Quant, TVM

Question 1

What do interest rates measure, according to the text?

Answer 1

Answer: Interest rates measure the time value of money.

Question 2

Why do financial securities have different equilibrium interest rates?

Answer 2

Answer: Financial securities have different equilibrium interest rates because of the risk differences associated with them.

Question 3

What is the relationship between interest rates and the required rate of return?

Answer 3

Answer: Equilibrium interest rates are the required rate of return for a particular investment. The market rate of return is the return that investors and savers require to willingly lend their funds.

Question 4

Are interest rates and discount rates the same thing? Why or why not?

Answer 4

Answer: Interest rates and discount rates are often used interchangeably, but they are not the same thing. Discount rates are used to discount payments to be made in the future at a certain rate in order to get their equivalent value in current dollars or other currencies.

Question 5

How can interest rates be viewed as the opportunity cost of current consumption?

Answer 5

Answer: If the market rate of interest on 1-year securities is 5%, earning an additional 5% is the opportunity forgone when current consumption is chosen rather than saving (postponing consumption).

Question 6

What is the real risk-free rate of interest?

Answer 6

Answer: The real risk-free rate of interest is a theoretical rate on a single-period loan that has no expectation of inflation in it.

Question 7

Why are T-bill rates nominal risk-free rates instead of real rates of return?

Answer 7

Answer: T-bill rates are nominal risk-free rates because they contain an inflation premium.

Question 8

What are the three types of risk associated with securities?

Answer 8

Answer: The three types of risk associated with securities are default risk, liquidity risk, and maturity risk.

Question 9

What is a default risk premium?

Answer 9

Answer: A default risk premium is the risk associated with the borrower not making the promised payments in a timely manner.

Question 10

Why do longer maturity bonds require a maturity risk premium?

Answer 10

Answer: Longer maturity bonds have more maturity risk than shorter-term bonds and require a maturity risk premium because their prices are more volatile.

Question 11

What is future value (FV)?

Answer 11

Answer: Future value is the amount to which a current deposit will grow over time when it is placed in an account paying compound interest.

Question 12

What is the formula for calculating the FV of a single cash flow?

Answer 12

Answer: The formula for the FV of a single cash flow is FV = PV(1+I/Y)N, where PV is the amount of money invested today, I/Y is the rate of return per compounding period, and N is the total number of compounding periods.

Question 13

What is the factor that represents the compounding rate on an investment, and what is it frequently referred to as?

Answer 13

Answer: The factor that represents the compounding rate on an investment is (1 + I/Y)N, and it is frequently referred to as the future value factor or the future value interest factor for a single cash flow at I/Y over N compounding periods.

Question 14

How can you calculate the FV of a $200 investment at the end of two years if it earns an annually compounded rate of return of 10%?

Answer 14

Answer: You can use the FV formula and input the relevant data: PV = -$200 (note the negative sign), I/Y = 10, N = 2. Compute FV, which equals $242.

Question 15

Is the negative sign on PV necessary when solving for FV, and why or why not?

Answer 15

Answer: No, the negative sign on PV is not necessary when solving for FV, but it makes the FV come out as a positive number. If you enter PV as a positive number, ignore the negative sign that appears on the FV.

Question 16

What is an annuity?

Answer 16

Answer: An annuity is a stream of equal cash flows that occurs at equal intervals over a given period.

Question 17

What are the two types of annuities?

Answer 17

Answer: The two types of annuities are ordinary annuities and annuities due.

Question 18

What is the most common type of annuity?

Answer 18

answer: The most common type of annuity is an ordinary annuity.

Question 19

How do you compute the future value (FV) or present value (PV) of an annuity?

Answer 19

Answer: Computing the FV or PV of an annuity with your calculator is no more difficult than it is for a single cash flow. You will know four of the five relevant variables and solve for the fifth (either PV or FV).

Question 20

What is the difference between single sum and annuity time value of money (TVM) problems?

Answer 20

Answer: The difference between single sum and annuity TVM problems is that instead of solving for the PV or FV of a single cash flow, we solve for the PV or FV of a stream of equal periodic cash flows, where the size of the periodic cash flow is defined by the payment (PMT) variable on your calculator.

Question 21

What is the future value of an ordinary annuity that pays $200 per year at the end of each of the next three years, given the investment is expected to earn a 10% rate of return?

Answer 21

Answer: The future value of this annuity is $662.

Question 22

What is the present value of an annuity that pays $200 per year at the end of each of the next three years, given a 10% discount rate?

Answer 22

Answer: The present value of this annuity is $497.37.

Question 23

What is the present value of four $100 end-of-year payments if the first payment is to be received three years from today and the appropriate rate of return is 9%?

Answer 23

Answer: The present value of this annuity is $272.68.

Question 24

What is a bond?

Answer 24

Answer: A bond is a debt security in which the issuer owes the bondholders a debt and is obliged to repay the principal and interest on the bond.

Question 25

What is the present value of a bond that makes coupon interest payments of 70 euros at the end of each year and pays its face value of 1,000 euros at maturity in six years, assuming a discount rate of 8%?

Answer 25

Answer: The present value of this bond is 940.79 euros.

Question 26

What is a perpetuity?

Answer 26

A perpetuity is a financial instrument that pays a fixed amount of money at set intervals over an infinite period of time.

Question 27

What is the discount factor for a perpetuity?

Answer 27

The discount factor for a perpetuity is just one divided by the appropriate rate of return (i.e., 1/r).

Question 28

What is the PV formula for a perpetuity?

Answer 28

PV (perpetuity) = PMT / IY

Question 29

What can we solve for using the PV perpetuity formula?

Answer 29

We can solve for any one of the three relevant variables (PV, PMT, or IY), given the values for the other two.

Question 30

What is an example of a perpetuity?

Answer 30

Most preferred stocks are examples of perpetuities since they promise fixed interest or dividend payments forever.

Question 31

What is the value of Kodon's preferred stock today, given an 8% rate of return and annual dividends of $4.50?

Answer 31

$56.25

Question 32

When is the value of a perpetuity calculated?

Answer 32

The PV of a perpetuity is its value one period before its next payment.

Question 33

What is a deferred perpetuity?

Answer 33

A deferred perpetuity is a financial instrument that starts paying a fixed amount of money at set intervals after a specified period of time.

Question 34

What is the value of Kodon's preferred stock today, given an 8% rate of return, annual dividends of $4.50, and the first dividend paid in four years?

Answer 34

$44.65

Question 35

How is the value of a deferred perpetuity calculated?

Answer 35

The PV of a deferred perpetuity is calculated by discounting the value of the perpetuity for the number of periods before the first payment.

Question 36

How is the PV of a 3-year ordinary annuity that starts at the beginning of Year 1 (t=0) different from that of a 3-year ordinary annuity that starts at Year 4 and ends at Year 6?

Answer 36

The PV of a 3-year ordinary annuity that starts at the beginning of Year 1 (t=0) is indexed to t=0, whereas the PV of a 3-year ordinary annuity that starts at Year 4 and ends at Year 6 is indexed to t=3.

Question 37

What are some examples of how to compute I/Y, N, or PMT in annuity problems?

Answer 37

xamples of how to compute I/Y, N, or PMT in annuity problems include computing an annuity payment needed to achieve a given FV, computing a loan payment, computing the number of periods in an annuity, computing the number of years in an ordinary annuity, and computing the rate of return for an annuity.

Question 38

What is the sign convention to remember when computing PMT and FV?

Answer 38

The sign convention to remember when computing PMT and FV is that they must have opposite signs, otherwise the calculator will issue an error message.

Question 39

What is the formula to calculate the annuity payment needed to achieve a given FV?

Answer 39

Answer: To calculate the annuity payment needed to achieve a given FV, the formula is N = number of periods, I/Y = expected rate of return, FV = future value, and CPT → PMT.

Question 40

If you are considering applying for a $5,000 loan that will be repaid with equal end-of-year payments over the next 10 years, and the annual interest rate is 8%, what will your payments be?

Answer 40

Answer: The size of the end-of-year loan payment can be determined by inputting values for the three known variables and computing PMT. N = 10; I/Y = 8; PV = -5,000; CPT → PMT = $814.76.

Question 41

How many $50 end-of-year payments are required to accumulate $500 if the discount rate is 6%?

Answer 41

Answer: The number of payments necessary can be determined by inputting the relevant data and computing N. I/Y = 6%; FV = $500; PMT = -$50; CPT → N = 8.19 years.

Question 42

Suppose you have a $1,500 ordinary annuity earning a 9% return. How many annual end-of-year $250 withdrawals can be made?

Answer 42

Answer: The number of years in the annuity can be determined by entering the three relevant variables and computing N. I/Y = 9; PMT = 250; PV = -1,500; CPT → N = 7.18 years.

Question 43

What is the formula to compute the rate of return for an annuity?

Answer 43

Answer: To compute the rate of return for an annuity, the formula is N = number of periods, FV = future value, PMT = payment per period, and CPT → I/Y.

Question 44

Suppose you have the opportunity to invest $500 at the end of each of the next three years in exchange for $2,000 at the end of the third year. What is the annual rate of return on this investment?

Answer 44

Answer: The rate of return on this investment can be determined by entering the relevant data and solving for I/Y. N = 3; FV = $2,000; PMT = -$500; CPT → I/Y = 20.96%.

Question 45

Suppose you deposit $1,000 at the end of each year for the next 20 years, and you want to accumulate $50,000. What is the expected rate of return if the annuity is an ordinary annuity?

Answer 45

Answer: The expected rate of return can be determined by entering the relevant data and solving for I/Y. N = 20; FV = $50,000; PMT = -$1,000; CPT → I/Y = 8.23%.

Question 46

If you want to have $10,000 in five years, and you can save $1,000 per year, what should be the expected rate of return?

Answer 46

Answer: The expected rate of return can be determined by entering the relevant data and solving for I/Y. N = 5; FV = $10,000; PMT = -$1,000; CPT → I/Y = 12.22%.

Question 47

Suppose you invest $2,000 at the end of each year for 10 years and expect to earn a 9% annual rate of return. How much will you have accumulated at the end of the 10-year period?

Answer 47

Answer: To solve this problem, enter the relevant data and compute FV. N = 10; I/Y = 9; PMT = −$2,000; CPT → FV = $28,355.94

Question 48

What is the impact of compounding frequency on FV and PV computations?

Answer 48

Answer: More frequent compounding increases the effective rate of interest, which in turn increases the future value (FV) of a given cash flow and decreases the present value (PV) of a given cash flow.

Question 49

What is the future value of $1,000 invested for one year at an annual interest rate of 6% with different compounding periods?

Answer 49

Answer: The future value (FV) of $1,000 invested for one year at an annual interest rate of 6% with different compounding periods are as follows: Annual (m = 1): $1,060.00 Semiannual (m = 2): $1,060.90 Quarterly (m = 4): $1,061.36 Monthly (m = 12): $1,061.68 Daily (m = 365): $1,061.83

Question 50

What is the present value of $1,000 to be received one year from now at an annual interest rate of 6% with different compounding periods?

Answer 50

Answer: The present value (PV) of $1,000 to be received one year from now at an annual interest rate of 6% with different compounding periods are as follows: Annual (m = 1): $943.396 Semiannual (m = 2): $942.596 Quarterly (m = 4): $942.184 Monthly (m = 12): $941.905 Daily (m = 365): $941.769

Question 51

What are the two ways to use a financial calculator to compute PVs and FVs under different compounding frequencies?

Answer 51

Answer: The two ways to use a financial calculator to compute PVs and FVs under different compounding frequencies are to either adjust the number of periods per year (P/Y) mode on the calculator to correspond to the compounding frequency, or to keep the calculator in the annual compounding mode (P/Y = 1) and enter I/Y as the interest rate per compounding period and N as the number of compounding periods in the investment horizon.

Question 52

What are the basic formulas for calculating PV and FV amounts using a financial calculator under different compounding frequencies?

Answer 52

Answer: The basic formulas for calculating PV and FV amounts using a financial calculator under different compounding frequencies are as follows: I/Y = the annual interest rate / m N = the number of years × m

Question 53

How does increasing the number of compounding periods per year affect the effective annual interest rate?

Answer 53

Answer: Increasing the number of compounding periods per year increases the effective annual interest rate.

Question 54

Why is it not recommended to adjust the number of periods per year (P/Y) mode on a financial calculator to correspond to the compounding frequency?

Answer 54

Answer: It is not recommended to adjust the number of periods per year (P/Y) mode on a financial calculator to correspond to the compounding frequency because it can lead to errors in the calculations.

Question 55

How does decreasing the compounding frequency affect the future value and present value of a given cash flow?

Answer 55

Answer: Decreasing the compounding frequency decreases the effective rate of interest, which in turn decreases the future value (FV) of a given cash flow and increases the present value (PV) of a given cash flow.

Question 56

What is the relationship between the effective annual rate and the stated annual interest rate?

Answer 56

Answer: The effective annual rate is always greater than the stated annual interest rate, as it takes into account the impact of