Chapter 19, Problem 24P

1.

To determine

Prepare a schedule for expected cash flows of company H.

Explanation of Solution

Net cash flow: Net cash flow is the difference between cash receipts and cash payments.

Year	Operating costs after tax (A)(1)	Savings (4) (B)	Depreciation expenses after tax (3) (C)	Net cash inflow $\left(A-B-C\right)$
0				$(630,000)
1	($31,500)	$218,700	$18,000	$205,200
2	($31,500)	$218,700	$36,000	$223,200
3	($31,500)	$218,700	$36,000	$223,200
4	($31,500)	$218,700	$36,000	$223,200
5	($31,500)	$218,700	$36,000	$223,200
6	($31,500)	$218,700	$36,000	$223,200
7	($31,500)	$218,700	$36,000	$223,200
8	($31,500)	$218,700	$18,000	$205,200
9	($31,500)	$218,700	-	$187,200
10	($31,500)	$218,700	-	$187,200

Table (1)

Working note (1):

Calculate the annual operating cost after tax:

$\begin{array}{c}\text{Annual operating cost after tax = Operating cost after tax}\times \left(1-\text{Tax rate}\right)\\ \text{=\$45,000}+\text{\$7,500}\times \left(1-\frac{40}{100}\right)\\ =\$52,500\times 0.60\\ =\$31,500\end{array}$

Working note (2):

Calculate the annual depreciation expense.

$\begin{array}{c}\text{Annual depreciation = }\frac{\text{Book value of assets}}{\text{Useful life}}\\ =\frac{\$630,000}{\text{7 years}}\\ =\$90,000\end{array}$

Working note (3):

Calculate the annual depreciation expense after tax:

Year	Annual deprecation (A) (2)	Deprecation after tax$\left(\text{A}\times 40\%\right)$
1	45,000	$18,000
2	90,000	$36,000
3	90,000	$36,000
4	90,000	$36,000
5	90,000	$36,000
6	90,000	$36,000
7	90,000	$36,000
8	45,000	$18,000

Table (2)

Note: The annual depreciation expense is $90,000; however the depreciation expense is calculated on the basis of straight line deprecation with half year convention method. Hence, the depreciation expense under half year convention method is $45,000$\left(\frac{\$90,000}{2}\right)$.

Working note (4):

Calculate the annual savings after tax:

$\begin{array}{c}\text{Savings}=\text{Total Saving}\times \left(1-\text{Tax rate}\right)\\ =\$364,500\times \left(1-40\%\right)\\ =\$218,700\end{array}$

2.

To determine

Calculate the payback period of company H.

Explanation of Solution

Payback period: Payback period is the expected time period which is required to recover the cost of investment. It is one of the capital investment method used by the management to evaluate the proposal of long-term investment (fixed assets) of the business. But payback method has high risk than other method, because it does not follow the time value of money concept in valuing the cash inflows.

Calculate the payback period of company H as follows:

Initial investment = $630,000.

Year	Cash inflow	Accumulated cash flow
1	$205,200	$205,200
2	$223,200	$428,400 $\left(\text{\$205,200}+\$223,200\right)$
3	$223,200	$651,600$\left(\text{\$428,400}+\$223,200\right)$
4	$223,200	$874,800 $\left(\text{\$651,600}+\$223,200\right)$
5	$223,200	$1,098,000$\left(\text{\$}874,800+\$223,200\right)$
6	$223,200	$1,321,200 $\left(\text{\$}1,098,000+\$223,200\right)$
7	$223,200	$1,544,400$\left(\text{\$}1,321,200+\$223,200\right)$
8	$205,200	$1,749,600 $\left(\text{\$}1,544,400+\$223,200\right)$
9	$187,200	$1,936,800 $\left(\text{\$}1,749,600+\$223,200\right)$
10	$187,200	$2,124,000$\left(\text{\$}1,936,800+\$223,200\right)$

Table (3)

In this case, the initial investment of $630,000 falls between $428,400 and $651,600. Hence, the payback period is calculated as follows:

$\begin{array}{c}\begin{array}{l}\text{Payback period for}\\ \text{ uneven cash flow}\end{array}\}\text{ = }\left[2\text{year +}\left(\frac{\text{Balance amount of intital investment}}{\text{Cash flow for particular year}}\right)\right]\\ =\text{2 year +}\left(\frac{\left(\$630,000-\$428,400\right)}{\$223,200}\right)\\ \text{=2 year + 0}\text{.90 year}\\ \text{=2}\text{.90 years}\end{array}$

Therefore, the payback period for the given investment is 2.90 years.

3.

To determine

Ascertain the Net present value of the closed-loop system and describe whether the company should invest in the system.

Explanation of Solution

Ascertain the Net present value of the closed-loop system and describe whether the company should invest in the system:

Year	Cash inflow	Present value factor @10%	Present value
1	$205,200	0.862	$ 176,882
2	$223,200	0.743	$ 165,838
3	$223,200	0.641	$ 143,071
4	$223,200	0.552	$ 123,206
5	$223,200	0.476	$ 106,243
6	$223,200	0.410	$ 91,512
7	$223,200	0.354	$ 79,013
8	$205,200	0.305	$ 62,586
9	$187,200	0.263	$ 49,234
10	$187,200	0.227	$ 42,494
Total present value			$ 1,040,080
Less: Cash outflow for investment			$ 630,000
Net present value			$ 410,080

Table (4)

The company should invest in the system because the net present value is positive.

4.

To determine

State the effect that the inclusion of after tax would have on the payback period and on the net present value.

Explanation of Solution

State the effect that the inclusion of after tax would have on the payback period and on the net present value:

Payback period:

In this case, the annual cash flows increase by $135,000. Therefore the cash inflow for year 1 would increase to $340,200 $\left(\$205,200+\$135,000\right)$ and $358,200 for Years 2–7$\left(\$223,200+\$135,000\right)$.

Initial investment = $630,000.

Year	Cash inflow	Accumulated cash flow
1	$340,200	$340,200
2	$358,200	$698,400
3	$358,200	$1,056,600
4	$358,200	$1,414,800
5	$358,200	$1,773,000
6	$358,200	$2,131,200
7	$358,200	$2,489,400

Table (5)

In this case, the initial investment of $630,000 falls between $340,200 and $698,400. Hence, the payback period is calculated as follows:

$\begin{array}{c}\begin{array}{l}\text{Payback period for}\\ \text{ uneven cash flow}\end{array}\}=\left[1\text{year +}\left(\frac{\text{Balance amount of intital investment}}{\text{Cash flow for particular year}}\right)\right]\\ =1\text{ year +}\left(\frac{\left(\$630,000-\$340,200\right)}{\$358,200}\right)\\ =\text{1 year + 0}\text{.81 year}\\ \text{=1}\text{.81 years}\end{array}$

Therefore, the payback period for the given investment is reduced by 1.81 years $\left(\text{2}\text{.90 years}-1.81\text{ years}\right)$.

Net present value:

Particulars	Amounts in ($)	Amounts in ($)
Fines and sales (a)	$135,000
NPV for 10 years (b)	$4.833
Fines and sales effect		$652,455
Lawsuit avoidance	$300,000
NPV for 3 years	$0.641
Add: Lawsuit avoidance		$192,300
Total NPV		$844,755

Table (6)

Therefore, the net present value is increased by $434,676$\left(\text{\$844,755}-\$410,079\right)$.