Question

Arnold Inc. is considering a proposal to manufacture​ high-end protein bars used as food supplements by body builders. The project requires use of an existing​ warehouse, which the firm acquired three years ago for $ 4 million and which it currently rents out for $ 111 comma 000 . Rental rates are not expected to change going forward. In addition to using the​ warehouse, the project requires an upfront investment into machines and other equipment of $ 1.6 million. This investment can be fully depreciated​ straight-line over the next 10 years for tax purposes. ​ However, Arnold Inc. expects to terminate the project at the end of eight years and to sell the machines and equipment for $ 422 comma 000 . ​ Finally, the project requires an initial investment into net working capital equal to 10 percent of predicted​ first-year sales. ​ Subsequently, net working capital is 10 percent of the predicted sales over the following year. Sales of protein bars are expected to be $ 4.8 million in the first year and to stay constant for eight years. Total manufacturing costs and operating expenses​ (excluding depreciation) are 80 percent of​ sales, and profits are taxed at 30 percent.

a. What are the free cash flows of the​ project?

b. If the cost of capital is 15 %, what is the NPV of the​ project?

Answer 1

a). Assumptions:

(1) The warehouse can be rented out again for $111,000 after 8 years.

(2) The NWC is fully recovered at book value after 8 years.

FCF = EBIT (1 – t) + Depreciation – CAPX – Change in NWC

FCF in year 0: – 1.6m CAPX – 0.48m Change in NWC = –2.08m

FCF in years 1 - 7:

Sales	$4.8m
Less: COGS(80%)	-$3.84m
= Gross Profit	$0.96m
Less: Lost rent	-$0.111m
Less: Depreciation	-$0.16m
= EBIT	$0.689m
Less: Tax (30%)	-$0.2067m
= EBIT x (1 - t)	$0.4823m
Add: Depreciation	+$0.16m
= FCF	$0.6423m

Note that there is no more CAPX nor investment into NWC in years 1 – 7.

FCF in year 8: $0.6423m + [$0.422m – 0.30 x ($0.422m – $0.32m)] + $0.48m = $1.5137m

Note that the book value of the machinery is still $0.32m when sold, and only the difference between the sale price ($0.422m) and the book value is taxed. The NWC ($0.48m) is recovered at book value and hence its sale is not taxed at all.

b). NPV = -$2.08m + [an annuity of $0.6423m for 7 years] + [$1.5137m /1.15⁸]

= -$2.08m + [($0.6423m / 0.15) x {1 - 1.15^-7}] + [$1.5137m / 3.0590]

= -$2.08m + [$4.282m x 0.6241] + $0.4948m

= -$2.08m + $2.6722 + $0.4948m = $1,087,068.81