Ch.7 The Time Value of Money Goals: Concept of the time value of money Present value and Future value Cash flows and time value calculation Compounding Schemes

Why we need FV and PV concepts? 1. Future value FV=PV*(1+r)^t Built in function: Fv(Rate, NPer, PMt, PV, Type) here rate : interest rate, NPer : total number of periods, PV: present value, PMt (0) and Type ( 0 =end and 1 =beginning) are used for annuities.

EX) deposit $1000 in a saving account with 10 % interest. FV? 2. Present Value PV=FV/((1+r)^t) Pv(Rate, NPer, PMt, FV, Type) Ex) How much you have to deposit on a saving account with 10% interest, if you want to receive $1100 in a year

3. Annuities: Equal payment, equally spaced in time. Ex) Car loans, Mortgage loans 3-1) PV of Annuity

Ex) You are supposed to need $100 at the end of each year for next 5 years. How much you have to deposit now in a saving account with 8% interest? PV(Rate, Nper, Pmt, FV, Type) To deal with a single payment in previous slides, we assume “0” for Pmt and Type. However, in annuity calculations, Pmt means the equal dollar amounts paid or given.

PV(8%, 5, 100,0,0) = $ ) FV of Annuity

Ex) if you deposit $2000 each year into your IRA (Individual Retirement Account with 7.5%), how much will you have after 30 years? FV(Rate, Nper, Pmt, PV, Type) 3-3) Solving for the Annuity Payment Pmt(Rate, NPer, PV, FV, Type) Ex) How much you have to deposit in a saving account with 5% to have $10000 in 5 years?

3-4) Solving for the number of periods NPer(Rate, Pmt, PV, FV, Type) Ex) You are supposed to need $10000 in future. To deal with this, you want to use a saving accounts with 4% interest. And you are planning to deposit $1846 every year. How long it will take to make $10000?

3-5) Solving for Interest rate in annuity Rate(Nper, Pmt, PV, FV, Type, Guess) Ex) You are supposed to have an offer to purchase an investment which will provide cash flows of $1500 per year for ten years. The cost of purchasing this investment is $ What is the return (rate) of this offer?

4. Deferred Annuities Annuity that won’t happen until a certain time. Ex) You will retire 30 years from now and will require income of per year during retirement. And you will need retirement income for 35 years and expect to earn 6% per year. How much you have to invest now, if you can earn 8% per year before retirement?

4-1) Graduated Annuity Annuity would change by % due to an expected inflation. Ex) You will retire 30 years from now and will require income of per year during retirement. And you will need retirement income for 35 years and expect to earn 6% per year. Three percent of growth in your annual retirement income is expected due to an 3% annual inflation. How much you have to invest now, if you can earn 8% per year before retirement?

5. Uneven Cash Flow Streams : Cash flows are different in each period. Therefore PV and FV functions can’t be used. We have to calculate individual PVs or FVs and then sum them up to come up with total PV or FV. 5-1) PV and FV NPV(Rate, Value1, Value2,….)

5-2) Yield for Uneven Cash Flow Stream IRR(Values, Guess) 5-3) Loan payment Ex) You are supposed to borrow $400 and promise to pay $100 per year for next 5 years. Pls generate your loan (schedule) table. 6. Non-annual Compounding Periods