Question

Book & Accounting Bookstore has used an old coding machine for 3 years and to buy a new coding machine to help control book inventories. The price of new machine is $35,000 and it requires working capital of $4,000. Its estimated useful life is 5 years and estimated salvage value for the calculation of depreciation is $5,000. The disposal value of the new machine will be $6,000 at the end of its useful life. Recovery of working capital will be $4.000 at the end of its useful life. Annual cash op incomes of the new machine will be $20,000. The disposal value of the old machine at the time of replacement is $6,500. The old machine requires working capital of $6,000 and is expected to have zero disposal value at the end of the five-year life. Annual cash operating incomes of the old machine are $10,000. The company has a required rate of return of 14%. The income tax rate is 30%. New $35,000 Purchase Price Current disposal value Useful Life Disposal value at the end Estimated Salvage value Annual Depreciation Working capital Before-tax operating income Old $40,000 $6,500 5 years $ 0 $ 0 $ 8,000 $ 6,000 $10,000 5 years $ 6,000 $5,000 $ 6,000 $ 4,000 $20,000 Income tax rate = 30% Required Rate of Return = 14% Present value factor of $1 for 5 periods at 14% =0.519 Present value factor of annuity for 5 periods at 14% = 3.433 Required: compute the net present value considering the tax effects of cash flows whether the company should buy a new coding machine or your works.) tax effects of cash flows and determine

Answer 1

Solution:

Calculation of after-tax cash flows and NPV of the old machine

year	0	1	2	3	4	5
Before-tax Operating Income		$        10,000.00	$             10,000.00	$              10,000.00	$             10,000.00	$             10,000.00
Less: taxes @ 30%		$          3,000.00	$               3,000.00	$                3,000.00	$               3,000.00	$               3,000.00
After tax operating Income		$          7,000.00	$               7,000.00	$                7,000.00	$               7,000.00	$               7,000.00
Add: Depreciation		$          8,000.00	$               8,000.00	$                8,000.00	$               8,000.00	$               8,000.00
After tax annual cash flows		$        15,000.00	$             15,000.00	$              15,000.00	$             15,000.00	$             15,000.00
Purchase price	$          (40,000.00)
Working capital requirement	$             (6,000.00)					$               6,000.00
Net Cash Flows	$          (46,000.00)	$        15,000.00	$             15,000.00	$              15,000.00	$             15,000.00	$             21,000.00
Present Value Factor at 14%	1.0000	0.8772	0.7695	0.6750	0.5921	0.5194
present Value of Cash Flows	$          (46,000.00)	$        13,157.89	$             11,542.01	$              10,124.57	$               8,881.20	$             10,906.74
NPV	$               8,612.43

The NPV of the old machine is $ 8,612.43

Calculation of after-tax cash flows and NPV of the new machine:

Year	0	1	2	3	4	5
Before-tax Operating Income		$        20,000.00	$             20,000.00	$              20,000.00	$             20,000.00	$             20,000.00
Less: taxes @ 30%		$          6,000.00	$               6,000.00	$                6,000.00	$               6,000.00	$               6,000.00
After tax operating Income		$        14,000.00	$             14,000.00	$              14,000.00	$             14,000.00	$             14,000.00
Depreciation		$          6,000.00	$               6,000.00	$                6,000.00	$               6,000.00	$               6,000.00
After tax annual cash flows		$        20,000.00	$             20,000.00	$              20,000.00	$             20,000.00	$             20,000.00
Purchase price	$          (35,000.00)
Working capital requirement	$             (4,000.00)					$               4,000.00
Disposal value of new machine						$               6,000.00
Replacement value of the old machine	$               6,500.00
Net Cash Flows	$          (32,500.00)	$        20,000.00	$             20,000.00	$              20,000.00	$             20,000.00	$             30,000.00
Present Value Factor at 14%	1.0000	0.8772	0.7695	0.6750	0.5921	0.5194
present Value of Cash Flows	$          (32,500.00)	$        17,543.86	$             15,389.35	$              13,499.43	$             11,841.61	$             15,581.06
NPV	$             41,355.31

The NPV of the new machine is $ 841,355.31

Since the NPV of the new machine is higher than the NPV of the old machine, it is better to buy the new machine.