# Suppose that new machines cost

Suppose that new machines cost \$504. The marginal benefit fromnew machines is: MB = 246 – 6K, where K is the number of machinespurchased. The depreciation rate is 12%, the dividend yield is 6%,and the corporate tax rate is 35%. What would be the marginal costof each dollar of machinery investment in the followingsituations?

a. Firms are allowed to expense the machine, and there is no taxcredit

b. Firms are allowed to depreciate the machine over 5 years anduse the dividend yield (6%) to discount depreciation allowances.Firms are also allowed an 8% investment tax credit (i.e. 8% of theamount invested).

Given information :

>Suppose the new machinery cost \$504

> Marginal benefit of new machine = 246 – 6 K

> k is the number of machine purchase

> depreciation rate = 12%

> dividend yield = 6%

> corporate tax = 35%

To provide the marginal cost of each dollar in the followingsituation

a) Firm allowed expenses with no tax credit

To find the optimal investment

Marginal Benefit = Marginal cost

in the given case the marginal cost of investment is sum ofdepreciation and dividends

ie., 0.12+0.6 = 0.18

setting that marginal cost equal to marginal benefit of 246-6Kand for solving for K yields

ie.,0.18=246-6K

> 6K=246-0.18

> K = (246-0.18)/6

>K =40.97 units of machines purchased

when firm can expense( take full depreciation immediately) thecost of investment is reduced by 35% of tax ie., 35 cents per eachdollar spent

Therefore., The marginal cost of the investment = (246-(6*40.97))(1-0.35)

= (246-245.82)(0.65)

= 0.117 per dollar

b) Investment tax credit of 8%

An investment tax credit reduces the cost of investment evenfurther. if the investment tax credit were included in the taxsystem described in question a, the net cost of the firm wouldbe

(Depreciation + Dividend)(1-0.35- the ITC)

=(0.12+0.06)(0.65-0.08)

=(0.18)(0.57)

=0.1026 per dollar

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