Topic 4 - Time Value Money And DCF Flashcards
What is the time value of money?
The principle that money today is worth more than the same amount in the future due to its potential earning capacity.
What is present value?
The current worth of a future sum of money given a specific rate of return.
What is future value?
The value of a current asset at a future date based on an assumed rate of growth.
What is compounding?
The process of earning interest on both the initial principal and the accumulated interest from previous periods.
What is discounting?
The process of determining the present value of a future amount by applying a discount rate.
What is a discount rate?
The interest rate used to calculate the present value of future cash flows.
What is an annuity?
A series of equal payments made at regular intervals over a period of time.
What is a perpetuity?
A series of equal payments made at regular intervals that continue indefinitely.
What is the formula for the present value of a perpetuity?
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.
What is the formula for future value with compounding interest?
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.
What is the formula for present value with discounting?
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.
What is the difference between simple interest and compound interest?
Simple interest is calculated only on the principal, while compound interest is calculated on the principal and previously earned interest.
What is an ordinary annuity?
An annuity where payments are made at the end of each period.
What is an annuity due?
An annuity where payments are made at the beginning of each period.
What is the formula for the future value of an annuity?
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.
What is the formula for the present value of an annuity?
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.
What is the difference between nominal and real interest rates?
Nominal interest rates do not account for inflation, while real interest rates are adjusted for inflation.
What is the effective annual rate (EAR)?
The annual rate of interest that accounts for compounding within the year.
What is the formula for the effective annual rate (EAR)?
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%.
What is the present value of a lump sum?
The value today of a single future payment, discounted at the appropriate rate.
What is the future value of a lump sum?
The value at a specific future date of a single payment made today, grown at the appropriate rate.
How does an increase in the discount rate affect present value?
An increase in the discount rate decreases the present value of future cash flows.
What is the rule of 72?
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.
What is continuous compounding?
A scenario where interest is compounded an infinite number of times per year, rather than a finite number.
What is the formula for future value with continuous compounding?
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.
What is the present value of an uneven cash flow stream?
The sum of the present values of each individual cash flow in the stream, discounted at the appropriate rate.
What is the future value of an uneven cash flow stream?
The sum of the future values of each individual cash flow in the stream, compounded at the appropriate rate.
How does an increase in time affect future value?
An increase in time generally increases future value due to the effect of compounding.
How does an increase in time affect present value?
An increase in time generally decreases present value as future cash flows are discounted more.
What is an interest-only loan?
A loan where the borrower pays only interest during the loan term, with the principal repaid at the end.
What is an amortizing loan?
A loan where the borrower repays both interest and principal in each payment.
What is the present value of a growing perpetuity?
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.
What is the present value of a growing annuity?
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.
What is the future value of a growing annuity?
FV = C * [(1 + r)^n - (1 + g)^n] / (r - g)
What is the present value of a growing annuity?
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.
What is the future value of a growing annuity?
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.
What is a zero-coupon bond?
A bond that pays no periodic interest but is issued at a discount and repays the face value at maturity.
What is the time value of money’s role in bond pricing?
Bond prices reflect the present value of future cash flows (coupon payments and principal repayment) discounted at the market interest rate.
How does compounding frequency affect future value?
More frequent compounding increases future value as interest is earned on previously earned interest more often.
How does compounding frequency affect present value?
More frequent compounding decreases present value, as future cash flows are discounted more frequently.
What is a deferred annuity?
An annuity where the payments begin at a future date, rather than immediately or within one period.
What is the present value of a deferred annuity?
The present value of an annuity that starts payments at a future date, discounted to the present day.
What is the present value of a growing perpetuity?
PV = C / (r - g)
C is the first cash flow, r is the discount rate, and g is the growth rate.
What is a sinking fund?
A sinking fund is a reserve set aside by the bond issuer to repay the bond at maturity or to buy back bonds early.
What is the difference between ordinary annuity and annuity due?
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.
What is the future value of a lump sum?
The amount that a present sum of money will grow to in the future at a specified interest rate.
What is an effective interest rate?
The actual interest rate when compounding is considered.
What is a nominal interest rate?
The stated interest rate before adjusting for compounding or inflation.
What is simple interest?
Interest calculated only on the principal amount of a loan or deposit.
How do interest rates affect the time value of money?
Higher interest rates increase future value and decrease present value.
What is a cash flow stream?
A series of cash inflows and outflows over a period of time.
What is the difference between a lump sum and an annuity?
A lump sum is a one-time payment, while an annuity is a series of equal payments over time.
