Quantitative Methods

Question 1

Time Value of Money

Answer 1

The time value of money (TVM) surmises that money is worth more now than at a future date based on its earning potential. Because money can grow when invested, any delay is a lost opportunity for growth. The time value of money is a core financial principle known as the present discounted value.

The time value of money as a topic in investment mathematics deals with equivalence relationships between cash flows with different dates. Mastery of time value of money 88concepts and techniques is essential for investment analysts

Question 2

Discounting

Answer 2

the process of determining the present value of a payment or a stream of payments that is to be received in the future.8

Question 3

Discount Rate

Answer 3

a discount rate is the rate of return used to discount future cash flows back to their present value. This rate is often a company’s Weighted Average Cost of Capital (WACC), required rate of return, or the hurdle rate that investors expect to earn relative to the risk of the investment.

Question 4

Interest Rate

Answer 4

is a rate of return that reflects the relationship between differently dated cash flows.

Question 5

Opportunity Cost

Answer 5

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

Question 6

Real-Risk Free Interest

Answer 6

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

Question 7

Inflation Premium

Answer 7

Compensates investors for expected inflation and reflects the average inflation rate expected over the maturity of the debt. Inflation reduces the purchasing power of a unit of currency—the amount of goods and services one can buy with it.

Question 8

Nominal Risk-Free Interest Rate

Answer 8

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

Question 9

Default Risk Premium

Answer 9

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 10

Liquidity Premium

Answer 10

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

Question 11

Maturity Premium

Answer 11

Compensates investors for the increased sensitivity of the market value of debt to a change in market interest rates as maturity is extended, in general (holding all else equal).

Question 12

Present Value (PV)

Answer 12

• The current value of a future sum of money or stream of cash flows.
• Determined by discounting the future value by the estimated rate of return that the money could earn if invested.
• Useful in investing and strategic planning for businesses.
• Measured by accounting for the time value of money and the risk associated with the investment.
• A valuable tool for making investment and capital allocation decisions.

Question 13

Future Value (FV)

Answer 13

refers to a method of calculating how much the present value (PV) of an asset or cash will be worth at a specific time in the future.

Question 14

Future Value Formula requires:

Answer 14

The future value formula requires three numbers:

• Present value, or how much the asset or cash is worth now (PV)
• What the annual interest rate is (r)
• Length of time/how many years the assets or cash will be left (n)

Question 15

Simple Interest

Answer 15

an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest. Simple interest relates not just to certain loans. It’s also the type of interest that banks pay customers on their savings accounts.

Question 16

Principle

Answer 16

Principal refers to the baseline sum in financial transactions: the initial amount invested or borrowed.

Question 17

Compounding Interest or Interest on Interest

Answer 17

Earnings from an asset (such as capital gains or interest) are reinvested to generate additional earnings over time

Question 18

Opportunity Cost

Question 19

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 compounded 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?

Answer 19

To solve this problem, compute the future value of the $5 million investment using the following values in Equation 2:

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

At the end of five years, you will have $7,012,758.65 if your money remains invested at 7 percent with no withdrawals.

Question 20

An institution offers you the following terms for a contract: For an investment 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?

Answer 20

Use the following data in Equation 2 to find the future value:

PV = ¥2, 500, 000
r = 8% = 0.08
N = 6
FVN = PV(1 + r)N
= ¥2, 500, 000 (1.08)6
= ¥2, 500, 000 (1.586874)
= ¥3, 967, 186

You can expect to receive ¥3,967,186 six years from now

Question 21

Stated Annual Interest Rate or Quoted Interest Rate

Question 22

Effective Annual Rate (EAR)

Question 23

Annuity

Question 24

Ordinary Annuity

Question 25

Annuity Due

Question 26

Perpetuity

Question 27

Time Line

Answer 27

is simply a diagram of the cash

Question 28

. Equilibrium interest rates

Question 29

When we analyze two-time series in regression analysis, we need to ensure that:
1. neither the dependent variable series nor the independent
variable series has a unit root, or
2. that both series have a unit root and are not cointegrated.
Unless Condition 1 or Condition 2 holds, one cannot rely on the validity of the estimated regression coefficients.

DeMolay’s statement that the coefficients depicted in Exhibit 1 are consistent with a random walk is most likely:

A correct.
B incorrect because b1 should be close to 0.
C incorrect because b0 should be close to 1

Answer 29

A is correct. When modeled using a AR(1) model random walks will have an estimated intercept coefficient near zero and an estimated
slope coefficient on the first lag near 1. Therefore, his statement is correct.
B is incorrect because random walks are likely to have a slope coefficient (b1) close to one.
C is incorrect because random walks are likely to have an intercept coefficient (b0) close to zero.

Question 30

The nominal risk-free rate is best described as the sum of the real risk-free rate and a premium for:
A maturity.
B liquidity.
C expected inflation

Answer 30

C is correct. The sum of the real risk-free interest rate and the inflation premium is the nominal risk-free rate

Question 31

Which of the following risk premiums is most relevant in explaining the difference in yields between 30-year bonds issued by the US Treasury and 30-year bonds issued by a small private issuer?

A Inflation
B Maturity
C Liquidity

Answer 31

C is correct. US Treasury bonds are highly liquid, whereas the bonds of small issuers trade infrequently and the interest rate includes a liquidity premium. This liquidity premium reflects the relatively high costs (including the impact on price) of selling a position

Question 32

A bank quotes a stated annual interest rate of 4.00%. If that rate is equal to an effective annual rate of 4.08%, then the bank is compounding interest:

A daily.
B quarterly.
C semiannually

Answer 32

A is correct. The effective annual rate (EAR) when compounded daily is 4.08%.
EAR = (1 + Periodic interest rate)m – 1
EAR = (1 + 0.04/365)365 – 1
EAR = (1.0408) – 1 = 0.04081 ≈ 4.08%

Question 33

18. A perpetual preferred stock makes its first quarterly dividend payment of $2.00 in five quarters. If the required annual rate of return is 6% compounded quarterly, the stock’s present value is closest to:

A $31.
B $126.
C $133.

Answer 33

B is correct. The value of the perpetuity one year from now is calculated as:
PV = A/r, where PV is present value, A is annuity, and r is expressed as a quarterly required rate of return because the payments are quarterly.
PV = $2.00/(0.06/4)
PV = $133.33.
The value today is (where FV is future value)
PV = FVN(1 + r)–N
PV = $133.33(1 + 0.015)–4
PV = $125.62 ≈ $126