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**Interest Rates and the Time Value of Money (Chapter 4)**

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Learning Objectives Write down and explain the present and future value formulas. Define and price major types of debt instruments including discount bonds, simple loans, fixed payment loans, coupon bonds, and perpetuities. Define and compute yield to maturity. Explain why bond prices move inversely to market interest rates. Define rate of return and explain how it differs from yield to maturity. Explain the difference between real and nominal interest rates.

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Cash Flow Timeline Horizontal length represents time over which interest is earned. Cash in-flows are represented by lines pointing upwards from the time line. Cash out-flows are represented by lines pointing downward from the time line.

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**Rule of the Cash Flow Timeline**

Cash flows at the same date can be added together, but cash flows at different dates cannot be added together.

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**Present Value Formula PV present value FV future value**

i periodic interest rate in decimal form n number of periods

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Future Value Formula

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**If the interest rate is positive,**

Present Value If the interest rate is positive, PV < FV

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Present Value i PV

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Present Value i PV

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**Present Value of an Annuity**

An annuity pays a fixed amount every period. The present value could be calculated by taking the PV of each payment and summing. Alternatively, one could use a financial calculator.

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**Using financial calculator**

Given four of five values for PV, FV, I/Y, N and PMT, the calculator will compute the remaining one.

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On your seventieth birthday, you learn that your grandma, bless her soul, deposited $50.00 for you on the day of your birth in a savings account bearing 5 percent interest. How much is in the account?

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You won $1 million in the lottery but unfortunately the money is payable in a year and you want to start spending it right away. If interest is at 8 percent, how much can you receive today in exchange for that $1 million in year?

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You’ve won a scholarship for your senior year worth $1,500, but it is payable only after graduation, a year hence. If interest is at 15 percent, how much is your scholarship worth today?

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You won the lottery and netted a million bucks, but you need $5 million to buy a little island that you have had your eye on. If interest is at 12 percent, will you be able to buy your island in 30 years, assuming its price is unchanged at that time?

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**Bond prices and interest rates move in opposite directions**

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**Five Types of Credit Market Instruments**

1. Simple loan

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**2. Fixed Payment, or Amortized, Loan**

Examples: car loans, mortgages, annuities

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3. Coupon Bond Most bonds with maturities greater than a year are of this form. Coupons bonds issued by Federal government (Treasurys) State and local governments (munis) Corporations (corporates)

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4. Consol or Perpetuity Fixed coupon received forever, no face value.

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**5. Discount, or Zero Coupon, Bond**

Identical in cash flow structure to a simple loan. The difference is that there’s an active secondary market for zero coupon bonds.

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Yield to Maturity The rate of discount that equates the present value of future cash flows with the price of the credit instrument.

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**Relationship Between Price and Yield to Maturity**

.

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**Ex post real rate of interest**

The nominal interest rate minus the actual inflation rate.

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**Ex ante real rate of interest**

The nominal interest rate minus the expected inflation rate.

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**TIPS (Treasury Inflation Protection Securities)**

Originally issued in 1997. Interest and principal payments are adjusted for inflation. In times of high inflation the $ amount paid to investors rises. Return on TIPS relative to regular Treasurys provides information on expected inflation.

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