# Finance

Hello. This is kind of long, but I would truly appreciate it if someone could help me validate my solutions for the three questions listed below. Thank you in advance.

A firm is considering acquiring a new segment to add to its product line. The estimated sales growth rate is 6.75% and the firm forecasts to sell 3000 units of its new product, which is priced at 37.50 per unit. COGS is estimated at 48% of current years sales.

The expansion will need an investment of \$90,000 in new equipment, which will be depreciated at \$25,000/year over three years. Net working capital is estimated to be 20% of sales per year.

The firm also builds up initial inventory of 10% of the first year’s anticipated COGS before beginning the project. The firm’s tax rate is 30% and the firm’s WACC is 10.5%. The equipment will be sold at the end of three years for \$10,000.

Questions

1. What are project free cash flows per year?
2. What is the terminal value?
3. What is the NPV and IRR for this project? Should you accept it?

My Calculations

Sales (3000 unites at 37.50 per unit) = \$112,500

COGS (112,500 x 0.48) = \$54,000

\$58,500

Depreciation (25,000 / 3) = \$8,333

EBIT = \$50,167

Taxes (30%) = \$15,050.10

NOPAT (Net Income) = \$35,116.90

Change in NWC = 0.20 x 112,500 = \$22,500

CAPEX = \$90,000

Operating Cash Flow = EBIT + Depreciation - Taxes

= 50,167 + 8333 - 15,050.10

= \$43,449.90

Sale Price - Taxes = 112,500 - 15,050.10 = \$97,449.90

FCF in terminal year = 35,116.90 + 8333 - 22,500 - 90,000 = -\$69,050

FCF in terminal year x (1 + Gss) = -69,050 x (1 + 0.0675) = -\$73,710.88

TV in steady state = -73,710.88 / (0.105 - 0.0675) = \$1,965,623.47

\$1,965,623.47+ (-69,050) =\$1,896,573.47

NPV = Enterprise Value = \$1,286,628.72

Accept project

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1. You seem to have deducted machine depreciation as 25000/3 instead of 25000/year.
Also, you have provided the first year cash flow without taking into account of the WACC.

I suggest you make a cash-flow diagram for three years, using following information (if you agree with it, if not, make modifications) as follows:

Positive cash-flows:
===================
Sales (increases by 6.5% annually)
Y(0)=0
Y(1)=112500
Y(2)=119812.50
Y(3)=127600.31
Salvage of equipment
Y(3)=10000
Recovery of 10% COGS
Y(3)=6124.82 (10% of COGS for year 3)
Recover of NWC
Y(3)=25520.06 (20% of sales)

Negative cash-flows (negative signs omitted)
===================
Inventory
Y(0)=5400 (10% COGS)
Y(1)=731.25 (additional due to increase in sales)
Y(2)=778.78 (additional amount due to increase in sales)
NWC
Y(0)=22500 (20% of expected sales)
Taxes
Y(0)=0
Y(1)=8700 (30% of Sales-COGS less machine depreciation of 25000)
Y(2)=9753
Y(3)=10874.45

Net Cash-flow / NPV
===================
Y(0)=-117900 / -117900
Y(1)=49068.75 / 44406.11
Y(2)=51770.72 / 42399.39
Y(3)=97122.59 / 62526.33

So NPV=31431.82
IRR=(31431.82/117900)^(1/3)=0.082 or 8.2%

So if IRR of 8.2% is acceptable for the entreprise, then go ahead.

I am not sure how to proceed with terminal value, because machines may cost more after three years, and sales may or may not remain at a growth of 6.5%, WACC may change....etc.

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2. Oh yes, please add machine cost Y(0)=90000 to negative cash-flows. All other calculations remain valid.

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