Financial Math Flashcards
What is the basic rule of financial math?
you can only compare/combine cash-flows when they are in the same point in time
What types of cash-flows are there?
Inflows (positive) and outflows (negative)
Why do we use the future-value formula?
To move one cash-flow forward in time (cash-flow needs to be compounded).
Why do we use the present-value formula?
To move one cash-flow back in time (cash-flow needs to be discounted).
What are the conditions for the present-value and future-value formulas?
1) T>t
2) the end of the periods are counted in the same frequency as the discount/compounding rate
What is the formula of a future stream of cash-flows?
T∑i=t CFi/(1 + r)^(i-t)
What is the formula of a present value of a stream of future cash-flows and its condition?
PV=T∑i=t CFt/(1 + r)^t
The 1st element must already be at time 0.
What is the Net Present Value?
The NPV is a tool that allows us to evaluate the quality of a potential investment. It represents the wealth creation associated with the project’s implementation.
NPV0 = PV(Future Benefits) - PV(Future Costs)
What is the Net Present Value’s formula?
NPV = -I0 + T∑t=1 CFt/(1 + r)^t
(I0 initial investment)
What is the Net Present Value’s formula in excel?
NPV(rate, value 1, [ value 2],…) and then subtract the initial investment
rate is the rate of discount, only 1st value is required
When should we use perpetuities and annuities?
We use perpetuities and annuities when cash-flows follow a regular pattern.
What is a perpetuity?
A perpetuity is an infinite sequence of cash-flows with a constant growth rate (positive, negative or zero).
What is the formula for the perpetuity?
Vt-1 = CFt/(r-g)
What are the conditions to use the perpetuity formula?
1) r>g
2) r and g need to be in the same frequency as the sequence of cash-flows
3) r and g need to be constant
4) the only cash-flow to insert is the same
What is the formula to find one cash-flow knowing another one?
CFT = CFt * (1 + g)^(T-t)
if g is constant
What is an annuity?
An annuity is a finite sequence of cash-flows with a constant growth rate (positive, negative or zero).
What is the formula for annuities?
Vt-1 = CFt/(r - g) * [ 1- ((1+ g)/(1 + r))^N]
How do you calculate N?
N = Last - First + 1
What are the conditions to use the annuity’s formula?
1) only cash-flow you insert is the first
2) r and g need to be constant
3) r is different from g
4)r and g need to be in the same frequency as the cash-flows
How can you decompose the annuity’s formula?
V0(Annuity) = V0(Perpetuity) - ((1 + g)/(1 + r))^N * V0(Perpetuity)
What is the annuity’s formula in Excel?
PV(rate, nper, pmt, [ fv])
rate is the interest rate
nper is the number of payments
pmt is the payment each period (g needs to be 0)
fv is optional and it means the cash balance you want to attain after the last payment is made
What is the excel formula to find a cash-flow within an annuity?
PMT(rate, nper, pv, [ fv])
nper is the number of payments
pv is the present value of the annuity
fv is optional and it means the cash balance you want to attain after the last payment is made
What is an effective interest rate?
An interest rate that incorporates compounded interest.
What is an annual percentage rate (APR)?
Interest rates that only incorporate simple interest and not compounded interests.
What is the most used effective rate?
Effective Annual Rate (EAR), which indicates the total amount of interest that will be earned at the end of one year (including simple interest and interest-on-interest).
What is the assumption made to compare different rates?
The investor can renew these deposits indefinitely and, if they mobilise the money before the deposit expires, they get all the respective interests up to the mobilisation date.
What is the formula to find interest-on-interest?
Interest-on-Interest = FV - Principal - Simple Interest
What are the main formulas for loan exercises?
1) Paymentt = Interestt + ∆Principalt
2) Interest t = r * Principalt-1
What is the main formula for savings/payments exercises?
V(Savings) = V(Payments)
True or false: The annuity formula always brings the value of a finite sequence back one year in
respect to the first cash-flow of that sequence.
False
True of false: The same APR for difference compounding frequencies generates different effective
annual rates.
True
True of false: In a bank loan with constant payments, the fraction of the principal repaid is always
constant.
False
True or false: In a bank loan, the principal left to pay is given by the present value of all payments
counted from when the agent asked for the loan.
False
True or false: In a bank loan, interest payments equal the interest rate times the principal left to pay
in the previous period.
True
True or false: The annuity formula moves the value of a finite sequence of cash-flows to time 0.
False
True or false: The annuity formula moves the value of a finite sequence of cash-flows to the period before the first cash-flow of that sequence.
True
True or false: The annuity formula uses the variable “N”. N stands for the number of periods between the first and last cash-flows.
False
True or false: The annuity formula cannot be applied if the growth rate among cash-flows is changing.
True
True or false: The “=NPV(.)” formula in Excel does not include the initial investment.
True
True or false: The “=PV(.)” formula in Excel can be used to find the value of a perpetuity today.
False
True or false: The “=PV(.)” formula in Excel can be used to find the value of an annuity today.
False
When given the growth rate of purchasing power and the inflation rate, how do you calculate the annuity’s formula?
(1 + gpp) * (1 + i) -1
how do you calculate the growth when you have the inflation and purchasing power?
1 + g = (1 + pp) * (1 + i)
don’t forget everything needs to be in the same frequency
