that shows short term financial plan and the net cash cost.

Explanation of Solution

The statement of financial plan is,

Particulars	Q1 ($) millions	Q2 ($) millions	Q3 ($) millions	Q4 ($) millions
Beginning cash balance	15	15	15	15
Net cash inflows	5.5	(24.7)	3.6	25.4
New short term investment	(6.14)		(2.53)	(25.45)
Income from short term Investment	0.34	0.46		0.05
Sale of short term investment		22.84
New short term borrowing		1.1
Interest on short term borrowing			(0.03)
Short term borrowing repaid			(1.1)
Ending cash balance	15	15	15	15
Minimum cash balance	(15)	(15)	(15)	(15)
Cumulative surplus (deficit)	0	0	0	0
Beginning short term Investment	17	22.84		2.53
Ending short term Investment	22.84	0	2.53	28.07
Beginning short term debt	0	0	1.1	0
Ending short term debt	0	1.1	0	0

Table (3)

Calculation of net cash cost,

$\begin{array}{c}\text{Net cash cost}=\text{Income earned}-\text{Expenses paid}\\ =\$0.34+\$0.46-\$0.03+\$0.05\\ =\$0.82\end{array}$

Working Note:

Calculation of new short term investment in Q1 is,

$\begin{array}{c}\text{New short term investment}=\left[\begin{array}{l}\text{Net cash flow }\left(\text{Q1}\right)+\\ \left(\text{Beginning cash}-\$15\text{ million}\right)\times 2\%\end{array}\right]\\ =\left[\$5.80\text{ million}+\left(\$32\text{ million}-\$15\text{ million}\right)\times 2\%\right]\\ =\left[\$5.80\text{ million}+\$0.34\text{ million}\right]\\ =\$6.14\text{ million}\end{array}$

Calculation of income from new short term investment in Q1 is,

$\begin{array}{c}\text{Income}=\left(\text{Beginning cash}-\$15\text{ million}\right)\times 2\%\\ =\left(\$32\text{ million}-\$15\text{ million}\right)\times 2\%\\ =\$0.34\text{ million}\end{array}$

Calculation of beginning short term investment Q1,

$\begin{array}{c}\text{Beginning investment}=\text{Beginning cash balance}-\text{Targent cash balance}\\ =\$32\text{ million}-\$15\text{ million}\\ =\text{\$17 million}\end{array}$

Calculation of ending short term investment Q1,

$\begin{array}{c}\text{Ending investment}=\text{Cummulative surplus}+\text{Income from short term investment}\\ =\$22.5\text{ million}+\$0.34\text{ million}\\ =\$22.84\text{ million}\end{array}$

Calculation of income from new short term investment in Q2 is,

$\begin{array}{c}\text{Income}=\left(\text{Income in Q1}+\text{Cummulative cash flow}\right)\times 2\%\\ =\left(\$0.34\text{ million}+\$22.50\text{ million}\right)\times 2\%\\ =\$0.46\text{ million}\end{array}$

Calculation of new short term borrowing Q2,

$\begin{array}{c}\text{New short term borrowing}=\left[\begin{array}{l}\text{Cummulative deficit}\\ +\text{Q1 income on short term investment}\\ +\text{Q2 income on short term investment}\end{array}\right]\\ =\left[-\$1.9\text{ million}+\$0.34\text{ million}+\$0.46\text{ million}\right]\\ =\$1.1\text{ million}\end{array}$

Calculation of new short term investment Q3,

$\begin{array}{c}\text{New short term investment}=\left[\begin{array}{c}\text{Net cash inflow}-\text{Q1 short term borrowing}+\\ \text{ Interest on short term borrowing}\end{array}\right]\\ =\$3.6\text{ million}-\$1.1\text{ million}+\left(\$1.1\text{ million}\times 3\%\right)\\ =\$2.5\text{ million}+\$0.03\text{ million}\\ =\$\text{2}\text{.53 million}\end{array}$

Calculation of income from short term investment in Q4,

$\begin{array}{c}\text{Income from short term investment}=\text{Q3 short term investment}\times 2\%\\ =\$2.53\text{ million}\times 2\%\\ =\$0.05\text{ million}\end{array}$

Calculation of new short term investment in Q4,

$\begin{array}{c}\text{New short term investment}=\text{Net cash flows}+\text{ Income from investment}\\ =\$25.4\text{ million}+\$0.05\text{ million}\\ =\$25.45\text{ million}\end{array}$

Calculation of ending short term investment Q4,

$\begin{array}{c}\text{Ending investment}=\left[\begin{array}{l}\text{New short term investment}\\ +\text{Beginning short term investment}\\ +\text{Income from short term investment}\end{array}\right]\\ =\left[\$25.45\text{ million}+\$2.57\text{ million}+\$0.05\text{ million}\right]\\ =\$28.07\text{ million}\end{array}$