Chapter 4: The Meaning of Interest Rates

Question 1

The Meaning of Interest Rates

Overview

Answer 1

4. 1 The Timeline
5. 2 The Three Rules of Time Travel
6. 3 Valuing a Stream of Cash Flows
7. 4 Perpetuities and Annuities
8. 5 MS Excel
9. 6 Non-Annual Cash Flows
10. 7 Solving for the Cash Payments
11. 8 Solving for the Number of Periods
12. 9 The Internal Rate of Return
13. 10 Determinants of Interest rates
14. 11 Bond Cash Flows, Prices, and Yields
15. 12 Dynamic Behavior of Bond Prices

Question 2

A timeline is

Answer 2

A timeline is a linear representation of the timing of

potential cash flows.

Question 3

The Timeline Differentiate between two types of cash flows:

Answer 3

• Inflows are positive cash flows.

* Outflows are negative cash flows, which are indicated with a –(minus) sign.

Question 4

The Three Rules of Time Travel:

Answer 4

Financial decisions often require combining cash flows or comparing values.

• Rule 1: only the values at the same point in time can be Compared or Combined.
• Rule 2: to move a cash flow forward in time, you must compound it.
• Rule 3: to move cash flow backward in time, you must discount it.

Question 5

Perpetuities

Answer 5

When a constant cash flow will occur at regular intervals forever it is called a perpetuity.
(goes on forever)

Question 6

Annuities

Answer 6

When a constant cash flow will occur at regular intervals for a finite number of N periods, it is called an annuity. (stops at a certain time)

Question 7

Growing Cash Flows

Answer 7

• Growing Perpetuity

* Growing Annuity

Question 8

Growing Perpetuity

Answer 8

• Assume you expect the amount of your perpetual payment to increase at a constant rate, g.

Question 9

Growing Annuity

Answer 9

• The present value of a growing annuity with the initial cash flow c, growth rate g, and interest rate r

Question 10

Non-Annual Cash Flows

Answer 10

• The same time value of money concepts apply if the cash flows occur at intervals other than annually.
• The interest and number of periods must be adjusted to reflect the new time period.

Question 11

how to solve the Cash Payments

Answer 11

• Sometimes we know the present value or future value, but do not know one of the variables we have
previously been given as an input.

Question 12

Solving for the Number of Periods

Answer 12

• In addition to solving for cash flows or the interest rate, we can solve for the amount of time it will take a sum of money to grow to a known value.

Question 13

The Internal Rate of Return

Answer 13

• In some situations, you know the present value and cash flows of an investment opportunity, but you do not know the internal rate of return (IRR), the interest rate that sets the net present value of the cash flows equal to zero.

Question 14

The Determinants of Interest Rates

Answer 14

• Inflation

* Real Vs Nominal Rates

Question 15

Nominal Interest Rate:

Answer 15

The rates quoted by financial institutions and used for discounting or compounding cash flows

Question 16

Real Interest Rate:

Answer 16

The rate of growth of your purchasing power, after adjusting for inflation

Question 17

Investment and Interest Rate Policy

Answer 17

• An increase in interest rates will typically reduce the PV of an investment.

Question 18

Bond Cash Flows, Prices, and Yields

• Bond Terminology

Answer 18

• Bond Certificate (States the terms of the bond)
• Maturity Date (Final repayment date)
• Term (The time remaining until the repayment date)
• Coupon (Promised interest payments)
• Face Value (Notional amount used to compute the interest payments)
• Coupon Rate (Determines the amount of each coupon payment, expressed as an APR)
• Coupon Payment

Question 19

Zero-Coupon Bond

Answer 19

• Does not make coupon payments
• Always sells at a discount (a price lower than face value), so they are also called pure discount bonds.
• Treasury Bills are U.S. government zero-coupon bonds with a maturity of up to one year.

Question 20

Yield to Maturity (of zero coupon bonds)

Answer 20

The discount rate that sets the present value of the promised bond payments equal to the current market price of the bond.

Question 21

Risk-Free Interest Rates

Answer 21

• Spot Interest Rate = Another term for a default-free, zero-coupon yield
• Zero-Coupon Yield Curve = A plot of the yield of risk-free zero-coupon bonds as a function of the bond’s maturity date

Question 22

Coupon Bonds (+ eg)

Answer 22

Coupon Bonds
• Pay face value at maturity
• Pay regular coupon interest payments

Treasury Notes
• U.S. Treasury coupon security with original maturities of 1–10 years

Treasury Bonds
• U.S. Treasury coupon security with original maturities over 10 years

Question 23

Yield to Maturity of a Coupon Bond

Answer 23

• The YTM is the single discount rate that equates the present value of the bond’s remaining cash flows to its current price.

Question 24

Dynamic Behavior of Bond Prices

Answer 24

• Discount= A bond is selling at a discount if the price is less than the face value.
• Par= A bond is selling at par if the price is equal to the face value.
• Premium= A bond is selling at a premium if the price is greater than the face value.

Question 25

If a coupon bond trades at a discount,

Answer 25

an investor will earn a return both from receiving the coupons and from receiving a face value that exceeds the price paid for the bond.

• If a bond trades at a discount, its yield to maturity will exceed its coupon rate.

Question 26

If a coupon bond trades at a premium,

Answer 26

it will earn a return from receiving the coupons, but this return will be diminished by receiving a face value less than the price paid for the bond.

Question 27

There is an inverse relationship between interest rates and bond prices.

Answer 27

• As interest rates and bond yields rise, bond prices fall.

* As interest rates and bond yields fall, bond prices rise.

Question 28

Valuing a Coupon Bond Using Zero-Coupon

Yields

Answer 28

then: • The price of a coupon bond must equal the present value of its coupon payments and face value.

Question 29

Treasury Yield Curves

Answer 29

Treasury Coupon-Paying Yield Curve
• Often referred to as “the yield curve”

On-the-Run Bonds
• Most recently issued bonds
• The yield curve is often a plot of the yields on these bonds.