18. Taxes are a cost, and, therefore, changes in tax rates can affect consumer prices, project lives, and the value of existing firms. The following problem illustrates this. It also illustrates that tax changes that appear to be “good for business” do not always increase the value of existing firms. Indeed, unless new investment incentives increase consumer demand, they can work only by rendering existing equipment obsolete.

The manufacture of bucolic acid is a competitive business. Demand is steadily expanding, and new plants are constantly being opened. Expected cash flows from an investment in a new plant are as follows:

0 1 2 3 1. Initial investment 100 2. Revenues 100 100 100 3. Cash operating costs 50 50 50 4. Tax depreciation 33.33 33.33 33.33 5. Income pretax 16.67 16.67 16.67 6. Tax at 40% 6.67 6.67 6.67 7. Net income 10 10 10 8. After-tax salvage 15 9. Cash flow (7 8 4 − 1) −100 43.33 43.33 58.33 NPV at 20% 0 Assumptions:

1. Tax depreciation is straight-line over three years.

2. Pretax salvage value is 25 in year 3 and 50 if the asset is scrapped in year 2.

3. Tax on salvage value is 40% of the difference between salvage value and depreciated investment.

4. The cost of capital is 20%.

a. What is the value of a one-year-old plant? Of a two-year-old plant?

b. Suppose that the government now changes tax depreciation to allow a 100% writeoff in year 1. How does this affect the value of existing one- and two-year-old plants? Existing plants must continue using the original tax depreciation schedule.

c. Would it now make sense to scrap existing plants when they are two rather than three years old?

d. How would your answers change if the corporate income tax were abolished entirely?