Chapter 14 - Investment

Builds on Chapter 13 - Consumption and Saving by examining the other major component of private spending. Investment is the most volatile component of GDP and the primary channel through which the real interest rate affects the economy.

Key Concepts

• Investment = purchases of new physical capital, residential housing, and inventories
• The rational rule for investors: invest if the present value of future revenues exceeds the up-front cost
• User cost of capital offers an equivalent one-year perspective: invest if next year’s revenue > $(r+d)\times C$
• Higher real interest rates → lower present values → less investment (movement along the investment line)
• Four factors shift the investment line: technological advances, expectations, corporate taxes, lending standards
• The market for loanable funds determines the long-run real interest rate

1. Macroeconomic Investment

Investment in macroeconomics means buying new capital, not trading existing financial assets.

Three types of investment:

• Business fixed investment: purchases of physical capital — machinery, equipment, buildings
• Residential investment: construction of new housing (houses are capital that produce housing services)
• Inventory investment: changes in unsold goods held by firms

Exam Alert

Investment is the most volatile component of GDP. Small changes in business confidence can cause large swings in investment spending.

Investment is forward-looking: firms invest today based on expected future revenues.

2. Tools to Analyze Investments

Compounding

Money grows over time via compound interest: $FV=PV\times (1+r{)}^n$

• $FV$ = future value
• $PV$ = present value
• $r$ = interest rate per period
• $n$ = number of periods

Compounding

$1,000 invested at 5% for 10 years: $FV=\$1,000\times (1.05{)}^{10}=\$1,629$

Present Value

Running the compounding formula backwards: how much is a future cash flow worth today? $PV=\frac{FV}{(1+r{)}^n}$

The higher the interest rate, the lower the present value of any future amount.

Net Present Value (NPV)

For a long-lived investment generating annual revenue $R$ forever (a perpetuity), with the asset depreciating at rate $d$:

$PV=\frac{\text{Next year’s revenue}}{r+d}$

The denominator $(r+d)$ reflects two costs:

• $r$: the opportunity cost of tying up capital
• $d$: the annual depreciation of the asset

Exam Alert

Rational Rule for Investors: Invest if $\frac{\text{Next year’s revenue}}{r+d}>C$ where $C$ is the up-front cost of the capital.

Wind Turbine

Cost C = \4$million.Annualrevenue=$$600{,}000$.Depreciationrate$d = 4%$.

At $r=6\%$: $PV=\frac{\$600,000}{0.06+0.04}=\$6\text{ million}>\$4\text{ million}✓\text{ Invest!}$

At $r=12\%$: $PV=\frac{\$600,000}{0.12+0.04}=\$3.75\text{ million}<\$4\text{ million}\times \text{ Don’t invest!}$

3. Making Investment Decisions: User Cost of Capital

An alternative (equivalent) framing: instead of asking “is the present value of all future revenues greater than the cost?”, ask “should I buy one more machine for one more year?”

User cost of capital: the extra cost associated with using one more machine for one more year.

$\text{User cost of capital}=(r+d)\times C$

• $r$: interest rate — the return you forgo by tying up your money
• $d$: depreciation rate — the proportion of value lost each year
• $C$: purchase price of the capital

Exam Alert

Rational Rule (user cost form): Invest if $\text{Next year’s revenue}>(r+d)\times C$ This is mathematically identical to the NPV form.

Car Ownership

You bought a car for 10,000. Real interest rate = 3%. Depreciation rate = 15%. $$\text{User cost} = (0.03 + 0.15) \times \10{,}000 = $1{,}800 \text{ per year}$$ If you didn’t own the car, you’d be $1,800 wealthier at year’s end.

Common Mistake

When calculating the true cost of owning an asset, students forget the opportunity cost of the capital tied up (the $r\cdot C$ term). Out-of-pocket costs like insurance and gas are only part of the story.

4. The Macroeconomics of Investment

Total investment in the economy = sum of all individual investments.

Investment will depend on four macro variables:

1. Expectations about future revenues
2. Real interest rate $r$
3. Depreciation rate $d$
4. Real cost of capital $C$

The Investment Line

The investment line plots the real interest rate ($y$-axis) against total investment ($x$-axis).

Real interest
    rate
      |
  A · |· · · · ·           Higher r → Low investment  (Point A)
      |          \
  B · |· · · · · ··        Lower r  → High investment (Point B)
      |             \
      |              \ Investment line
      +----+----------+-----> Total investment
         Low        High

• Higher real interest rate → lower PV of future revenues → fewer projects pass the cost-benefit test → less investment (move up-left along the line)
• A change in $r$ causes a movement along the investment line

What Shifts the Investment Line?

Four factors shift the entire line (at any given interest rate):

Exam Alert

Four Investment Shifters (these shift the line, not move along it):

1. Technological advances → capital more productive / lower depreciation → rightward shift
2. Expectations → optimism about future profits → rightward; pessimism → leftward
3. Corporate taxes → high taxes reduce after-tax profits → leftward shift; tax breaks → rightward
4. Lending standards and cash reserves → easier credit / more cash → rightward shift

Rightward shift = more investment at any given interest rate. Leftward shift = less investment at any given interest rate.

5. The Market for Loanable Funds

So far we have taken the real interest rate as given. The market for loanable funds determines the long-run real interest rate.

Market for Loanable Funds

The market for the funds used to buy, rent, or build capital. It brings together savers (suppliers) who want to lend their funds and investors (demanders) who want to borrow.

Role	Actor
Suppliers	Savers — supply funds to businesses
Demanders	Investors — demand funds to buy new capital
Marketplace	Financial sector (banks, bond market, stock markets)
Price	Real interest rate — cost to borrow $100 for one year

Long-run vs. short-run real interest rate:

• Long-run: evolves slowly over many years in response to the balance of saving and investment
• Short-run: rises and falls monthly with adjustments from the central bank (e.g., the Federal Reserve / Bank of Canada)

Connection

The market for loanable funds (Ch14) is the supply side of the Chapter 15 - The Financial Sector — banks, bond markets, and stock markets are the mechanisms through which savers and investors meet.

Definitions

Investment The purchase of new capital goods, including business fixed investment (physical capital), residential investment (new housing), and inventory investment (changes in unsold goods).

Compounding The process by which interest earns interest over time: $FV=PV\times (1+r{)}^n$.

Present Value (PV) The current worth of a future sum of money, discounted at the interest rate: $PV=FV/(1+r{)}^n$.

Net Present Value (NPV) The present value of future revenues minus the up-front cost. For a perpetuity: $PV=\text{Revenue}/(r+d)$.

User Cost of Capital The extra cost of using one more unit of capital for one more year: $(r+d)\times C$. Represents the opportunity cost ($r\cdot C$) plus the depreciation cost ($d\cdot C$).

Depreciation Rate ($d$) The proportion of an investment’s remaining productive capacity lost each year due to wear and tear or obsolescence.

Interest Rate ($r$) The rate of return you could get from investing your funds in your next best alternative (opportunity cost principle).

Investment Line A downward-sloping curve showing the negative relationship between the real interest rate and the total quantity of investment in the economy.

Market for Loanable Funds The market that brings together savers (suppliers of funds) and investors (demanders of funds), with the real interest rate as the equilibrating price.

Rational Rule for Investors Pursue an investment opportunity if $\frac{\text{Next year’s revenue}}{r+d}>C$, or equivalently, if Next year’s revenue $>(r+d)\times C$.