Ch.7 The Time Value of Money Goals: Concept of the time value of money

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) = $399.27 3-2) 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 $10500. 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 125000 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 125000 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

Ch.7 The Time Value of Money Goals: Concept of the time value of money