Question

# A company can increase its share of the market if it invests \$40,000 annually. The increased...

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?

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

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