Time Value of Money : Introduction to Financial Planning Time Value of Money
Slide 2 : Introduction to Financial Planning Which of the two would you prefer?
Rs. 10000 now
OR
Rs. 10000 at the end of the year
Time Value of Money : Introduction to Financial Planning Time Value of Money The time value of money is one of the most important concepts in personal finance decision-making. Money does not have the same value over time as it earns interest & its value is diminished by inflation
Consequently,a rupee today is not the same as a rupee in the future.
Time Value of Money : Introduction to Financial Planning CF0 CF1 CF3 CF2 0 1 2 3 i% Tick marks at ends of periods, so Time 0 is today; Time 1 is the end of Period 1; or the beginning of Period 2. Time Lines Time Value of Money
Time line for a Rs.100 lump sum due at the end of Year 2. : Introduction to Financial Planning Time line for a Rs.100 lump sum due at the end of Year 2. 100 0 1 2 Year i% - 75
Time line for an ordinary annuity of Rs.100 for 3 years. : Introduction to Financial Planning Time line for an ordinary annuity of Rs.100 for 3 years. 100 100 100 0 1 2 3 i% - 220
What’s the FV of an initial Rs.100 after 3 years if i = 10%? : Introduction to Financial Planning What’s the FV of an initial Rs.100 after 3 years if i = 10%? FV = ? 0 1 2 3 10% Finding FVs (moving to the right
on a time line) is called compounding. -100
Slide 8 : Introduction to Financial Planning Mathematically: FV3 = PV(1+i)3
= 100(1.10)3
= 133.10. FVn = PV(1 + i)n.
Slide 9 : Introduction to Financial Planning Using a Spreadsheet …. Remember this sequence:
=XXX(Rate,Nper,PMT,PV,FV,Type)
To find FV ; FV will come in place of XXX
= FV(Rate, Nper, Pmt, PV)
= FV(10%, 3, 0, -100) = 133.10
What’s the PV of 100 due in 3 years if i = 10%? : Introduction to Financial Planning 10% What’s the PV of 100 due in 3 years if i = 10%? Finding PVs is discounting, and it’s the reverse of compounding. 100 0 1 2 3 PV = ?
Slide 11 : Introduction to Financial Planning Solve FVn = PV(1 + i )n for PV: PV = 100 1 1.10 = 100 0.7513 = 75.13. 3
Slide 12 : Introduction to Financial Planning Spreadsheet Solution Use the PV function: see spreadsheet.
= PV(Rate, Nper, Pmt, FV)
= PV(10%, 3, 0, 100) = -75.13
Slide 13 : Introduction to Financial Planning Finding the Time to Double 20% 2 0 1 2 ? -1 FV = PV(1 + i)n
2 = 1(1 + 0.20)n
(1.2)n = 2/1 = 2
nLN(1.2) = LN(2)
n = LN(2)/LN(1.2)
n = 0.693/0.182 = 3.8.
Slide 14 : Introduction to Financial Planning Spreadsheet Solution Use the NPER function:
= NPER(Rate, Pmt, PV, FV)
= NPER(20%, 0, -1, 2) = 3.8
Slide 15 : Introduction to Financial Planning Finding the Interest Rate ?% 2 0 1 2 3 -1 FV = PV(1 + i)n
2 = 1(1 + i)3
(2)(1/3) = (1 + i)
1.2599 = (1 + i)
i = 0.2599 = 25.99%.
Slide 16 : Introduction to Financial Planning Spreadsheet Solution Use the RATE function:
= RATE(Nper, Pmt, PV, FV)
= RATE(3, 0, -1, 2) = 0.2599
Slide 17 : Introduction to Financial Planning Ordinary Annuity PMT PMT PMT 0 1 2 3 i% PMT PMT 0 1 2 3 i% PMT Annuity Due What’s the difference between an ordinary annuity and an annuity due? PV FV
Time line for uneven CFs: -150 at t = 0 and 100, 75, and 50 at the end of Years 1 through 3. : Introduction to Financial Planning Time line for uneven CFs: -150 at t = 0 and 100, 75, and 50 at the end of Years 1 through 3. 100 50 75 0 1 2 3 i% -150
What’s the FV of a 3-year ordinary annuity of 100 at 10%? : Introduction to Financial Planning What’s the FV of a 3-year ordinary annuity of 100 at 10%? 100 100 100 0 1 2 3 10% 110
121
FV = 331
Slide 20 : Introduction to Financial Planning FV Annuity Formula The future value of an annuity with n periods and an interest rate of i can be found with the following formula:
Slide 21 : Introduction to Financial Planning Spreadsheet Solution Use the FV function: see spreadsheet.
= FV(Rate, Nper, Pmt, Pv)
= FV(0.10, 3, -100, 0) = 331.00
What’s the PV of this ordinary annuity? : Introduction to Financial Planning What’s the PV of this ordinary annuity? 100 100 100 0 1 2 3 10% 90.91 82.64 75.13 248.69 = PV
What’s the PV of this ordinary annuity? : Introduction to Financial Planning What’s the PV of this ordinary annuity? 100 100 100 0 1 2 3 10% 90.91 82.64 75.13 248.69 = PV
Slide 24 : Introduction to Financial Planning PV Annuity Formula The present value of an annuity with n periods and an interest rate of i can be found with the following formula:
Slide 25 : Introduction to Financial Planning Spreadsheet Solution Use the PV function: see spreadsheet.
= PV(Rate, Nper, Pmt, Fv)
= PV(10%, 3, 100, 0) = -248.69
Find the FV and PV if theannuity were an annuity due. : Introduction to Financial Planning Find the FV and PV if theannuity were an annuity due. 100 100 0 1 2 3 10% 100
Excel Function for Annuities Due : Introduction to Financial Planning Excel Function for Annuities Due Change the formula to:
=PV(10%,3,-100,0,1)
=FV(10%,3,-100,0,1)
End of SessionThank You : Introduction to Financial Planning End of SessionThank You