Question

The Greentree Lumber Company is attempting to evaluate the profitability of adding another cutting line to its present sawmill operations. They would need to purchase two more acres of land for ​$25,000 ​(total). The equipment would cost ​$125,000 and could be depreciated over a​ five-year recovery period with the MACRS method. Gross revenue is expected to be ​$47,000 per year for five​ years, and operating expenses will be ​$18,000 annually for five years. It is expected that this cutting line will be closed down after five years. The​ firm's effective income tax rate is 46​%. If the​ company's after-tax MARR is 5​% per​ year, is this a profitable​ investment? Assume that land recovered at original cost of ​$25,000 at the end of five years. The market value of equipment is negligible at the end of year 5.

ܝ ܝ GDS Recovery Rates (rk) Year 5-year Property Class 0.2000 0.3200 0.1920 0.1152 0.1152 0.0576 ܚ ܠ ܗ ܗ

For i = 5%,

a) Calculate the PW value for this investment.
PW(5%) = [ ]

b) Based on the PW​ value, the company [should] or [should not] add another cutting line to its present sawmill operations. (Pick one)

Answer 1

Working notes:

(a) Annual net benefit (NAB) = Revenue - Operating Cost = 47,000 - 18,000 = 29,000

• NAB in year 5 = 29,000 + 25,000 land recovery = 54,000

(b) First cost = 25,000 + 125,000 = 150,000

(c) MACRS depreciation schedule as follows.

Year	Cost ($)	Depreciation Rate	Depreciation ($)
1	1,25,000	0.2	25,000
2	1,25,000	0.32	40,000
3	1,25,000	0.192	24,000
4	1,25,000	0.1152	14,400
5	1,25,000	0.1152	14,400

(d) Taxable income (TI) ($) = Annual NAB - Depreciation

(e) After-tax income = TI x (1 - Tax rate) = TI x (1 - 0.46) = TI x 0.54

(f) After-tax cash flow (ATCF) = After-tax income + Depreciation

(1) Present worth (PW) of ATCF is computed as follows.

Year	NAB ($)	First Cost ($)	Depreciation ($)	TI ($)	After-tax Income ($)	ATCF ($)	PV Factor @5%	Discounted ATCF ($)
0		1,50,000				-1,50,000	1.0000	-1,50,000
1	29,000	0	25,000	4,000	2,160	27,160	0.9524	25,867
2	29,000	0	40,000	-11,000	-5,940	34,060	0.9070	30,893
3	29,000	0	24,000	5,000	2,700	26,700	0.8638	23,064
4	29,000	0	14,400	14,600	7,884	22,284	0.8227	18,333
5	54,000	0	14,400	39,600	21,384	35,784	0.7835	28,038
							PW ($) =	-23,805

(2) Company should not add another line since PW is negative.