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Lecture

TIME VALUE OF MONEY

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Department
Business
Course
BU111
Professor
Sofy Carayannopoulos
Semester
Fall

Description
Keith Diaz Time value of money  The dollar one year from today is worth less than the dollar today, because of 1. Risk: a dollar today is certain, whereas a dollar later may not materialize due to reduction 2. Real interest: interest before we consider inflation 3. Inflation: it is worth more today because inflation reduces buying power  Concept important to leases, mortgages, bonds, retirement contributions, stock valuation, etc.  Compounding interest means you calculate the interest not just on the dollar amount (base) but also on any other interest accumulated Single Amount – Future Value (FV) - r = interest or discount rate - PMT = amount of payment - N = number of periods in years Example: what will you have in 3 years if you deposit $100 into an account that earns 4% interest compounded annually? - r = 0.04 - PMT = $100 - N = 1 Example: how much money will you have in 5 years if you deposit $200 into an account that earns 3% compounded annually? Single Amount – Present Value (PV) Example: how much do you have to deposit today to have $100 in a year (assume 4% interest compounded annually?)  What’s the PV of $100 to be received in 1 year (assume 4% discount 1rate) = $96.15 Example: how much money do you have to deposit today to have $100 after 3 years (assuming 4% interest compounded annually)? Example: how much do you have to deposit today to have $3000 four years from now (assuming a 5% discount rate)? = $2468.11 Keith Diaz Multiple Amounts – Future Value (FV)  Annuity: multiple payments of the same value, equally apart from each other in time [ ]  used when you deposit starting at the end of this year [ ]  used when you deposit starting today, time zero Example: What will you have after 3 years if you deposit $100 each year for 3 years (beginning at the end of this year) into an account that earns 4% interest compounded annually? [ ] = $312.16 Example: what will you have after 3 years if you deposit $100 each year for 3 years (starting today) into an account today that earns 4% interest compounded annually? [ ] = $324.65 Example: how much must we put into an account each year earning 4% if we want to have $20 000 at the end of 10 years? [ ]  [ ] [ ]  If question doesn’t mention if the deposit is today, assume it is in the future and usordinaryannuity Multiple Amounts – Present Value (PV) [ ] use if starting at end of year [ ]  use if starting today  One less period if you use annuity due than if you use ordinary annuity, during which your money accumulates interest before starting your withdrawals Example: how big must your trust fund be today if you want to receive a payment of $500 each year for the next 3 years? Assume an interest/discount rate of 4%.  1 1  PV ordinaryannuity00   3 0.04 0.04(10.04)  = $1387.55 Keith Diaz Example: you borrowed $20 000 to fund your education. How big will you educational loan payment be if you want to have the loan paid off in 4 years, you make the first payment at the end of this year, and the discount rate is 3%? [ ] [ ] PMT = 5380.54 Example: how big must your trust fund be today if you want to receive a payment of $500 each year for the next 3 years starting today? Assume an interest/discount rate of 4%. [ ] = $1443.05 Combinations example Example: how much would you pay for an investment that will give you $1000 after 4 years and a payment of $50 a year as well? Assume 3% interest compounded annually. [ ] + = [ ] = 1074.34 Perpetuity  Annuity that goes on forever (ex: dividend on a preferred share) Example: what is the value of an investment in a 5% preferred with a par value of $12 if interest rates are 3%? Payment and compounding periods  Payment and interest periods are not always the same  Always multiply “n” (number of years) by number of payments per year - n must always represent the number of payments you give/receive over the time of the investment period  Adjust compounding rate to match payment frequency (r must match n)  this is your new “r” - If payment and interest periods are the same, but more than once per year (or single payment but compounding more than once a year), divide r by the number of payments per year Keith Diaz Example: what is the present value of 4 years of $50 payments received every 6 months and compounded semi-annually at 3%? - Payment = $50 -
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