Finance - Time value of money Flashcards
Explain the concept of the “time value of money”
- It is used for decisions related to capital budgeting (Ex. IRR, NPV)
-Can also assess many Financial reporting issues: Recoverability of the asset impairment, FV of pension asset and pension obligation, PV of asset retirement obligation
What is compounding and provide three types of periods
Compounded interest - is interest that is earned on interest accumulated in the prior period
Ex. monthly, semi-annually, quarterly
Quoted rate (stated or nominal rate) - Quoted as an annual rate and not adjusted for compounding
What is the formula for effective annual interest rate and what is it used for
EAR - annual rate of interest compounded annually made equivalent to an interest that is compounded over some period other than annually
Formula = (1+r/n)^n-1
r= quoted rate n = # of compounded period
- The higher number of periods of compounding during the year, higher EAR given same quoted rate
Explain what present value is and the formula to calculate present value
- Present value is the value of a dollar today in the future discounted at a specified interest rate
Formula = PV = FV/ (1+r))^n
r= quoted rate n = # of compounded period
Can use three types of methods to calculate: Financial Calculator, excel, formula
What is the difference between an ordinary annuity, annuity due, and perpetuity ? In addition, provide the formula to calculate
Ordinary annuity - Where payments are made at the end of the period
PV= PMT ((1/i)- 1/i(1+i)^n)) i= discount rate
-The higher PV occurs because discount period is shorted by accelerating the payment
Annuity due - Where payment are made at the beginning of the period
PV = PMT + PMT((1/i)- 1/i(1+i)^(n-1))
- Annuity due has payment made at time and then will be n-1 payment since last period is not included
Perpetuity - is where cash flow will never end
PV= PMT/i
PV= PMT/ i-g
g= Growth in perpetuity constantnt
How does the PV of an annuity for a single payment at the end, additional payment not at the end and when an annuity starts at a later date
- PV annuity with single payment at the end is the lump sum amount at the end of the entire investment used on excel. Made in two parts - PV of ordinary annuity and PV of single payment
- Annuity with additional payment not at the end - The PV of the lump sum payment must be separately calculated from recurring payment * use excel
- PV annuity start at a later date
- Cash flow of annuity do not begin in first year, two calculations to be performed
- Annuity payment need to be discounted back to the time it begin
- Value of this amount needs to be discounted back to present time
What is future value and how is it calculated
- FV is cash flow at a specific date in the future given a specified interest rate
- Determines how much cash must be invested each period to have a certain amount at a specified date in the future
Formula = FV = PV*(1+r)^n
r= discounted rate n = number of periods
Ordinary annuity FV
- FV= PMT ((1+r)^n -1 /r)
Explain how mortgage rates are calculated and provide the formula used
Mortgage uses the EAR to calculate mortgage at compounded semi-annually and then monthly
Step 1: EAR = (1+0.7 /2)^2 -1 = 7.12%
Step 2: Effective monthly rate = (1+.0712)^(1/12) - 1 = .575%
- Monthly payments are calculated based on the amortization period to maturity, even though the mortgage contract will be for a much longer shorter period
Explain inflation and real rate of return
Inflation - erodes the spending power of a dollar over time making it worth less in the future
Cuases a rise in price of goods and service and reduces the real value of money over time
Real rate of return - return after the adjustment of inflation
Fisher effect - formula used to relate the real rate of return and nominal rate of return
(1+inflation rate ) * (1+ real rate of return) = (1+ nominal rate of return)
Deflation - rate at which the general level of prices for goods and services are declining and subsequently, purchasing power is increased
