Chapter 7, Problem 7.30P

1

To determine

Introduction: The variability between present value of all cash outflow and present value of all cash inflow is known as net present value (NPV). The discount rate at which the net present value is equal to zero is knows as Internal rate of return (IRR). The ratio of income and capital gain is known as simple rate of return.

To compute: The net annual cost saving.

Answer to Problem 7.30P

The annual net cost saving if the robot is purchased is $580,000.

Explanation of Solution

Annual saving inventory carrying costs $210,000

Saving in labor cost is 25000 direct labor hour each year the labor rate is $16 per hour

Particular	Amount
Saving in labor costs	400,000
Saving in inventory carrying cost	210,000
Total	610,000
Less: increase in power and maintenance costs	30,000
Annual net cost saving	580,000

The annual net cost saving if the robot is purchased is $580,000.

2.

To determine

Introduction: The variability between present value of all cash outflow and present value of all cash inflow is known as net present value (NPV). The discount rate at which the net present value is equal to zero is knows as Internal rate of return (IRR). The ratio of income and capital gain is known as simple rate of return.

To compute: The net present value of the proposed investment in the robot is $46,120.

Answer to Problem 7.30P

The net present value of the proposed investment in the robot is $46,120.

Explanation of Solution

Explanation:

Particular	New $	Year	Year
Cost of robot	(1600000)
Installation and software	450000
Cash released from inventory		400000
Annual net cost saving			580000
Salvage value				70000
Cash flows	(2050000)	400000	580000	70000
Discount	1	0.833	2.991	0.402
Present value of cash	(2050000)	333200	1734780	28140
Net present value	46120

The net present value of the proposed investment in the robot is $46,120.

3.

To determine

Introduction: The variability between present value of all cash outflow and present value of all cash inflow is known as net present value (NPV). The discount rate at which the net present value is equal to zero is knows as Internal rate of return (IRR). The ratio of income and capital gain is known as simple rate of return.

To compute: The actual net present value of the investment.

Answer to Problem 7.30P

The actual net present value is (148520)

Explanation of Solution

Particular	Amount $
Saving in labor cost ($22500hours\times \$16perhour$)	360000
Saving inventory carrying costs	210000
Total	570000
Less: increase in power and maintenance	30000
Annual net cost saving	540000

Calculation of NPV.

Particular	New $	Year	Year
Cost of robot	(1600000)
Installation and software	(524000)
Cash released from inventory		400000
Annual net cost saving			540000
Salvage value				70000
Cash flows	(2125000)	400000	540000	70000
Discount	1	0.833	2.991	0.402
Present value of cash	(2125000)	333200	1615140	28140
Net present value	(148520)

The actual net present value is (148520)

4

To determine

Introduction: The variability between present value of all cash outflow and present value of all cash inflow is known as net present value (NPV). The discount rate at which the net present value is equal to zero is knows as Internal rate of return (IRR). The ratio of income and capital gain is known as simple rate of return.

The benefit other than cost benefits and compute amount of annual cash inflow that would be needed from the benefit.

Answer to Problem 7.30P

The new automated machine gives intangible benefits such as speed reliability and high quality, more variety of products, reduction in inventories etc. Rate of return worth at least $49,646 per year.

Explanation of Solution

1. The new automated machine gives intangible benefits such as speed reliability and high quality, more variety of products, reduction in inventories etc.

These intangible benefits will result in saving costs from the reduced labor hours.

2. Net present value excluding intangible benefits (negative)- ($148,520)
Present value actor for annuity at 20% for 5 periods − 2.991

  $\begin{array}{l}=\frac{Negativenetpresentvaluetobeoffset}{presentvaluefactorforannuity}\\ =\frac{\$148,520}{2.991}\\ =\$49,656\end{array}$

Rate of return worth at least $49,646 per year.