Time Value of Money Flashcards
(47 cards)
What is the Time Value of Money (TVM)?
The principle that a dollar today is worth more than a dollar in the future due to inflation and opportunity cost. Money can earn interest over time.
Why is the Time Value of Money important in finance?
It allows us to compare cash flows across different times by discounting or compounding them, helping with investment, loan, and valuation decisions.
What is a timeline and why is it useful?
A timeline is a visual representation of cash flows at different points in time. It helps organise and solve TVM problems by showing when each cash flow occurs.
What is the formula for future value (FV) of a single cash flow?
FV n=C×(1+r)^n
What is the formula for present value (PV) of a future cash flow?
PV = C/(1+r)^n
What are the rules for valuing cash flows?
Only compare/combine cash flows at the same point in time.
Use compounding to calculate future value.
Use discounting to calculate present value.
What is a perpetuity?
A stream of equal cash flows that continues forever.
Formula: PV= C/r
Example of a perpetuity:
To endow a $30,000 yearly graduation party at 8% interest, donate:
PV= 30,000/0.08=375,000
What is an annuity?
A stream of equal cash flows over a fixed number of periods. Types:
Ordinary Annuity (payments at end)
Annuity Due (payments at beginning)
Deferred Annuity (starts in future)
PV of an ordinary annuity formula?
PV=C×[(1-(1+r)^-n)/r]
FV of an annuity formula?
FV = C(((1+r)^n)-1)/r
Lottery example—Which is better: $30M over 30 years or $15M now at 8% interest?
PV=1M+1M×[ (1−(1+0.08) ^−29)/0.08]=12.16M
Retirement example—Saving $10,000 annually for 30 years at 10%?
FV=10,000×[ ((1.10) ^30−1/0.10]=1.645M
What is a growing perpetuity? Formula?
A perpetuity with payments growing at constant rate
PV=C/r-g
Growing perpetuity example—Party cost grows at 4% per year, interest is 8%, C = $30,000. What is PV?
PV=
30,000/(0.08−0.04) =750,000
What is a growing annuity?
A fixed-length stream of payments that grow at a constant rate.
PV=C×[ (1-((1+g)/(1+r))^n)/(r-g)]
Growing annuity example—Save $10,000 in first year, increase by 5% annually for 30 years, r = 10%. What is PV and FV?
PV = 10,000×15.0463=150,463
FV = 150,463×(1.10) ^30=2.625M
How do you adjust for non-annual cash flows (e.g. monthly)?
Use monthly rate = annual rate/12
Use number of months:
n=years×12
Credit card example—2% monthly interest, $1,000 balance, no payments for 6 months. What is balance in 6 months?
FV=1,000×(1.02)^6=$1,126.16
What is the Time Value of Money (TVM)?
TVM is the concept that money available today is worth more than the same amount in the future due to its potential earning capacity. This is influenced by inflation and opportunity cost.
Why is $1 today worth more than $1 in the future?
Because you can invest it and earn interest, or inflation may reduce future purchasing power.
What is the purpose of a timeline in TVM problems?
A timeline helps visualize the timing and amount of cash flows, making it easier to calculate present or future values.
What are the three rules for valuing cash flows?
Only compare/combine cash flows at the same point in time.
Future value (FV) is found by compounding: FVₙ = C × (1 + r)ⁿ
Present value (PV) is found by discounting: PV = C / (1 + r)ⁿ
How do you calculate the FV of multiple cash flows?
Compute the FV of each cash flow separately (using compounding), then add them together at the same future point.
