Chapter 28: Money, Interest Rates, and Economic Activity
28.1 understanding bonds
Present value and the interest rate
A bond is a financial asset that promises to make one or more specified payments at specified dates in the
Present value (PV): the value now of one or more payments or receipts made in the future; often referred to as
discounted present value.
Present value depends of the interest rate because when we calculate presents value, the interest rate is used
to discount the value of the future payments into their present value.
Consider an asset that pays $X in one years time. If the interest rate is i% per year, the PV of the asset is
PV = $X/(1+i)
Notice that, ceteris paribus, the PV is negatively related to the interest rate
A Sequence of Future Payments?
Suppose a $1000 bond pays 10% at the end of each of three years, at which point it is redeemed. What is the PV
if the interest rate is 7 percent?
PV = $100 + $100 +2$1100 3
1.07 (1.07) (1.07)
A general relationship:
Some bonds make no coupon payments and only a single payment (the face value) at some point in the
future. This is the case for short-term government bonds call Treasury Bills.
Other bonds are long-term government or corporate bonds, make regular coupon payments as well as a final
payment of the bonds face value.
The present value of any bond that promises a future payment or sequence of future payments is negatively
related to the market interest rate.
Present value and market price
Most bonds are bought and sold in financial markets in which there are large numbers of both buyers and
sellers. The present value of a bond is important because it establishes the price at which a bond will be
exchanged in the financial markets.
The present value of a bond is the most someone would be willing to pay now to own the bonds future
stream of payments.
At any price below the bonds present value, the abundance of demand will cause the price to rise.
If the market price of any asset is greater than the present value of its income stream, no one will want to buy it,
and the resulting excess supply will push down the market price.
If the market price is below its present value, there will be a rush to buy it, and the resulting excess demand will
push up the market price.
When the bonds market price is exactly equal to its present value, there is no pressure for the price to change.
Consider a competitive market for bonds.
- buyers should be prepared to pay no more than the bonds PV
- sellers should be prepared to accept no less than the bonds PV
The equilibrium market price of a bond (or other financial asset) should be the PV of the stream of income
generated by the bond.
The eqm market price of any bond will be the present value of the income stream that it produces.
Interest rates, market prices and bond yields
1. The present value of a bond is negatively related to the market interest rate.
2. A bonds eqm market price will be equal to its present value.
An increase in the market interest rate leads to a fall in the price of any given bond. A decrease in the market
interest rate leads to an increase in the price of any given bond. A bond is a financial investment for the purchasers. The cost of the investment is the price of the bond, and the
return on the investment is the sequence of future payments. Thus, for a given sequence of future payments, a
lower bond price implies a higher rate of return on the bond, or a higher bond yield.
The bond yield is a function of the sequence of payments and the bond price.
The market interest rate is the rate at which you can borrow or lend money in the credit market.
A rise in the market interest rate will lead to a decline in the present value of any bond and thus to a decline in
its equilibrium price. As the bond price falls, its yield or rate of return rises. Thus, we see that market interest
rates and bond yield tend to move in the same direction.
An increase in the market interest rate will reduce bond prices and increase bond yields. A reduction in the
market interest rate will increase bond prices and reduce bond yields. Therefore, market interest rates and
bond yields tend to move together.
Since a bonds yield is inversely related to its price, we conclude that:
3. Market interest rates and bond yields tend to move together.
Sometimes the yield on specific bonds rise or fall even there is no change in the market interest rate. This occurs
when there is a change in the perceived riskiness of the bond.
If the bond purchasers (lenders) perceive that bond issuers (borrowers) are unlikely to be able to fulfill their
future repayments obligations, the expected present value of the bond declines.
A lower expected present value leads fewer buyers to be interested in purchasing that bond and, as a result, its
eqm market price declines.
As the market price falls, the yield on that bond rises. Bonds with high yields reflect high-risk investments.
An increase in the riskiness of any bond leads to a decline in its expected present value and thus to a decline
in the bonds price. The lower bond price implies a higher bond yield.
28.2 the demand for money
Demand for money: the total amount of money balance that the public wants to hold for all purposes
For simplification if we assume that there are only 2 types of assets bond and money then if households and
firms are choosing how to divide their given stock of assets between money and bonds, it follows that if we
know the demand for money, we also know the demand for bonds.
Three reasons for holding money
1. Households and firms hold money in order to carry out transactions. Economists call this the transactions
demand for money. You carry money in your upcoming transactions and firms are continually making
expenditures on intermediate inputs and payments to labour and they keep money available in their chequeing
accounts to pay these expense.
2. Firms and household hold money is that they are uncertain about when some expenditures will be necessary
and they hold money as a precaution to avoid the problems associated with missing a transaction, this is called
the precautionary demand for money.
3. Holding money applies more to large business and to professional money managers than to individuals
because it involves speculating about how interest rate are likely to change in the future, this is called the
speculative demand for money. If the interest rate is expected to rise in the future, the bond prices will expect
to fall and bondholders experience a decline in the value of their bond holding. If the expectation of increase in
future interest rates will therefore lead to the holding of more money (and fewer bonds) now as financial
managers adjust their portfolios in order to preserve their values.
The determinants of money demand
The interest rate:
The cost of holding money is the income that could have been earned if that wealth were instead held in the
form of interest-earning bonds. This is the opportunity cost of holding money.
Increase in the interest rate leads firms and households to reduce their desired money holding. Conversely, a
reduction in the interest rate means that holding money is less costly and so firms and households are assumes
to increase their desired money holdings.
Other things being equal, the demand for money is assumed to be negatively related to the interest rate. In the graph below this negative relationship between interest rates and desired money holding is drawn as the
money demand (Md) curve. The decision to hold money is also the decision not to hold bonds, and so
movements along the Md curve imply the substitution of assets between money and bonds.
The amount of transactions that firms and households want to make is positively related to the level of income
and production in the economy which is the real GDP. This positively relationship between real GDP and desired
money holdings in shown in the graph above by a rightward shift of the Md curve to the Md.
At any given interest rate an increase in Y is assumed to generate more transactions and thus greater desired
An increase in real GDP increases the volume of transaction in the economy and is assumed to cause an
increase in desired in desired money holding.
The price level:
An increase in the price level leads to an increase in the dollar value of transactions even if there is a change in
the real value of transaction. That is as P rises, households and firms will need to hold more money in order to
carry out the same real value of transaction. This positively relationship between the price level and desired
money holdings is shown in the graph above as a rightward shift to the Md curve to the Md.
An increase in the price level is assumed to cause an increase in desired money holdings.