CF2 : Time, Money and Interest Rates

Three Rules of Time Travel

1. Combining and comparing values is only possible at the same point in time.

2. Moving cash forward in time is compounding —> x(1+r)^n (n being the number of periods)

3. Moving cash back in time is discounting —> /(1+r)^n

Perpetuities

a stream of equal cash flows that occur at regular intervals and last forever eg: disability insurance if you become disabled. Present value = C/r

Annuities

Stream of N equal cash flows paid at regular intervals (limited) Present value = C/r(1-(1/(1+r)^n))

Future Value = C(1/r)((1+r)^n - 1)

Growing perpetuities or annuities

They have a stream of cash flows that occur at regular intervals and grow at a constant rate g

The internal rate of return (IRR)

The interest rate that sets the NPV of the cash flow at zero, the break even point for an investment decision

Effective Annual Rate (EAR)

- Total amount of interest that will be earned at the end of one year

-considers compounding

- The discount rate has to match the period of the cash flow ( sqn (1+r)-1

Annual percentage rate (APR)

-simple interest earned in one period (typically one year)

-without compounding

-not reflective of the true amount

-typically less than the EAR

Converting APR to an EAR (k=period)

1 + EAR = (1+APR/k)^k

Determinants of interest rates

- adjusted by inflation/deflation

- higher demand for money and or credits = higher interest rates

-The higher the risk, the higher the interest rate

- Taxes reduce the cash flow of the investor

-The opportunity cost of capital : Interest rate of the best alternative option

Interest rate policy

Central bank actions to influence short-term interest rates as a tool of monetary policy, to manage the money supply and credit conditions in an economy.

Term structure

the relationship between the investment term and the interest rate

Yield Curve

graph of the term structure of interest rates

Yield Curve Shapes

Normal, inverted or flat.

bond certificate

states the terms of a bond as well as the amounts and dates of all payments to be made

maturity date

Final repayment date

Term

Time remaining until the repayment date

Coupon

Promised interest payment in currency

Face value

Notional amount used to compute the interest payments

Coupon rate

Coupon payment expressed as an APR %

Coupon Payment

CPN = (Coupon Rate x Face Value)/(Number of Coupon Payments per Year)

Zero-coupon Bonds

-do not make coupon payments

-always sell at adiscount (lower than the face value)

- eg. Treasury bills issued ny the US government (maturity up to one year)

yield to maturity

the rate of return a bondholder will receive if the bond is held to maturity

Yield to maturity of a Zero-coupon bond

The risk free interest rate equals the yield

Discount Bond price

A bond is selling at a discount if the price is less than the face value

Par bond price

A bond is selling at par if the price is equal to the face value

Premium Bond Price

A bond is selling at a premium if the price is higher than the face value

Relationship between Interest Rates and Bond Prices

As interest rates increase, bond prices decrease and vice versa. It's an inverse relationship.

Sensitivity of a bond's price to changes in interest rates

It is measured by the bond's duration, so its average maturity. Those with high durations are highly sensitive to interest rate changes, and those with low durations are less sensitive.

Corporate bonds

issued by corporations, credit risk = risk of default, investors pay less for bonds with credit risk than they would for default free bonds, although the yield of credit risk bonds will be higher than that of identical default free bonds.

Government Bonds

Issuead by national governments, risk depends on the rating of the country, possibility of default or inflate away the debt