Chapter 16, Problem 52P

1.

To determine

Calculate the net present value of the machine replacement for Company T.

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.

Calculate the net present value of the machine replacement for Company T as follows:

Year	Cash inflow (5) (M)	Present value factor @12% (N)	Present value $\left(M\times N\right)$
20x2	$313,320	0.893	$ 279,795
20x3	$357,800	0.797	$ 285,167
20x4	$239,240	0.712	$ 170,339
20x5	$209,640	0.636	$ 133,331
Total present value			$ 868,632
Less: Cash outflow for investment (4)			$ 964,000
Net present value of machine			($ 95,368)

Table (1)

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

Working note (1):

Calculate the depreciation expense of the machine under MACRS.

Depreciation Schedule
Year	MACRS Percentage (A)	Depreciation $B=\left(A\times \$1,000,000\right)$	Tax Rate (C)	Depreciation Tax Shield $\left(B\times C\right)$
20x2	33.33%	$ 333,300	40%	$133,320
20x3	44.45%	$444,500	40%	$177,800
20x4	14.81%	$148,100	40%	$59,240
20x5	7.41%	$74,100	40%	$29,640

Table (2)

Working note (2):

Calculate the after tax annual operating cost saving.

$\begin{array}{c}\begin{array}{l}\text{After tax operating}\\ \text{ cost savings }\end{array}\}\text{= Operating cost savings}\times \left(\text{1}-\text{Tax}\text{rate}\right)\\ =\$300,000\times \left(1-\frac{40}{100}\right)\\ =\$180,000\end{array}$

Working note (3):

Calculate the salvage value of old machine.

$\begin{array}{c}\text{After tax salvage value = Replacement cost of old machine}\times \text{Tax rate}\\ \text{=\$60,000}\times \frac{40}{100}\\ =\$24,000\end{array}$

Working note (4):

Calculate the net cash outflow of machine.

$\begin{array}{c}\text{Net cash outflow = }\left(\left(\text{Acquisation cost+Salvage value}\right)-\text{Gain on sale}\right)\\ =\left(\$1,000,000+\$24,000\right)-\$60,000\\ =\$964,000\end{array}$

Working note (5):

Calculate the net cash inflow of machine.

Year	After tax operating cost savings (2) (C)	Depreciation expense (1) (D)	Incremental Profit $E=\left(C+D\right)$
20x2	$180,000	$133,320	$313,320
20x3	$180,000	$177,800	$357,800
20x4	$180,000	$59,240	$239,240
20x5	$180,000	$29,640	$209,640

Table (3)

2.

To determine

Calculate the internal rate of return on the machine replacement.

Explanation of Solution

Internal rate of return method (IRR): Internal rate of return method is one of the capital investment methods which determine the rate of return, wherein the net present value of all the cash flows (both positive and negative) from an investment is zero. This method is also called as the time-adjusted rate of return method. It used to evaluate the different proposal’s expected rate of return.

Calculate the internal rate of return on the machine replacement as follows:

Year	Total After-Tax Cash Flow (5) (G)	Present value factor at 6% discount rate (H)	Present Value under 6% discount rate $\left(G\times H\right)$	Present value factor at 8% discount rate (I)	Present Value under 8% discount rate $\left(G\times I\right)$
20x1	-$ 964,000	1.000	$-964,000	1.000	$-964,000
20x2	$ 313,320	0.943	295,461	0.926	290,134
20x3	$ 357,800	0.890	318,442	0.857	306,635
20x4	$ 239,240	0.840	200,962	0.794	189,957
20x5	$ 209,640	0.792	166,035	0.735	154,085
Net present value			$ 16,900		-$ 23,189

Table (4)

The internal rate of return of machine replacement is between 6% and 8%, because the net present value is positive under 6% discount rate but the net present value is negative when 8% discount rate is used.

3.

To determine

Identify the consecutive whole number amounts in which the payback period for the machine replacement is computed.

Explanation of Solution

Identify the consecutive whole number amounts in which the payback period for the machine replacement is computed as follows:

Initial net cash outflow = $964,000.

Year	After tax cash inflow	Accumulated cash flow
20x2	$ 313,320	$ 313,320
20x3	$ 357,800	$671,120$\left(\$313,320+\$357,800\right)$
20x4	$ 239,240	$910,360 $\left(\$671,120+\$239,240\right)$
20x5	$ 209,640	$1,120,000 $\left(\$910,360+\$209,640\right)$

Table (5)

The initial net cash outflow of the investment falls between $910,360 and $1,120,000. Hence the two whole number of payback period is 3 years (20x4) and 4 years (20x5).

4.

To determine

Calculate the salvage of value of new machine on December 31, 20x5 if machine replacement is considered as an acceptable investment.

Explanation of Solution

Calculate the salvage of value of new machine on December 31, 20x5 if machine replacement is considered as an acceptable investment as follows:

The net present value of machine is ($95,368) with zero salvage value. Before the discount factor, the salvage value of old machinery would be $149,950$\left(\frac{\$95,368}{0.636}\right)$ hence the salvage value of new machine should exceed $149,950. The salvage value of new machinery is calculated as follows:

$\begin{array}{c}\left(X-0.4X\right)=149,950\\ 0.6X=149,950\\ X=\$249,917\end{array}$

Note: X denotes the salvage value of new machinery.

Therefore, the salvage value of new machine must exceed $249,917 in order to consider the machine replacement is an acceptable investment.