Question

Your firm is interested in selling a new type of headphone. The machinery to build these headphones costs $300,000 (at year 0) and will be used for 10 years. At the end of these 10 years, the machine is worth nothing. The price of these headphones is $175 and the cost to produce each pair is $45. There are annual (years 1 through 10) fixed costs of $320,000 to produce the headphones. You will depreciate the machine using straightline depreciation. The appropriate discount rate is 13% and your firm's marginal tax rate is 35%. Use GOALSEEK to find the minimum number of headphones you need to sell each year in order to breakeven (i.e. have an NPV of zero).

Hint: You are going to have to find the annual free cash flow (FCF) produced by this project each year.

Answer 1

Time line		0	1	2	3	4	5	6	7	8	9	10
Cost of new machine		-300000
=Initial Investment outlay		-300000
Unit sales			2991.560553	2991.5606	2991.5606	2991.5606	2991.5606	2991.5606	2991.560553	2991.5606	2991.561	2991.561
Profits	=no. of units sold * (sales price - variable cost)		388902.8719	388902.87	388902.87	388902.87	388902.87	388902.87	388902.8719	388902.87	388902.9	388902.9
Fixed cost			-320000	-320000	-320000	-320000	-320000	-320000	-320000	-320000	-320000	-320000
-Depreciation	Cost of equipment/no. of years		-30000	-30000	-30000	-30000	-30000	-30000	-30000	-30000	-30000	-30000
=Pretax cash flows			38902.87192	38902.872	38902.872	38902.872	38902.872	38902.872	38902.87192	38902.872	38902.87	38902.87
-taxes	=(Pretax cash flows)*(1-tax)		25286.86675	25286.867	25286.867	25286.867	25286.867	25286.867	25286.86675	25286.867	25286.87	25286.87
+Depreciation			30000	30000	30000	30000	30000	30000	30000	30000	30000	30000
=after tax operating cash flow			55286.86675	55286.867	55286.867	55286.867	55286.867	55286.867	55286.86675	55286.867	55286.87	55286.87
+Tax shield on salvage book value	=Salvage value * tax rate											0
=Terminal year after tax cash flows												0
Total Cash flow for the period		-300000	55286.86675	55286.867	55286.867	55286.867	55286.867	55286.867	55286.86675	55286.867	55286.87	55286.87
Discount factor=	(1+discount rate)^corresponding period	1	1.13	1.2769	1.442897	1.6304736	1.8424352	2.0819518	2.35260548	2.6584442	3.004042	3.394567
Discounted CF=	Cashflow/discount factor	-300000	48926.43075	43297.726	38316.572	33908.471	30007.496	26555.306	23500.27117	20796.7	18404.16	16286.87
NPV=	Sum of discounted CF=	5.45697E-10