7. Last year (2013) if a firm, Hobbit Inc., sold adventure vacation packages and

Question

7. Last year (2013) if a firm, Hobbit Inc., sold adventure vacation packages and faces a corporate tax rate of 38%, there is an investment tax credit of 10%, the depreciation rate is 6%, and dividend yield is 5%. The official depreciation schedule is such that the PDV of depreciation allowances is 20% of the purchase price of a satellite that tracks Hobbit Inc's clients. The marginal product of a satellite is 50-0.2D where D is the number of dollars spent on the machine. a. What will be the optimal “D”? In other words, how much money should be spent on this new satellite? (4 points) b. How would the optimal amount of “D” change if the corporate tax rate fell to 10%? (4 points)

Explanation / Answer

corporate tax rate = 38%

Investment tax credit(ITC) = 10%

Depreciation rate = 6%

Dividend yields = 5%

PDV of depreciation allowances = 20%

In the absence of taxation, Marginal Cost = depreciation rate + dividend yield =6% + 5% = 11%.

The corporate tax rate of 38% does not directly change the cost of the investment, but the ITC and the PDV of depreciation do.

Depreciation generates a deduction from taxes, and thus lowers the cost of investment by the corporate tax rate × the PDV of depreciation that is 38% × 20% = 7.6%;

Thus, ITC lowers the cost by another 10%.

The final calculation for marginal cost is (depreciation + dividend yield)(1 – [corporate tax rate xPDV of depreciation] – ITC)

= (11%)(1 – 0.076 – 0.10) = 11*0.824% = 9.064%

(a) For the optimal D set marginal product of 50 - 0.2D = marginal cost of 9.064%

> 50 – 0.2D =0.09064

0.2D = 49.91 that gives D = 249.55

(b) If corporate tax rate fell to 10% then

Marginal cost is (depreciation + dividend yield)(1 – [corporate tax rate xPDV of depreciation] – ITC)

MC = (11%)(1-0.1*0.2 - 0.1) = 11*0.88 = 9.68%

Solve for Optimal D, 50 - 0.2D = 0.0968

0.2D = 49.9032 that gives D = 249.51

The decrese in corporate tax rate decreses value of D.

Related Questions

Navigate

• Browse (All)
• Browse 7
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.