Download presentation

Presentation is loading. Please wait.

Published byMichaela Ackerman Modified over 2 years ago

1
Management 3 Quantitative Methods The Time Value of Money Part 2

2
Scenario #2 – the PVof a series of future deposits We can trade single sums of money today (PV) for multiple payments (FV’s) paid-back periodically in the future: a)Borrow today (a single amount) and make payments (periodically in the future) to repay the Loan.

3
Annuities An annuity is a “fixed” periodic payment or deposit: 1.$ 1,000 per year/month for 36 months. These payments can be made at the beginning, or at the end, of the financing period: a)Annuities “Due” are payments made at the beginning of the period; b)“Ordinary” Annuities are payments made at the end.

4
Annuities If you win the Lottery, you receive an Annuity Due because you get the first payment now. If you borrow (take a mortgage), you agree to pay an Ordinary Annuity because your 1 st payment is not due the day you borrow, but one month later.

5
The Annuity Tables The PVFA – present value factor annuity – Table is a sum of the PVF’s up to any point in Table 3. This will always be less than the number of years, since PVF’s are each < 1. The FVFA – future value factor annuity – Table is a sum of the FVF’s up to any point in Table 4. This will always be greater than the number of years, since FVF’s are each > 1.

6
Annuity Factors Table 3 is constructed using this formula Each PVFA (r, t) = [ 1- PVF(r, t)] / r = [ 1- (1+r) -t ] / r These are called Present Value Factors of Annuities and are found on the PVFA Table 3.

7
Annuity Factors Table 4 is constructed using this formula Each FVFA (r, t) = [ FVF(r, t) -1] /r = [(1+r) t -1] /r These are called Future Value Factors of Annuities and are found on the FVFA Table 4

8
The PV of an Annuity We can calculate the PV of an Annuity by determining the PV of each payment, which would be tedious – there could be dozens of calculations. The fact that the Annuity amount is constant allows us to factor-out the payment from the series of PVFs. For example: the PV of $1,000 per year for 10 years = $1,000 x ( (1.10) -t ) for t=1 to 10 = $1,000 x PFVA (r=10%, t=10) = $1,000 x 6.144 from Table 3 = $6,144 This means that if you gave someone $ 6,144 today (and rates were 10%), then they should repay you $ 1,000 per year for 10 years.

9
Annuities Monthly Compounding What is the PV of $100 per month for 3 years @ 6%? PV of $100 for 36 months ½ % per month = $ 100 x PVFA (r /12, t x12) = $ 100 x PVFA (0.005, 36) = $ 100 x [1- 1/(1.005) 36 ] / 0.005 There is no Table for these calculations, unless you make one yourself, so you will need to calculate it. = $ 100 x [1- 0.1227] / 0.005 = $ 100 x 32.87 = $ 3,287 Thus, if you borrowed $ 3,287 today and agreed to repay the loan over 36 months at 6% interest – you payments would be $100 each month.

10
Scenario #2 : the FV of a series of future deposits We deposit multiple small sums of money regularly (FV’s) to achieve a single large accumulation (FV) in the future: a)Save an amount each year to achieve a future goal.

11
The FV of an Annuity We can calculate the FV of an Annuity by determining the FV of each payment, but this too would tedious. For example: The FV of $1,000 per year (ordinary annuity) for 10 years @ 10% = $ 1,000 x (1.10) t ) for t=0 to 10-1 = $ 1,000 x FVFA (r=10%, t=10) = $ 1,000 x 15.937 from Table 4. = $ 15,937 So, if you put $ 1,000 in the bank @ 10%, each year starting in one-year, for 10 years – you should have $ 15,937 ready ten years from now.

12
Summary of the Factor Tables and their Functions Future Value Factors “FVF” = (1+r)^t Turn a present value into a FV Present Value Factors “PVF” = 1/(1+r)^t Turn a future value into a PV Future Value Annuity Factors “FVFA” = (FVF-1)/r Turn an Annuity into a FV Present Value Annuity Factors “PVFA” = (-1PVF)/r Turn an Annuity into a PV

13
Five Fundamental Practical Problems 1.Do I make “this” Investment today, i.e. does it offer a good return? 2.When do I take my Pension? 3.What will my payments be on this Loan 4.When and how much do I need to save for something – a house, a car, or my retirement? 5.Should I Lease or Buy this equipment?

Similar presentations

OK

Chap 8. The Time Value of Money Compound interest Future value and Present value Annuities Multiple Cash Flows NPV and internal rate of return.

Chap 8. The Time Value of Money Compound interest Future value and Present value Annuities Multiple Cash Flows NPV and internal rate of return.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on polynomials of 98 Ppt on world book day books Ppt on ms powerpoint tutorial Ppt on different layers of atmosphere Ppt on solid dielectrics in electric fields Ppt on two point perspective letters Ppt on collection framework in java Ppt on teachers day download Download ppt on turbo generator aircraft Maths ppt on surface area and volume class 10