Loanable Funds Model Notes

The Financial System

Obtaining Funds

  • Firms can obtain funds by:
    • Reinvesting profits.
    • Taking on a partner.
    • Borrowing from banks, government, friends, or family.

Sources of Borrowing

  • Indirect finance: Funds flow from savers to borrowers through financial intermediaries (e.g., banks).
  • Direct finance: Funds flow from savers to firms through financial markets (e.g., New York Stock Exchange).

Financial System

  • Financial system: Network of financial markets and intermediaries through which firms obtain funds from households.
  • Financial intermediaries: Firms that borrow funds from savers and lend to borrowers (e.g., banks, mutual funds, pension funds, insurance companies).
  • Financial markets: Markets where financial securities (stocks, bonds) are traded.

Bond Market

  • A bond is a certificate of debt specifying the borrower's obligations to the bondholder.
    • The borrower issues the bond.
    • The lender (saver/investor) holds the bond.
    • Lenders can buy and sell bonds.
Sources of External Funds: Bonds
  • Bond: A financial security promising to repay a fixed amount of funds.
  • Principal (Face Value): The amount promised to be repaid.
  • Coupon payment: An interest payment on a bond.
    • The principal and coupon payment are fixed once the bond is issued.
  • Bond Price: The bond's price in the bond market, which can fluctuate due to supply and demand changes.
Bond Market Example
  • A firm issues a bond with a principal of $1000, a coupon payment of $60, and a maturity of 1 year.
  • Interest rate = 601000×100=6%\frac{60}{1000} \times 100 = 6 \%. Six months later, a bondholder sells the bond for $900.
  • The original investor might sell at $900 due to a need for cash or changes in market conditions.
    *The interest rate is now 60900×100=6.67%\frac{60}{900} \times 100 = 6.67 \%.
Interest Rate and Bond Price Relationship
  • Interest Rate: The cost of borrowing funds, calculated as Interest Rate=Coupon PaymentBond Price×100\text{Interest Rate} = \frac{\text{Coupon Payment}}{\text{Bond Price}} \times 100.
  • Inversely related to the bond price: as bond price increases, the interest rate decreases, and vice versa.
  • When a firm's default risk increases:
    • Bond price falls.
    • Interest rate rises.
    • Cost of borrowing rises.
Determinants of Interest Rate
  • Term: The time until the bond matures. Longer loans typically have higher interest rates.
  • Credit Risk: The probability that the borrower will fail to pay interest or principal. Good credit history lowers interest rates.

Stock Market

  • Stock: Represents a claim to partial ownership in a firm and a claim to the firm's profits.
    • Dividends: Payments by a corporation to its shareholders.
  • Equity financing: Raising money through the sale of stock.
    • Stocks offer higher risk and potentially higher returns compared to bonds.
  • Major U.S. stock exchanges include the New York Stock Exchange, the American Stock Exchange, and NASDAQ.

Market Information

  • Stock and bond markets provide capital and information.
  • Changes in stock and bond values offer important information for firm managers and investors.
  • Stock prices reflect confidence in a company's future.
  • Bond prices indicate the cost of new borrowing.
    • A higher bond price indicates a lower cost of new external funds.
  • Bond prices and interest rates are related to the risk of default.

Mutual Funds

  • Mutual Funds: Institutions that sell shares to the public and use the proceeds to buy a diversified portfolio of stocks, bonds, or both.
  • Mutual funds allow individuals with small amounts of money to diversify easily.

Banks

  • Banks take deposits from savers and use them to make loans to borrowers.
  • Banks pay interest on deposits and charge borrowers a slightly higher interest on their loans.

Saving & Investment

GDP and National Saving

  • GDP (Y) represents both total income and total expenditure: Y=C+I+G+NXY = C + I + G + NX.
  • In a closed economy (no international trade): Y=C+I+GY = C + I + G.
  • Subtracting C and G from both sides: Y–C–G=IY – C – G = I.
  • National Saving (S): The total income in the economy after paying for consumption and government purchases.

Private Saving

  • Private saving: Income households have after receiving government transfers (TR), paying taxes (T), and paying for consumption (C).
  • Private saving = (Y+TR–C–T)(Y + TR – C – T)

Public Saving

  • Public saving: Tax revenue (T) that the government has left after paying for its spending (G) and transfers (TR).
  • Public saving = (T–G−TR)(T – G -TR)
  • Budget Surplus: Positive public saving.
  • Budget Deficit: Negative public saving.

National Saving

  • National Saving = Private Saving + Public Saving
  • Y–C−G=(Y+TR–T–C)+(T–G−TR)Y – C - G = (Y + TR – T – C) + (T – G - TR)
  • S=(Y+TR–T–C)+(T–G−TR)S = (Y + TR – T – C) + (T – G - TR)

Loanable Funds Market

The Market for Loanable Funds

  • Financial markets coordinate saving and investment.
  • Supply of loanable funds comes from savers (public and private).
  • Demand for loanable funds comes from borrowers (mainly businesses investing).

Real Interest Rate

  • Real Interest rate: The price of the loan.
  • The amount borrowers pay for loans and lenders receive on their saving; determined by the equilibrium of supply and demand for loanable funds.

Demand and Supply Equilibrium

  • The equilibrium interest rate is determined by the supply (S) and demand (I) for loanable funds.
  • At an equilibrium interest rate of 5%, the quantity of loanable funds supplied and demanded is $1.6 trillion.

Determinants of Supply & Demand

  • Supply Shifters:
    • Government Spending (Taxes or Bonds).
    • Wealth (Income).
    • Expectations of future income and price levels.
  • Demand Shifters:
    • Expectations of future profitability (positive expectations increase investment).
    • Productive technology.
    • Business taxes.

Effects of Changes in Supply and Demand

  • An increase in supply:
    • Decreases the equilibrium real interest rate.
    • Increases the equilibrium quantity of loanable funds (saving & investment).
  • An increase in demand:
    • Increases the equilibrium real interest rate.
    • Increases the equilibrium quantity of loanable funds (saving & investment).

Predicting Effects on Saving, Investment, and Interest Rates

  • Investment tax credit: Increases the demand for loanable funds, raising interest rates and increasing saving and investment.
  • Crowding out: A decline in private expenditures due to an increase in government purchases via deficits (G > T).
  • Consumption tax: Increases the supply of loanable funds.

Real-World Example: 2018-2019

  • Between 2018 and 2019, the quantity of loanable funds rose from $3.9 trillion to $4.0 trillion, and the interest rate fell from 2.91% to 2.14% (FRED data).
  • This is explained by a rightward shift of the supply curve due to increased gross saving.

Present Value

Concept of Present Value

  • Present Value: The amount of money needed today, given prevailing interest rates, to produce a given future amount of money.
  • Receiving money in the present is preferred to receiving it in the future.
  • Compare values at different times by comparing their present values.
  • Firms invest if the present value of the project exceeds the cost.

Present Value Formula

  • If r is the interest rate, the present value of a future value (FV) received in N years is:
    • Present Value=Future Value(1+r)N\text{Present Value} = \frac{\text{Future Value}}{(1 + r)^N}
  • The process of finding a present value is called discounting.

Tools to Analyze Investment Decisions

  • One-time future payment: PV=FV(1+r)NPV = \frac{FV}{(1 + r)^N}
  • Future payments over time: PV=FV<em>1(1+r)1+FV</em>2(1+r)2+FV<em>3(1+r)3+…+FV</em>N(1+r)NPV = \frac{FV<em>1}{(1 + r)^1} + \frac{FV</em>2}{(1 + r)^2} + \frac{FV<em>3}{(1 + r)^3} + … + \frac{FV</em>N}{(1 + r)^N}

Example: Contest Winnings

  • Prize 1: $50,000 immediately, plus $50,000 annually for the next four years.
  • Prize 2: $175,000 immediately.
  • Which prize do you choose?

Factors Influencing the Decision

  • The higher the expected rate of return (discount rate), the more likely one is to choose the immediate payment.
  • The further the future payment is from the present, the more likely you should choose the immediate payment.
  • Example: At a 10% interest rate, compare $50,000 now versus $60,000 two years from now. The present value calculation would help determine the better option. At 25% interest rate, which prize will you choose?