Question

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

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

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

Answer 1

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 following situation

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 of depreciation and dividends

ie., 0.12+0.6 = 0.18

setting that marginal cost equal to marginal benefit of 246-6K and 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) the cost of investment is reduced by 35% of tax ie., 35 cents per each dollar 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 even further. if the investment tax credit were included in the tax system described in question a, the net cost of the firm would be

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

=(0.12+0.06)(0.65-0.08)

=(0.18)(0.57)

=0.1026 per dollar