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. It will be depreciated 20% in year 1, 32% in year 2, and 19% in year 3. The machine will be sold for $15,000 in year 3.
The machine will result in sales of 2000 canes in year 1. Unit sales are estimated to grow by 10% per year through year three. Each cane costs $9 to produce and will be sold for $18.
Sisyphean will need to hold 2% of its annual sales in cash, 4% of its annual sales in accounts receivable, 9% of its annual sales in inventory, and 6% of its annual sales in accounts payable. Net working capital will return to its initial level of zero in year 4. The firm is in the 32% tax bracket, and has a cost of capital of 9%.
Compute the NPV and IRR.

Please show all work for each step.

Answer 1

1.

	t =0	t =1	t =2	t =3	t =4
Revenue		36000	39600	43560
COGS		18000	19800	21780
Depreciation		6000	9600	5700
EBIT		12000	10200	16080
Tax		3840	3264	5145.6
EBIT (1-t)		8160	6936	10934.4
CAPEX	-30000
Depreciation		6000	9600	5700
Change in NWC		3240	324	356.4	-3920.4
Net Salvage value after tax				12984
FCF	-30000	10920	16212	29262	3920.4
PVF (9%)	1	0.917431	0.84168	0.772183	0.708425
PVCF	-30000	10018.35	13645.32	22595.63	2777.31
NPV	19036.61

W.N

Year	1	2	3
Units	2000	2200	2420
Sales (Units * $18)	36000	39600	43560
Cash (2% of Sales)	720	792	871.2
Accounts Receivable (4% of sales)	1440	1584	1742.4
Inventory (9% of sales)	3240	3564	3920.4
Accounts Payable (6% of sales)	2160	2376	2613.6
NWC (Cash + Inventory +AR - AP)	3240	3564	3920.4

Sale Proceeds (1)	15000
Book Value	8700
Profit	6300
Tax (2)	2016
Net Salvage value after tax (1-2)	12984

2. IRR = Where NPV is Equal to zero

	t = 0	t = 1	t = 2	t = 3	t = 4	NPV
FCF	-30000	10920	16212	29262	3920.4
PVF (35%)	1	0.740741	0.548697	0.406442	0.301068
PVCF	-30000	8088.889	8895.473	11893.31	1180.308	57.97897
FCF	-30000	10920	16212	29262	3920.4
PVF (36%)	1	0.735294	0.540657	0.397542	0.29231
PVCF	-30000	8029.412	8765.138	11632.88	1145.974	-426.595

IRR = 35 % + ( 57.97897 - 0) / [57.97897 - (-426.595)]

= 35.12 %