Question

A company can increase its share of the market if it invests $40,000 annually. The increased income would be $30,000 annually, but increased expenses would be $23,000. The equipment salvage at the end of 12 years would be $6000. The income tax rate is 52% and double declining balance depreciation is used. The company's minimum attractive rate of return is 6%. What is the present worth of the investment?

Answer 1

Working notes:

(a)

Straight-line (SL) depreciation rate = 1 / Useful life = 1/12

DD depreciation rate = 2 x SL rate = 2/12 = 1/6 = 0.1667

DDB depreciation schedule as follows. This method ignores salvage value.

Year	Book value at year-start ($)	Depreciation Rate	Annual Depreciation ($)	Book value at year-end ($)
1	40,000	0.1667	6,667	33,333
2	33,333	0.1667	5,556	27,778
3	27,778	0.1667	4,630	23,148
4	23,148	0.1667	3,858	19,290
5	19,290	0.1667	3,215	16,075
6	16,075	0.1667	2,679	13,396
7	13,396	0.1667	2,233	11,163
8	11,163	0.1667	1,861	9,303
9	9,303	0.1667	1,550	7,752
10	7,752	0.1667	1,292	6,460
11	6,460	0.1667	1,077	5,384
12	5,384	0.1667	897	4,486

(b)

Taxable income (TI), years 1-11 = Annual income - Annual expense - Depreciation

= (30,000 - 23,000) - Depreciation

= 7,000 - Depreciation

(c)

TI, year 12 = 7,000 - Depreciation + 6,000 salvage value

= 13,000 - Depreciation

(d)

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

= TI x (1 - 0.52)

= TI x 0.48

(e)

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

(f)

PV Factor in year N = (1.06)-N.

Present worth (PW) of ATCF is as follows.

Year	Net Savings ($)	Depreciation ($)	TI ($)	After-tax Income ($)	ATCF ($)	PV Factor @6%	Discounted ATCF ($)
0					-40,000	1.0000	-40,000
1	7,000	6,667	333	160	6,827	0.9434	6,440.25
2	7,000	5,556	1,444	693	6,249	0.8900	5,561.49
3	7,000	4,630	2,370	1,138	5,767	0.8396	4,842.43
4	7,000	3,858	3,142	1,508	5,366	0.7921	4,250.51
5	7,000	3,215	3,785	1,817	5,032	0.7473	3,760.06
6	7,000	2,679	4,321	2,074	4,753	0.7050	3,350.80
7	7,000	2,233	4,767	2,288	4,521	0.6651	3,006.71
8	7,000	1,861	5,139	2,467	4,327	0.6274	2,715.12
9	7,000	1,550	5,450	2,616	4,166	0.5919	2,465.99
10	7,000	1,292	5,708	2,740	4,032	0.5584	2,251.37
11	7,000	1,077	5,923	2,843	3,920	0.5268	2,064.95
12	13,000	897	12,103	5,809	6,707	0.4970	3,332.96
						PW of ATCF ($) =	4,042.64