Chapter 16, Problem 60C

1.

To determine

Ascertain the net present value of the estimated after-tax cash flows and state which of these two options to pursue.

Explanation of Solution

Net present value method (NVP): Net present value method is the method which is used to compare the initial cash outflow of investment with the present value of its cash inflows. In the net present value, the interest rate is desired by the business based on the net income from the investment, and it is also called as the discounted cash flow method.

Compute the net present value of company P as follows:

Year	After-TaxCash Flow (5) (a)	Discount Factor (b)	Present value$\left(\text{a}\times \text{b}\right)$
20x0	$(956,600)	1.000	$(956,600)
20x1	$310,987	.893	277,711
20x2	$353,688	.797	281,889
20x3	$248,270	.712	176,768
20x4	$232,454	.636	147,841
20x5	$211,200	.567	$119,750
Net present value			$47,359

Table (1)

Corporation O should purchase the new equipment to manufacture waste containers.

Note: Refer Appendix A (table III) for the discount factor.

Working notes (1):

Compute the manufacturing savings per unit cost:

Particulars	Amounts in ($)	Amounts in ($)
Unit purchase cost		$27.00
New unit variable manufacturing cost:
Material	$8.00
Direct labor	7.50
Variable overhead	4.50	20.00
Savings per unit		$ 7.00

Table (2)

Working notes (2):

Compute the manufacturing savings:

Year	Unit Savings (1)		Estimated Production		Estimated Cost		(1 – Tax Rate)		After-Tax Cost Savings
20x1	$7	$\times$	50,000	$=$	$350,000	$\times$	0.6	$=$	$210,000
20x2	7	$\times$	50,000	$=$	350,000	$\times$	0.6	$=$	210,000
20x3	7	$\times$	52,000	$=$	364,000	$\times$	0.6	$=$	218,400
20x4	7	$\times$	55,000	$=$	385,000	$\times$	0.6	$=$	231,000
20x5	7	$\times$	55,000	$=$	385,000	$\times$	0.6	$=$	231,000

Table (3)

Working notes (3):

Compute the installed cost of depreciation:

Particulars	Amounts in ($)
Acquisition cost	$945,000
Less: Discount $\left(\$945,000 \times \frac{2}{100}\right)$	(18,900
Add: Freight	11,000
Installation	22,900
Net installed cost	$960,000

Table (4)

Working notes (4):

Compute the MACRS depreciation tax shield:

Year	Installed Cost (3)	MACRS Rate	Depreciation	Tax rate	Tax benefit
	(a)	(b)	$\left(\text{c}=\text{a}\times \text{b}\right)$	(d)	$\left(\text{c}\times \text{d}\right)$
20x1	$960,000	33.33%	$319,968	0.4	$127,987
20x2	960,000	44.45%	426,720	0.4	170,688
20x3	960,000	14.81%	142,176	0.4	56,870
20x4	960,000	7.41%	71,136	0.4	28,454

Table (4)

Working notes (5):

Compute the MACRS depreciation tax shield:

Particulars	20x0	20x1	20x2	20x3	20x4	20x5
Equipment cost	$(945,000)
Discount (3)	18,900
Freight	(11,000)
Installation cost	(22,900)
Savage value for—old equipment	900$\left[\begin{array}{l}\$1,500 \times \\ \left(1-0.40\right)\end{array}\right]$
Working capital reduction	2,500
Manufacturing savings (2)		$210,000	$210,000	$218,400	$231,000	$231,000
Supervision $\left[\begin{array}{l}\$45,000 \times \\ \left(1-0.40\right)\end{array}\right]$		(27,000	(27,000	(27,000	(27,000	(27,000
Depreciation tax shield (4)		1,27,987	1,70,688	56,870	28,454	-
Salvage value for new equipment $\left[\begin{array}{l}\$12,000 \\ \times \left(1-0.40\right)\end{array}\right]$						7,200
After-tax cash flow	$(956,600)	$310,987	$353,688	$248,270	$232,454	$211,200

Table (5)

2.

To determine

State the reason for the computation of the payback period of an investment in addition to the determination of net present value.

Explanation of Solution

Since the payback method provides a preliminary screening of projects, many companies prefer computing the payback method, along with the calculation of net present value. Moreover, it indicates the manner in which an original investment can be recovered speedily from the cash flows, when a project is considered risky.

3.

To determine

Identify the consecutive whole number amounts in which the payback period for the new equipment is computed.

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.

Compute the payback period for the new equipment:

The payback period is between 3 and 4 years. Because the initial net installed cost is $956,600 and the after tax cash flow for 20x3 year is $912,945$\left(\$310,987+\$353,688+\$248,270\right)$ which is less than the net installation cost whereas for the 20x4 year is $1,145,399$\left(\$310,987+\$353,688+\$248,270+\$232,454\right)$ which is greater than the net installation cost. Thus, it is clear that the payback period is between 3 and 4 years