Reading 6: Time Value of Money

Question 1

Required Rate of Return

Answer 1

Return (Interest Rate) that investors and savers require for them to willingly lend their funds I.e. “The Equilibrium Interest Rate”

Question 2

Discount Rates

Answer 2

The interest rate used to discounts payments/cash flows to be made/received in the future to get to their equivalent value in current dollars

Question 3

Opportunity Cost

Answer 3

The opportunity forgone when current consumption is chosen rather than saving.

Question 4

Real Risk Free Rate

Answer 4

Theoretical rate of a single-period loan that has no expectation of inflation on it

Question 5

Real Rate of Return

Answer 5

Investors increase in purchasing power (after adjusting for inflation)

Question 6

Nominal Risk-Free Rates

Answer 6

Real risk-free rate + expected inflation rate (e.g. U.S Treasury Bills – T-Bills) (Note that this is an approximate relationship)

Question 7

Default Risk

Answer 7

The risk that a borrower will not make the promised payments in a timely manner

Question 8

Liquidity Risk

Answer 8

The risk of receiving less than fair value for an investment if it must be sold for cash

Question 9

Maturity Risk:

Answer 9

Prices of long-term bonds are more volatile than shorter-term bonds. Longer-term bonds have more maturity risk and require a maturity risk premium

Question 10

Required Interest Rate on a Security (Required Rate of Return)

Answer 10

Nominal risk-free rate +
Default risk premium +
Liquidity premium +
maturity risk premium

Question 11

Effective Annual Rate (Definition)

Answer 11

Annual rate of return actually being earned after adjustments have been made for different compounding periods

Question 12

Effective Annual Rate (Formula)

Answer 12

EAR = (1+Periodic Rate)m - 1
Periodic Rate = stated annual rate/m
M = number of compounding periods per year

Question 13

What happens to EAR as compounding frequency increases?

Answer 13

EAR increases as the compounding frequency increases

Question 14

Continuous Compounding (Definition)

Answer 14

The limit of shorter and shorter compounding periods i.e. the mathematical limit that compound interest can reach

Question 15

Continuous Compounding (Formula)

Answer 15

Er - 1 = EAR

Question 16

Future Value (Definition)

Answer 16

Amount to which a current deposit will grow when it is placed in an account paying compound interest

Question 17

Future Value (Formula) (“Future Value Factor”)

Answer 17

FV = PV(1+I/Y)N

Question 18

Present Value (Definition)

Answer 18

Today’s value of a cash flow that is to be received at some point in the future

Question 19

Present Value (Formula) (“Present Value Factor”)

Answer 19

PV = FV/(1+1/Y)N

Question 20

Discounting

Answer 20

The process of finding the present value of a cash flow i.e. future cash flows are discounted back to the present (also known as opportunity cost, discount rate, required rate of return, cost of capital)

Question 21

Annuities

Answer 21

Stream of equal cash flows that occur at equal intervals over a given period

Question 22

What are the two types of Annuities? Define.

Answer 22

1. Ordinary Annuity: The most common type and characterized by cash flows that occur at the end of each compounding period (Typical cash flow pattern for many investment and business finance applications)
2. Annuities Due: Payments/receipts that occur at the beginning of each period

Question 23

Present Value of an Ordinary Annuity

Answer 23

The collective present value of a stream of cash flows that occur at the end of each compounding period over a stated number of periods

Question 24

Future Value of an Annuity Due (FVAd)

Answer 24

FVAo x (1+I/Y) (Because FV is calculated at the end of a period whereas Annuities Due is made at the beginning of the period)

Question 25

Present Value of an Annuity Due (PVAd)

Answer 25

PVAo x (1+I/Y)

Question 26

Perpetuity (Definition)

Answer 26

A financial instrument that pays a fixed amount of money at set intervals over an infinite amount of time (Perpetual Annuity)

Question 27

Perpetuity (Examples)

Answer 27

(1) British Consol Bonds
(2) Preferred Stock

As they promise fixed interest or dividend payments forever

Question 28

PV of a Perpetuity (Formula)

Answer 28

PV = PMT/I/Y

Question 29

I/Y of a Perpetuity (Formula)

Answer 29

I/Y = PMT/PV

Question 30

PV of a Perpetuity (Definition)

Answer 30

PV of a Perpetuity is its value one period before the first payment i.e. if the first dividend payment occurs at Y4 then the PV will be as of Y3. The “N” variable will therefore be one less

Question 31

Uneven Cash Flows

Answer 31

Stream of annual single sum cash flows (Sum of all the PVs/FVs of each individual cash flow)

Question 32

Uneven Cash Flows (Calculator Methodology)

Answer 32

Use the CF Function

Question 33

TVM Problems when compounding periods are other than annual

Answer 33

m =  # of compounding periods per year
I/Y = Annual Interest / m
N = # of compounding periods

Question 34

Loan Amortization

Answer 34

The process of paying off a loan with a series of periodic loan payments, whereby a portion of the loan is paid off, or amortized, with each payment

Question 35

Loan Amortization (Characteristics of Payment)

Answer 35

Size of the payment remains fixed over the course of the loan (monthly, quarterly or annually). However, the portion of the principal/interest component of the loan does not remain fixed.

Question 36

Funding a Future Obligation (Common Examples)

Answer 36

1. Funding program for future college tuition

2. Funding a retirement program

Question 37

Cash Flow Additivity Principle

Answer 37

Present value of any stream of cash flows equals the sum of the present values of the cash flows

Question 38

Compound Annual Growth Rate (Methodology)

Answer 38

If given a dividend/payment at t=0 and a dividend at t=x, then you can use t=0 as the PV and t=x as the FV and solve for I/Y on the calculator