Chapter 24, Problem 4PSB

a.

To determine

The net present value of alternative 1.

Explanation: The net present value of alternative 1 is -$5,921.3.

Explanation:

Calculate the net present value as shown below.

Particulars	Cash flow	Present value at 10%	Present value of net cash flow
Year 1	$8,000	0.9091	$7,272.8
Year 2	$8,000	0.8264	$6,611.2
Year 3	$8,000	0.7513	$6,010.4
Year 4	$8,000	0.6830	$5,464.0
Year 5	$8,000	0.6209	$4,967.2
Year 6	$8,000	0.5645	$4,516.0
Year 7	$8,000	0.5132	$4,105.6
Year 8	$11,000	0.4665	$5,131.5
Total cash flows			$44,078.7
Invested outflows	$67,000		($50,000.0)
Net present value			-$5,921.3

Table – 1

Therefore, the net present value of alternative 1 is -$5,921.3.

Working Notes:

(a) On deduction of yearly operating cost from yearly revenues, the yearly cash flow is obtained.

(b) The cash inflow of $11,000 is obtained by adding the salvage value of $3,000 is added in the actual cash inflow of the eighth year.

(c) The cost of old machine is not considered as the invested amount, as such cost is historical cost.

Conclusion:

Since the total cash flows are smaller than the invested amount, the net present value is negative.

b.

The net present value of alternative 2.

Explanation: The net present value of alternative 2 is $61,458.2.

Explanation:

Calculate the net present value as shown below.

Particulars	Cash flow	Present value at 10%	Present value of net cash flow
Year 1	$38,000	0.9091	$34,545.8
Year 2	$38,000	0.8264	$31,403.2
Year 3	$38,000	0.7513	$28,549.4
Year 4	$38,000	0.6830	$25,954.0
Year 5	$38,000	0.6209	$23,594.2
Year 6	$38,000	0.5645	$21,451.0
Year 7	$38,000	0.5132	$19,501.6
Year 8	$46,000	0.4665	$21,459.0
Total cash flows			$206,458.2
Invested outflows	$312,000		($145,000.0)
Net present value			$61,458.2

Table – 2

Therefore, the net present value of alternative 2 is $61,458.2.

Working Notes:

(a) On deduction of yearly operating cost from yearly revenues, the yearly cash flow is obtained.

(b) The cash inflow of $46,000 is obtained by adding the salvage value of $8,000 is added in the actual cash inflow of the eighth year.

(c) The cost of old machine is not considered as the invested amount, as such cost is historical cost.

Conclusion:

Since the total cash flows are greater than the invested amount, the net present value is negative.

c.

To ascertain: The alternative to be recommended to management.

Explanation: Alternative 2 should be selected.

Explanation:

The projects or alternatives with positive NPV should be accepted, as the total cash flows are greater than the invested amount. The net present value of the alternative 1 is -$5,921.3 and that of alternative 2 is $61,458.2.

Hence, alternative 1 shows the negative net present value and alternative 2 shows positive net present value.

Conclusion:

Hence, alternative 2 should be recommended to the management.

Explanation of Solution

The net present value of alternative 1 is -$5,921.3.

Conclusion

Since the total cash flows are smaller than the invested amount, the net present value is negative.

b.

To determine

The net present value of alternative 2.

Explanation of Solution

The net present value of alternative 2 is $61,458.2.

Conclusion

Since the total cash flows are greater than the invested amount, the net present value is negative.

c.

To determine

To ascertain: The alternative to be recommended to management.

Explanation of Solution

Alternative 2 should be selected.

Conclusion

Hence, alternative 2 should be recommended to the management.