Question

: The Sisyphean Corporation is considering investing in a new cane manufacturing machine that has an estimated life of three years. The cost of the machine is $30,000 and the machine will be depreciated straight line over its three-year life to a residual value of $0.

The cane manufacturing machine will result in sales of 2400 canes in year 1. Sales are estimated to grow by 9% each year through year 3. The price per cane that Sisyphean will charge its customers is $15 each and is to remain constant. The canes have a cost per unit to manufacture of $8 each.

Installation of the machine and the resulting increase in manufacturing capacity will require an increase in various net working capital accounts. It is estimated that the Sisyphean Corporation needs to hold 3% of its annual sales in cash, 5% of its annual sales in accounts receivable, 9% of its annual sales in inventory, and 6% of its annual sales in accounts payable. The firm is in the 35% tax bracket and has a cost of capital of 8%.

Requirement:

1-How much the Incremental Free Cash Flow?

2- How much the net present value of this project?

Answer 1

1 - calculation of Incremental Free Cash Flow is in the below table.

2 - net present value = sum of present value of Incremental Free Cash Flow - cost of the machine or initial investment

sum of present value of Incremental Free Cash Flow = Incremental Free Cash Flow year 1/(1+cost of capital) + Incremental Free Cash Flow year 2/(1+cost of capital)2 + Incremental Free Cash Flow year 3/(1+cost of capital)3

Increase in cash, accounts receivable and inventory is a cash outflow because this much money will be tied up in the business. increase in accounts payable is a cash inflow because this much money of suppliers we can use. at end of project's life increase in working capital will be recovered.

the net present value of this project is $9,296.69.

	Years	0	1	2	3	Total
	Cost of machine	-$30,000	0	0	0	-$30,000
	Sales quantity	0	2400	2616	2851
	Sales price/unit	0	$15.00	$15.00	$15.00
	Production cost/unit	0	$8.00	$8.00	$8.00
	Sales	$0	$36,000	$39,240	$42,772	$118,012
Less:	Production cost	$0	$19,200	$20,928	$22,812	$62,940
Less:	Depreciation	$0	$10,000	$10,000	$10,000	$30,000
	Pre-tax cash flow	$0	$6,800	$8,312	$9,960	$25,072
Less:	Taxes @35%	$0	$2,380	$2,909	$3,486	$8,775
	After-tax cash flow	$0	$4,420	$5,403	$6,474	$16,297
Add back:	Depreciation	$0	$10,000	$10,000	$10,000	$30,000
Less:	increase in cash	$0	$1,080	$1,177	$1,283	$3,540
Less:	increase in accounts receivable	$0	$1,800	$1,962	$2,139	$5,901
Less:	increase in inventory	$0	$960	$1,046	$1,141	$3,147
Add:	increase in accounts payable	$0	$2,160	$2,354	$2,566	$7,081
Add:	Recovery of working capital	$0	$0	$0	$5,507	$5,507
	Incremental free cash flow	-$30,000	$12,740	$13,572	$19,985	$16,297
	net present value	$9,296.69

Calculation