Vol. 1 LM1 Interest Rates

Question 1

Concept

is the value that investors forgo by choosing a particular course of action

p. 5

Answer 1

opportunity cost

Question 2

Describe

opportunity cost

p. 5

Answer 2

is the value that investors forgo by choosing a particular course of action

Question 3

Formula

interest rate, denoted r

p. 5

Answer 3

r = Real risk-free interest rate + Inflation premium + Default risk premium + Liquidity premium + Maturity premium

Question 4

Components

four premiums of interest rate r

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Answer 4

1. inflation premium
2. default risk premium
3. liquidity premium
4. maturity premium

Question 5

Concept

• is the single-period interest rate for a completely risk-free security if no inflation were expected
• in economic theory, this reflects the time preferences of individuals for current versus future real consumption

p. 5

Answer 5

real risk-free interest rate

Question 6

Define

real risk-free interest rate

p. 5

Answer 6

• is the single-period interest rate for a completely risk-free security if no inflation were expected
• in economic theory, this reflects the time preferences of individuals for current versus future real consumption

Question 7

Concept

compensates investors for expected inflation and reflects the average inflation rate expected over the maturity of the debt

p. 5

Answer 7

inflation premium

Question 8

Describe

inflation premium

p. 5

Answer 8

compensates investors for expected inflation and reflects the average inflation rate expected over the maturity of the debt

Question 9

Concept

The sum of the real risk-free interest rate and the inflation premium

p. 5

Answer 9

nominal risk-free interest rate

Question 10

Concept

The interest rate on a 90-day US Treasury bill, for example, represents this rate over that time horizon

p. 5

Answer 10

nominal risk-free interest rate

Question 11

Concept

compensates investors for the possibility that the borrower will fail to make a promised payment at the contracted time and in the contracted amount

p. 5

Answer 11

default risk premium

Question 12

Describe

default risk premium

Answer 12

compensates investors for the possibility that the borrower will fail to make a promised payment at the contracted time and in the contracted amount

Question 13

Concept

compensates investors for the risk of loss relative to an investment’s fair if the investment needs to be converted to cash quickly.

Answer 13

liquidity premium

Question 14

Describe

liquidity premium

Answer 14

compensates investors for the risk of loss relative to an investment’s fair if the investment needs to be converted to cash quickly.

Question 15

Concept

compensates investors for the increased sensitivity of the market value of debt to a change in market interest rates as the duration is extended

Answer 15

maturity premium

Question 16

Describe

maturity premium

Answer 16

compensates investors for the increased sensitivity of the market value of debt to a change in market interest rates as the duration is extended

Question 17

for N = 1

the expression for the future value of amount PV

p. 6

Answer 17

FV₁ = PV(1+r)

Question 18

Concept

is the amount of funds originally invested

p. 7

Answer 18

principal

Question 19

Describe

principal

p. 7

Answer 19

is the amount of funds originally invested

Question 21

formula

present value of an initial investment to its future value after N periods

p. 7

Answer 21

FV_N = PV(1+r)^N

Question 22

How much will you have at the end of 5 years at 7 percent for 5 years

You are the lucky winner of your state’s lottery of $5 million after taxes.
You invest your winnings in a five-year certificate of deposit (CD) at a local financial institution. The CD promises to pay 7 percent per year compound- ed annually. This institution also lets you reinvest the interest at that rate for the duration of the CD. How much will you have at the end of five years if your money remains invested at 7 percent for five years with no withdrawals?

p. 8

Answer 22

PV = $5,000,000
r = 7% = 0.07
N = 5
FV_N = PV(1+r)^N
* = $5,000,000(1.07)⁵
* = $5,000,000(1.402552)
* = $7,012,758.65

Question 23

The Future Value of a Lump Sum with No Interim Cash

An institution offers you the following terms for a contract: For an invest- ment of ¥2,500,000, the institution promises to pay you a lump sum six years from now at an 8 percent annual interest rate. What future amount can you expect?

p. 9

Answer 23

PV = ¥2,500,000 r = 8% = 0.08 N=6

= ¥2, 500, 000 (1.08) ⁶
= ¥2, 500, 000 (1.586874) = ¥3, 967, 186

Question 24

The Future Value of a Lump Sum

A pension fund manager estimates that his corporate sponsor will make
a $10 million contribution five years from now. The rate of return on plan assets has been estimated at 9 percent per year. The pension fund manager wants to calculate the future value of this contribution 15 years from now, which is the date at which the funds will be distributed to retirees. What is that future value?

p. 9

Answer 24

By positioning the initial investment, PV, at t = 5, we can calculate the future value of the contribution

PV = $10 million r = 9% = 0.09
N = 10

= $10,000,000(1.09)¹⁰
= $10,000,000 (2.367364) = $23,673,636.75

From the standpoint of today (t = 0), the future amount of $23,673,636.75 is 15 years into the future. Although the future value is 10 years from its present value, the present value of $10 million will not be received for another five years.

Question 25

The Future Value of a Lump Sum with Quarterly Compounding

Continuing with the CD example, suppose your bank offers you a CD with a two-year maturity, a stated annual interest rate of 8 percent compounded quarterly, and a feature allowing reinvestment of the interest at the same interest rate. You decide to invest $10,000. What will the CD be worth at maturity?

p. 11

Answer 25

PV = $10,000
r_s = 8% = 0.08
m=4
r_s / m = 0.08 / 4 = 0.02
N=2
mN = 4 (2) = 8 interest periods
FV_N =PV(1+r_s/m)^mN
= $10,000(1.02)⁸
= $10,000 (1.171659) = $11,716.59

Question 26

Calculate

EAR

p. 14

Answer 26

(1 + periodic interest rate)^m - 1
* where the periodic interest rate is the stated annual interest rate divided by m