 # 11. Invesment

### Contents

1. Introduction
2. Gross Investment, Net Investment, and Depreciation
3. Model 1 - Net Present Value (NPV)
4. Model 2 - Simple Accelerator Model
5. Model 3 - Neoclassical with Flexible Accelerator Model
6. Model 4 - Tobin's q
7. Complications with Empirical Analysis
8. Policy Implications

### 2. Gross Investment, Net Investment, and Depreciation

1. Can gross investment be negative? Can net investment ever be negative?

Answer: Gross investment represents total actual spending on capital goods and can be zero but it can never be negative. Net investment equals gross investment minus depreciation and represents the increase in the stock of useful capital goods. Net investment can be negative when the existing capital stock is depreciating faster than it is being replaced.

2. If an economy has reached its desired capital stock and does not want it to increase, will any investment occur?

Answer: Yes. Although net investment should equal 0, there will be investment spending to replace depreciating capital (i.e., wear and tear or because capital becomes obsolete).

### 3. Model 1 - Net Present Value (NPV)

1. The cash flows for an investment project are listed below. The firm will invest if the present value of the cash flows is positive.

 Beginning of year 1 - 200 Beginning of year 2 + 100 Beginning of year 3 + 120

a. Should the firm make this investment if the interest rate is 5%?

i = 0.05
NPV = R1 + R2/(1+i) + R3/[(1+i)(1+i)]
= - 200 + 100/1.05 + 120/(1.05)(1.05)
= 4.08 > 0
Profitable investment

b. Should the firm make this investment if the interest rate is 10%?

i = 0.10
NPV = R1 + R2/(1+i) + R3/[(1+i)(1+i)]
= - 200 + 100/1.10 + 120/(1.10)(1.10)
= - 9.92 < 0
Unprofitable investment

2. What is the relationship between the neolassical theory investment and the way individual firms make their investment decisions in practice?

Answer: The neoclassical theory of investment states that the level of desired capital stock increases with an increase in the product price relative to the costs of production (i.e., an increase in expected sales) and a decrease in the rental cost of capital. In practice, firms base their investment decisions on the discounted cash flow (net present value) analysis. If a firm expects an increase in product price, the cash flow associated with any investment project will be larger and the net present value of the investment will rise. At the same time, if the rental cost of capital decreases (e.g., a lower interest rate), then the net present discounted value of the project increases and the firm is more likely to undertake the investment. The decision making of firms using the discounted cash flow analysis is therefore consistent with the neoclassical theory of investment.

#### 4. Model 2 - Simple Accelerator Model

1. According to the simple accelerator model, the
1. level of investment is proportional to the level of GDP
2. change in investment is proportional to the change in GDP
3. change in investment spending is proportional to the level of GDP
4. level of investment spending is proportional to change in GDP
5. the change in investment spending is always greater than the change in GDP
6. the change in investment increases as the level of output increases
7. the level of investment increases as the change in output increases

Answer: D and G. The simple accelerator suggests the desired level of capital is proportional to the level of output or GDP. Since net investment represents the difference in the current level of capital and the desired level of capital, net investment is proportional to the change in the level of output (answer D). If the level of GDP remained unchanged (no economic growth) then there would be no need for new investment (other than to replace depreciated capital). The larger the expected change in output the greater the level of net investment (answer G).

#### 5. Model 3 - Neoclassical with Flexible Accelerator Model

1. If the nominal interest rate is 10 percent and the inflation rate is 6 percent, the real interest rate is
1. 16 percent
2. 10 percent
3. 6 percent
4. 4 percent
5. - 4 percent

Answer: D. the question could also have given you any combination of the two and asked you to calculate the third. A similar question could give you some combination of the rental cost of capital, the depreciation rate, and the real rate of interest.

2. Which of the following increases the rental cost of capital?
1. an increase in the rate of depreciation
2. a decrease in the rate of depreciation
3. an increase in the real interest rate
4. a decrease in the real interest rate
5. an increase in the nominal interest rate
6. a decrease in the nominal interest rate
7. an increase in the expected inflation rate
8. a decrease in the expected inflation rate

Answer: A, C, E, and H. The rental cost of capital is a positive function of both the real interest rate and depreciation. The real interest rate equals the nominal interest rate minus the expected rate of inflation. Thus a higher real interest rate (C), higher depreciation rate (A), a higher nominal interest rate (E), or lower expected inflation rate (H) would increase the rental cost of capital.

A similar version of this question would ask which of the following would reduce the desired capital stock and/or the investment rate. the answers would be the same. Variables that raise the cost of capital would lower the desired level of capital and the investment rate.

6. Model 4 - Tobin's q

1. Tobin's q theory of investment states that firms should add physical capital whenever
1. the value of q is greater than 1
2. the market value of the firm divided by the replacement cost of capital is greater than 1
3. the value of q is less than 1
4. the market value of the firm divided by the replacement cost of capital is less than 1
5. the replacement cost of capital is equal to the cost of capital
6. the value of q is lower than the market interest rate

Answer: A and B. Tobin's q is defined as the market value of the firm divided by the replacement cost of capital. Tobin's q greater than 1 implies a firm can spend \$1 in investment and the stock market value of the firm will increase by more than \$1.

### 7. Complications with Empirical Analysis

1. What contribution might credit rationing make towards output fluctuations (business cycles) in the U.S.?

Answer: If firms have a difficult time borrowing money for investment, these firms will have to finance the investment using retained earnings or on the stock market. Firms will likely invest less in a recession because earnings will be lower and less can be raised in the stock market. During economic booms, on the other hand, firms may invest more because retained earnings and stock prices are higher and they may also want to compensate for the lack of investment during the past downturn.

### 8. Policy Implications

1. Suppose that a temporary investment tax credit is enacted that will last only 1 year.

1a. What is the effect in the current year and in the following year?

Answer: Investment during the current year with the tax credit will be higher, and the second year with no tax credit lower. Investment spending is accelerated to take advantage of the tax credit. But there is a limit to how much investment can be accelerated because of increasing costs (e.g., having to pay overtime for construction).

1b. What is the effect of this temporary tax credit on investment in the long run (say after 4 or 5 years)?

Answer: A temporary investment tax credit should have a positive effect on investment only for the period to which it applies. In the long run, however, we should not expect to see a significant effect on total investment. The desired capital stock depends mainly on the firm's estimate of the price of it's product (demand) and the cost of capital and labor and a temporary investment tax credit should not affect the firm's desired long-run capital stock.

1c. How would your answers in (a) and (b) differ if the tax credit were permanent?

Answer: A permanent tax credit would not induce firms to accelerate spending. It may increase the desired level of capital stock and investment since the cost of capital is now permanently lower.

2. If a firm invests out of retained profits rather than borrowed funds, will its investment decisions still be affected by the changes in the interest rate?

Answer: Yes. In a firm's decision to make an investment, the interest rate is a key variable regardless where the funds come from. The interest rate represents the opportunity cost of using money (retained earnings or borrowed funds) to invest in new machinery rather than to make a loan to someone else.