Question

The Federation Inc is considering a new shuttle project. The information below is provided and we have been asked to determine the NPV break-even level of unit sales for a year. Purchase price of new equipment = $482,000. Shipping and installation costs for the new equipment = $24,000. The expansion will be financed half with equity and half with debt. The interest rate on the debt = 8% with principal due in full in exactly 4 years. Variable cost per unit = $49. Sales price per unit = $90. Annual fixed operating costs excluding depreciation = $156,000. Unit sales are assumed to be the same each year. Straight-line depreciation will be taken over the 7 year life of the project. The equipment will be depreciated so that book value equals expected salvage value at the end of the project. Working capital of $130,000 is required up front and an additional $41,000 of working capital is needed at the end of year one. Tax rate = 29%. Required rate of return (RRR) = 14%. Salvage value of the new equipment in 7 years = $64,000. (Answer in units, unrounded to whole units, keeping 2 decimal places).

Answer 1

Here We have to find out the number of units which must be sold so that the net outflow in begnning will equal to the net inflows in future

Net Outflow in the beginning of the year = $4,82,000+$24,000+$1,30,000 = $636,000 it is financed half by equity and half by debt.

So by debt will be 318,000 on which yearly interest @8% = $25,440 and adjusted interest rate will be = 25440*0.71=$18062.4

Depreciation = ($482000+24000-64000)/7=$63142.86

Now in the following table you can analyse different inflows and outflows. Also we know that the yearly units are same so We can take them as 'Y'

Years	1	2	3	4	5	6	7
Sales	90Y	90Y	90Y	90Y	90Y	90Y	90Y
Less: Variable Cost	49Y	49Y	49Y	49Y	49Y	49Y	49Y
Contribution	41Y	41Y	41Y	41Y	41Y	41Y	41Y
less- Fixed operating Cost	156000	156000	156000	156000	156000	156000	156000
Profit before tax and depreciation ( cash flow)	41Y-156000	41Y-156000	41Y-156000	41Y-156000	41Y-156000	41Y-156000	41Y-156000
cash flow after tax but before depreciation	(41Y-156000)X0.71	(41Y-156000)X0.71	(41Y-156000)X0.71	(41Y-156000)X0.71	(41Y-156000)X0.71	(41Y-156000)X0.71	(41Y-156000)X0.71
add: tax on depreciation	63142.86X0.29 =18311.43	63142.86X0.29 =18311.43	63142.86X0.29 =18311.43	63142.86X0.29 =18311.43	63142.86X0.29 =18311.43	63142.86X0.29 =18311.43	63142.86X0.29 =18311.43
Net cash flow (solving above two rows)	29.11Y-92448.57	29.11Y-92448.57	29.11Y-92448.57	29.11Y-92448.57	29.11Y-92448.57	29.11Y-92448.57	29.11Y-92448.57
Less: interest adjusted by taxation	18062.4	18062.4	18062.4	18062.4
less: debt payment				$318,000
less additional working capital change	41000
add slavage value							64000
add working capital release							171000
Net total Cash flow	29.11Y-151510.97	29.11Y-110510.97	29.11Y-110510.97	29.11Y-428510.97	29.11Y-92448.57	29.11Y-92448.57	29.11Y+142551.43
PVF@14%	0.8772	0.7695	0.6750	0.5921	0.5194	0.4556	0.3996
PV of Cash flows	25.54Y-132905.42	22.4Y-85038.19	19.65Y-74594.90	17.24Y-253721.35	15.12Y-48017.79	13.26Y-42119.57	11.63Y+56963.55
Total of Future inflows							124.84Y-579433.67

s

Now for Break even we have to equate the inflows and outflows

124.84Y-579433.67 = 636000

Y = 9735.93 units (approx.) or 9736 units