Chapter 26, Problem 14QP

a.

Summary Introduction

To identify: The company would be able or not to boost the profit, if it changes the cash management policy.

Cash management:

Cash management refers to that arrangement in which the company manages the cash inflows and cash outflows to maintain a surplus situation and to avoid the cash deficit.

Explanation of Solution

Statement to show the surplus or deficit

Particulars	Quarter 1 (million $)	Quarter 2 (million $)	Quarter 3 (million $)	Quarter 4 (million $)
Beginning cash balance	20	20	20	20
Net cash inflow	5.80	(24.64)	3.64	25.40
Less: New short-term investments	6.14			22.53
Income on short-term investment	0.24	0.36
Short-term investments sold		18.04
New short-term borrowings		6.24
Less: Interest on short-term borrowings			0.19	0.08
Short-term borrowing repaid			3.45	0.279
Ending cash balance	19.90	20	20	22.51
Minimum cash balance	20	20	20	20
Cumulative Surplus/deficit	(0.10)			2.51
Beginning short-term investments	12	18.04
Ending short-term investments	18.04			22.53
Beginning short-term debt	0	0	6.24	2.79
Ending short-term debt	0	6.24	2.79	0

Table (1)

Compute the net cash cost

The interest income in Quarter 1 is $0.24.

The interest income in Quarter 2 is $0.36.

The interest expense in Quarter 3 is $0.19.

The interest expense in Quarter 4 is $0.08.

Formula to compute the net cash cost:

$\text{Net}\text{cash}\text{cost}=\left[\begin{array}{l}\text{Interest}\text{earned}\text{in}\text{Quarter}1+\text{Interest}\text{earned}\text{in}\text{Quarter}2\\ -\text{Interest}\text{expense}\text{in}\text{Quarter}3-\text{Interest}\text{expense}\text{in}\text{Quarter}4\end{array}\right]$

Substitute $0.24 for interest earned in Quarter 1, $0.36 for interest earned in Quarter 2, $0.19 for interest expense in Quarter 3 and $0.08 for interest expense in Quarter 4,

$\begin{array}{c}\text{Net}\text{cash}\text{cost}=\$0.24+\$0.36-\$0.19-\$0.08\\ =\$0.60-0.27\\ =\$0.33\end{array}$

Working Note:

Statement to show the computation of net cash inflows:

Particular	Quarter 1 (million $)	Quarter 2 (million $)	Quarter 3 (million $)	Quarter 4 (million $)
Beginning receivables	34	52.50	45	61
Add: Sales	105	90	122	140
Less: Collection of accounts	86.5	97.50	106	131
Ending receivables	52.5	45	61	70
Payment of accounts	43.20	49.14	59.76	57.6
Add: Wages, taxes, and expenses	31.5	27	36.6	42
Add: Capital expenditures		40
Add: Interest and dividends	6	6	6	6
Total cash disbursements	80.70	122.14	102.36	105.60
Total cash collections	86.50	97.50	106	131
Total ash disbursements	80.70	122.14	102.36	105.60
Net cash inflow	5.80	(24.64)	3.64	25.40

Table (2)

Compute the interest income in Quarter 1:

$\begin{array}{c}\text{Interest}\text{income}=\text{Amount}\text{invested}\times \text{Interest}\text{rate}\\ =\$12\times 0.02\\ =\$0.24\end{array}$

Compute the interest income in Quarter 2:

$\begin{array}{c}\text{Interest}\text{income}=\text{Amount}\text{invested}\times \text{Interest}\text{rate}\\ =\$18.04\times 0.02\\ =\$0.36\end{array}$

Compute the interest expenditure in Quarter 3:

$\begin{array}{c}\text{Interest}\text{expense}=\text{Amount}\text{borrowed}\times \text{Interest}\text{rate}\\ =\$6.24\times 0.03\\ =\$0.19\end{array}$

Compute the interest expenditure in Quarter 4:

$\begin{array}{c}\text{Interest}\text{expense}=\text{Amount}\text{borrowed}\times \text{Interest}\text{rate}\\ =\$2.79\times 0.03\\ =\$0.08\end{array}$

Conclusion

Hence, the net cash cost is $0.33.

b.

Summary Introduction

To identify: The company would be able or not to boost the profit, if it changes the cash management policy.

Explanation of Solution

Statement to show the surplus or deficit:

Particulars	Quarter 1 (million $)	Quarter 2 (million $)	Quarter 3 (million $)	Quarter 4 (million $)
Beginning cash balance	10	20	20	20
Net cash inflow	5.80	(24.64)	3.64	25.40
Less: New short-term investments	6.24		3.72	25.56
Income on short-term investment	0.44	0.56	0.08	0.16
Short-term investments sold		24.08
New short-term borrowings
Less: Interest on short-term borrowings
Short-term borrowing repaid
Ending cash balance	19.90		20	22.51
Less: Minimum cash balance	10	10	10	10
Cumulative Surplus/deficit
Beginning short-term investments	22	28.247	4.16	7.89
Ending short-term investments	28.24	4.16	7.89	33.6
Beginning short-term debt	0	0	0	0
Ending short-term debt	0	0	0	0

Table (3)

Compute the net cash cost

The interest income in Quarter 1 is $0.44.

The interest income in Quarter 2 is $0.56.

The interest income in Quarter 3 is $0.08.

The interest income in Quarter 4 is $0.16.

Formula to compute the net cash cost:

$\text{Net}\text{cash}\text{cost}=\left[\begin{array}{l}\text{Interest}\text{earned}\text{in}\text{Quarter}1+\text{Interest}\text{earned}\text{in}\text{Quarter}2\\ \text{+Interest}\text{earned}\text{in}\text{Quarter}3-\text{Interest}\text{earned}\text{in}\text{Quarter}4\end{array}\right]$

Substitute $0.44 for interest earned in Quarter 1, $0.56 for interest earned in Quarter 2, $0.08 for interest expense in Quarter 3 and $0.16 for interest expense in Quarter 4,

$\begin{array}{c}\text{Net}\text{cash}\text{cost}=\$0.44+\$0.56+\$0.08+\$0.16\\ =\$1.25\end{array}$

Working Note:

Compute the interest income in Quarter 1:

$\begin{array}{c}\text{Interest}\text{income}=\text{Amount}\text{invested}\times \text{Interest}\text{rate}\\ =\$22\times 0.02\\ =\$0.44\end{array}$

Compute the interest income in Quarter 2:

$\begin{array}{c}\text{Interest}\text{income}=\text{Amount}\text{invested}\times \text{Interest}\text{rate}\\ =\$28.24\times 0.02\\ =\$0.56\end{array}$

Compute the interest income in Quarter 3:

$\begin{array}{c}\text{Interest}\text{expense}=\text{Amount}\text{borrowed}\times \text{Interest}\text{rate}\\ =\$4.16\times 0.02\\ =\$0.08\end{array}$

Compute the interest income in Quarter 4:

$\begin{array}{c}\text{Interest}\text{expense}=\text{Amount}\text{income}\times \text{Interest}\text{rate}\\ =\$7.89\times 0.02\\ =\$0.16\end{array}$

No, the company should not change the cash management policy as these policies give the more net cash cost and the company can consider any other factors but it is not necessary for it.

Conclusion

Company should not change its cash management policy as its net cash cost increases.