Topic 4 - Time Value Money And DCF

Question 1

What is the time value of money?

Answer 1

The principle that money today is worth more than the same amount in the future due to its potential earning capacity.

Question 2

What is present value?

Answer 2

The current worth of a future sum of money given a specific rate of return.

Question 3

What is future value?

Answer 3

The value of a current asset at a future date based on an assumed rate of growth.

Question 4

What is compounding?

Answer 4

The process of earning interest on both the initial principal and the accumulated interest from previous periods.

Question 5

What is discounting?

Answer 5

The process of determining the present value of a future amount by applying a discount rate.

Question 6

What is a discount rate?

Answer 6

The interest rate used to calculate the present value of future cash flows.

Question 7

What is an annuity?

Answer 7

A series of equal payments made at regular intervals over a period of time.

Question 8

What is a perpetuity?

Answer 8

A series of equal payments made at regular intervals that continue indefinitely.

Question 9

What is the formula for the present value of a perpetuity?

Answer 9

PV = C / r, where C is the cash flow per period and r is the discount rate.

Example sentence: If the cash flow per period is $100 and the discount rate is 5%, the present value would be $2,000.

Question 10

What is the formula for future value with compounding interest?

Answer 10

FV = PV * (1 + r)^n, where PV is the present value, r is the interest rate, and n is the number of periods.

Example sentence: If the present value is $1,000, the interest rate is 3%, and there are 5 periods, the future value would be $1,159.27.

Question 11

What is the formula for present value with discounting?

Answer 11

PV = FV / (1 + r)^n, where FV is the future value, r is the interest rate, and n is the number of periods.

Example sentence: If the future value is $5,000, the interest rate is 4%, and there are 3 periods, the present value would be $4,310.34.

Question 12

What is the difference between simple interest and compound interest?

Answer 12

Simple interest is calculated only on the principal, while compound interest is calculated on the principal and previously earned interest.

Question 13

What is an ordinary annuity?

Answer 13

An annuity where payments are made at the end of each period.

Question 14

What is an annuity due?

Answer 14

An annuity where payments are made at the beginning of each period.

Question 15

What is the formula for the future value of an annuity?

Answer 15

FV = C * [(1 + r)^n - 1] / r, where C is the payment per period, r is the interest rate, and n is the number of periods.

Example sentence: If the payment per period is $200, the interest rate is 6%, and there are 4 periods, the future value would be $902.36.

Question 16

What is the formula for the present value of an annuity?

Answer 16

PV = C * [1 - (1 + r)^-n] / r, where C is the payment per period, r is the interest rate, and n is the number of periods.

Example sentence: If the payment per period is $150, the interest rate is 4%, and there are 6 periods, the present value would be $774.83.

Question 17

What is the difference between nominal and real interest rates?

Answer 17

Nominal interest rates do not account for inflation, while real interest rates are adjusted for inflation.

Question 18

What is the effective annual rate (EAR)?

Answer 18

The annual rate of interest that accounts for compounding within the year.

Question 19

What is the formula for the effective annual rate (EAR)?

Answer 19

EAR = (1 + r/n)^n - 1, where r is the nominal interest rate and n is the number of compounding periods per year.

Example sentence: If the nominal interest rate is 8% and there are 4 compounding periods per year, the effective annual rate would be 8.39%.

Question 20

What is the present value of a lump sum?

Answer 20

The value today of a single future payment, discounted at the appropriate rate.

Question 21

What is the future value of a lump sum?

Answer 21

The value at a specific future date of a single payment made today, grown at the appropriate rate.

Question 22

How does an increase in the discount rate affect present value?

Answer 22

An increase in the discount rate decreases the present value of future cash flows.

Question 23

What is the rule of 72?

Answer 23

A quick formula to estimate the number of years required to double an investment at a given annual rate of return. Divide 72 by the interest rate.

Question 24

What is continuous compounding?

Answer 24

A scenario where interest is compounded an infinite number of times per year, rather than a finite number.

Question 25

What is the formula for future value with continuous compounding?

Answer 25

FV = PV * e^(r * t), where e is the base of the natural logarithm, r is the interest rate, and t is time.

Example sentence: If the present value is $500, the interest rate is 2%, and the time is 3 years, the future value would be $530.58.

Question 26

What is the present value of an uneven cash flow stream?

Answer 26

The sum of the present values of each individual cash flow in the stream, discounted at the appropriate rate.

Question 27

What is the future value of an uneven cash flow stream?

Answer 27

The sum of the future values of each individual cash flow in the stream, compounded at the appropriate rate.

Question 28

How does an increase in time affect future value?

Answer 28

An increase in time generally increases future value due to the effect of compounding.

Question 29

How does an increase in time affect present value?

Answer 29

An increase in time generally decreases present value as future cash flows are discounted more.

Question 30

What is an interest-only loan?

Answer 30

A loan where the borrower pays only interest during the loan term, with the principal repaid at the end.

Question 31

What is an amortizing loan?

Answer 31

A loan where the borrower repays both interest and principal in each payment.

Question 32

What is the present value of a growing perpetuity?

Answer 32

PV = C / (r - g), where C is the first cash flow, r is the discount rate, and g is the growth rate of the cash flows.

Example sentence: If the first cash flow is $150, the discount rate is 6%, and the growth rate is 3%, the present value would be $3,000.

Question 33

What is the present value of a growing annuity?

Answer 33

PV = C * [1 - ((1 + g) / (1 + r))^n] / (r - g), where C is the cash flow, r is the discount rate, g is the growth rate, and n is the number of periods.

Example sentence: If the cash flow per period is $100, the discount rate is 5%, the growth rate is 2%, and there are 5 periods, the present value would be $421.51.

Question 34

What is the future value of a growing annuity?

Answer 34

FV = C * [(1 + r)^n - (1 + g)^n] / (r - g)

Question 35

What is the present value of a growing annuity?

Answer 35

PV = C * [1 - ((1 + g) / (1 + r))^n] / (r - g)

C is the cash flow, r is the discount rate, g is the growth rate, and n is the number of periods.

Question 36

What is the future value of a growing annuity?

Answer 36

FV = C * [(1 + r)^n - (1 + g)^n] / (r - g)

C is the cash flow, r is the interest rate, g is the growth rate, and n is the number of periods.

Question 37

What is a zero-coupon bond?

Answer 37

A bond that pays no periodic interest but is issued at a discount and repays the face value at maturity.

Question 38

What is the time value of money’s role in bond pricing?

Answer 38

Bond prices reflect the present value of future cash flows (coupon payments and principal repayment) discounted at the market interest rate.

Question 39

How does compounding frequency affect future value?

Answer 39

More frequent compounding increases future value as interest is earned on previously earned interest more often.

Question 40

How does compounding frequency affect present value?

Answer 40

More frequent compounding decreases present value, as future cash flows are discounted more frequently.

Question 41

What is a deferred annuity?

Answer 41

An annuity where the payments begin at a future date, rather than immediately or within one period.

Question 42

What is the present value of a deferred annuity?

Answer 42

The present value of an annuity that starts payments at a future date, discounted to the present day.

Question 43

What is the present value of a growing perpetuity?

Answer 43

PV = C / (r - g)

C is the first cash flow, r is the discount rate, and g is the growth rate.

Question 44

What is a sinking fund?

Answer 44

A sinking fund is a reserve set aside by the bond issuer to repay the bond at maturity or to buy back bonds early.

Question 45

What is the difference between ordinary annuity and annuity due?

Answer 45

In an ordinary annuity, payments are made at the end of each period. In an annuity due, payments are made at the beginning of each period.

Question 46

What is the future value of a lump sum?

Answer 46

The amount that a present sum of money will grow to in the future at a specified interest rate.

Question 47

What is an effective interest rate?

Answer 47

The actual interest rate when compounding is considered.

Question 48

What is a nominal interest rate?

Answer 48

The stated interest rate before adjusting for compounding or inflation.

Question 49

What is simple interest?

Answer 49

Interest calculated only on the principal amount of a loan or deposit.

Question 50

How do interest rates affect the time value of money?

Answer 50

Higher interest rates increase future value and decrease present value.

Question 51

What is a cash flow stream?

Answer 51

A series of cash inflows and outflows over a period of time.

Question 52

What is the difference between a lump sum and an annuity?

Answer 52

A lump sum is a one-time payment, while an annuity is a series of equal payments over time.