Intermediatemicroeconomics
Capital Markets: Interest, Investment, and Present Value
Overview
Capital markets channel savings into investment — the factories, machines, software, and infrastructure that raise future output. The interest rate is the price that balances savers' willingness to wait against investors' demand for funds. This lesson covers the time value of money and present-value calculations firms use to judge projects, the loanable-funds model of interest-rate determination, the user cost of capital, and the roles of risk, inflation, and financial intermediaries.
Learning objectives
- Compute present value and explain discounting and the time value of money
- Use net present value to evaluate an investment project
- Explain interest-rate determination in the loanable-funds model
- Define the user cost of capital and the firm's investment rule
- Distinguish real from nominal interest rates and describe the role of risk
Time value of money and present value
A dollar today is worth more than a dollar next year because today's dollar can be invested to earn interest. Present value (PV) converts future payments into today's dollars: PV = FV / (1 + r)^t, where r is the discount (interest) rate and t the years ahead. At a 5 percent rate, 95.24 today.
Discounting is the foundation of all investment analysis. Firms, governments, and individuals constantly compare money across time — a college degree's future earnings, a machine's future output, a bond's coupon stream. The higher the discount rate, the less the future matters: distant payoffs shrink toward zero in present value, which is why long-run projects like climate mitigation are so sensitive to the chosen rate.
Net present value: the investment rule
A firm evaluating a project computes its net present value (NPV): the present value of all expected future cash flows minus the upfront cost. The rule is simple — invest if NPV > 0, reject if NPV < 0. A positive NPV means the project earns more than the opportunity cost of capital; a negative one destroys value even if accounting profits look positive.
The internal rate of return (IRR) — the discount rate that makes NPV zero — is a popular alternative: invest if IRR exceeds the cost of capital. But NPV is the sounder criterion when projects differ in scale or timing, because IRR can misrank mutually exclusive projects. Both tools force the same discipline: every investment must beat the return available elsewhere at comparable risk.
Loanable funds: how interest rates are determined
The loanable-funds model treats the interest rate as the price equilibrating the supply of savings with the demand for investment funds. Savers (households, and governments running surpluses) supply funds: higher rates reward waiting, so supply slopes upward. Investors (firms, homebuyers, governments in deficit) demand funds: higher rates raise borrowing costs, so demand slopes downward.
Equilibrium allocates society's savings to their highest-valued uses. A surge in investment opportunities — a tech boom — shifts demand right and raises rates; a rise in thrift — aging populations saving for retirement — shifts supply right and lowers them. Government deficits absorb savings and push rates up (crowding out private investment), while central-bank policy shifts the supply of funds in the short run.
The user cost of capital and firm investment
A firm's investment decision balances the expected marginal return on new capital against its user cost — the effective rental price of owning capital for a period. The user cost has three parts: the interest cost of funds tied up (r), depreciation (δ, the wear and obsolescence rate), minus any expected capital gain if the asset appreciates. Roughly: user cost = (r + δ − expected appreciation) × asset price.
The firm invests until the expected marginal product of capital equals its user cost. This rule explains investment's sensitivity to interest rates (higher r raises user cost and chokes off marginal projects), to tax policy (investment tax credits and accelerated depreciation lower the effective cost), and to expectations (optimism about future demand raises expected returns). Because capital is long-lived and partially irreversible, uncertainty also matters — firms often wait for clearer signals before committing, the 'option value of waiting.'
Real vs. nominal rates, risk, and financial intermediation
The nominal interest rate is the dollar return; the real rate subtracts inflation and measures the true growth in purchasing power (approximately: real ≈ nominal − inflation). Savers and investors care about real rates: a 6 percent nominal return with 5 percent inflation is barely positive in real terms. Unexpected inflation transfers wealth from lenders to borrowers, which is why credible low inflation anchors capital markets.
Risk commands a premium: corporate bonds pay more than Treasuries, and equities must offer higher expected returns than bonds to compensate for volatility. Financial intermediaries — banks, bond markets, stock markets, venture capital — bridge savers and investors, pooling risk, producing information, and transforming short-term deposits into long-term loans. Their efficiency determines how cheaply an economy converts savings into productive capital.
The Fisher equation links nominal rate i, real rate r, and expected inflation πᵉ: (1+i) = (1+r)(1+πᵉ), approximately i ≈ r + πᵉ. Central banks watch real rates because those drive saving and investment decisions.
Key points
- Present value discounts future payments: PV = FV / (1+r)^t
- Invest when net present value is positive (NPV > 0)
- Interest rates equilibrate the supply of savings with investment demand (loanable funds)
- Firms invest until expected marginal return equals the user cost of capital
- Real interest rates (nominal minus inflation) drive saving and investment choices
- Risk premia and financial intermediaries shape how savings become investment
Common misconceptions
✓ Truth: Accounting profit ignores the time value of money and the opportunity cost of capital. A project can show accounting profits yet have negative NPV — destroying value relative to investing the funds elsewhere.
✓ Truth: Investment also needs profitable opportunities and confidence. In deep recessions, even near-zero rates may not spur investment if expected returns are bleak — the 'pushing on a string' problem.
✓ Truth: Central banks influence short-term rates, but the underlying real rate reflects the balance of desired saving and investment across the whole economy. Governments cannot repeal that balance indefinitely.
Practice questions
Q1. At a 10% discount rate, the present value of $121 received in two years is:
- $100
- $110
- $121
- $99
PV = 121 / (1.10)² = 121 / 1.21 = $100. Discounting reverses compounding: the future sum is divided by the accumulation factor.
Q2. A firm should undertake a project when its net present value is:
- positive
- zero regardless of risk
- negative but small
- equal to accounting profit
NPV > 0 means the project's discounted cash flows exceed its cost including the opportunity cost of capital — it creates value. Negative NPV projects destroy value even with positive accounting profits.
Q3. In the loanable-funds model, a large government budget deficit tends to:
- lower interest rates
- raise interest rates by absorbing savings
- leave rates unchanged
- eliminate private saving
Deficit borrowing adds to the demand for loanable funds, shifting demand right. At the new equilibrium the interest rate is higher, which crowds out some private investment.
Q4. The user cost of capital rises when:
- the interest rate falls
- depreciation rates increase
- the asset is expected to appreciate rapidly
- investment tax credits expand
User cost ≈ (r + δ − expected appreciation) × price, adjusted for taxes. Higher depreciation (δ) raises the cost of holding capital, while lower rates, expected appreciation, and tax credits lower it.
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Frequently asked questions
What is the difference between NPV and IRR?
NPV discounts all cash flows at the cost of capital and subtracts the upfront cost — invest if positive. IRR is the discount rate that makes NPV zero — invest if it exceeds the cost of capital. NPV is more reliable for comparing projects of different sizes or timing.
What makes up the user cost of capital?
Three components: the interest (opportunity) cost of the funds, depreciation and obsolescence, minus expected appreciation of the asset. Taxes and investment credits adjust it further. Firms invest until capital's expected marginal return equals this cost.
Why do riskier investments need higher returns?
Investors are risk-averse: they require compensation for bearing volatility. The risk premium is the extra expected return over safe assets. Projects whose returns covary with bad economic times need the largest premia.
How does inflation affect lenders and borrowers?
Expected inflation is priced into nominal rates via the Fisher equation. Unexpected inflation benefits borrowers (they repay in cheaper dollars) and hurts lenders — which is why long-term capital markets depend on credible, stable inflation.