1. CDA COLLEGE BUS235: PRINCIPLES OF FINANCIAL ANALYSIS Lecture 4 Lecture 4 Lecturer: Kleanthis Zisimos

2. Lecture Topic List Time lines Time lines Future Value of an annuity Future Value of an annuity Present Value of an annuity Present Value of an annuity Perpetuities Perpetuities

3. Time value of money In finance the value of money is different in different time periods. For example 100 euro in 2012 worth more than 100 euro in 2013. In finance the value of money is different in different time periods. For example 100 euro in 2012 worth more than 100 euro in 2013. This is happening basically because money have the possibility to produce interests. This is happening basically because money have the possibility to produce interests. So if we deposit now 100 euro in the bank with an interest rate 5% then in 2015 our investment will increase to 105. So if we deposit now 100 euro in the bank with an interest rate 5% then in 2015 our investment will increase to 105. In conclusion 100 euro today worth 105 euro in 2013 In conclusion 100 euro today worth 105 euro in 2013

4. Time lines One of the most important tools in time value of money analysis is the time line, which is used to help us visualize what is happening in a particular problem and then to help us set up the problem for solution. One of the most important tools in time value of money analysis is the time line, which is used to help us visualize what is happening in a particular problem and then to help us set up the problem for solution. 5% 5% 6% 6% 5% 5% 6% 6% 0 1 2 3 4 Time 0 is today, time 1 is period 1 from today and 5% is the interest rate in year 1 and 2 Time 0 is today, time 1 is period 1 from today and 5% is the interest rate in year 1 and 2

5. Time lines exercises 1. Draw a time line to illustrate how much a deposit of 10000 will worth in year 3 with an interest rate of 5% each year. 2. Draw a time line to illustrate how much the deposits of 1000 today and 1000 in year 1 will worth in year 3 with an interest rate of 5% each year. 3. A 4 year bond has a face value 500 euro and annual coupon rate 10%. Its pays the dividend every 6 months. Draw the time line of the coupon

6. Present and Future values A euro in hand today is worth more than a euro to be received in the future because, if you had it now, you could invest it, earn interest, and end up with more than one euro in the future. A euro in hand today is worth more than a euro to be received in the future because, if you had it now, you could invest it, earn interest, and end up with more than one euro in the future. The process of going from today’s values, or present values (PV), to future values (FV) is called compounding. The process of going from today’s values, or present values (PV), to future values (FV) is called compounding.

7. Future Value formula FVn = PV(1+i)^n PV = Present Value. i = Interest rate of bank per period. FVn = Future value at the end of n periods N= number of periods Example. What is the future value in year 7 of a deposit 100 euro with interest rate 5%. FVn = 100(1+0,05)^7=140,71

8. Present Value formula PV = FVn (1+i)^n (1+i)^n Example. In 2020 I will inherited 40000 euro from my family. What is the present value if the interest rate 5%. PV = 40000 (1+0,05)^8 (1+0,05)^8 PV=27073 euro

9. Future Value of an annuity An annuity is a series of equal payments made at fixed intervals for a specified number of periods. An annuity is a series of equal payments made at fixed intervals for a specified number of periods. The payments are given the symbol PMT, and they can occur at either the beginning or the end of each period. The payments are given the symbol PMT, and they can occur at either the beginning or the end of each period. If the payments occur at the end of each period, as they typically do, the annuity is called an ordinary or deferred, annuity. If the payments occur at the end of each period, as they typically do, the annuity is called an ordinary or deferred, annuity. If payments are made at the beginning of each period, the annuity is an annuity due If payments are made at the beginning of each period, the annuity is an annuity due

10. FVAn = PMT ( (1+i)^n -1 ) i Example. An investor wants to deposit each year 1000 euro in his bank account with an interest rate of 4%. What is the future value of his money in year 3 Example. An investor wants to deposit each year 1000 euro in his bank account with an interest rate of 4%. What is the future value of his money in year 3 FVA 3 =1000 ( (1+0,04)^3 -1 ) 0,04 0,04 FVA 3= 3121 Lecturer: Elena Antoniou10 Future Value of an ordinary annuity equation

11. Example continued To demonstrate the importance of time lines which we saw in the beginning of the lecture we shall investigate this example by drawing a time line To demonstrate the importance of time lines which we saw in the beginning of the lecture we shall investigate this example by drawing a time line 4% 4% 4% 4% 4% 4% 0 1000 1000 1000 In year 3 the FV of the 1st 1000 is 1000(1.04)^2=1081 In year 3 the FV of the second 1000 is 1000(1,04)^1=1040 In year 3 the FV of the 3rd 1000 is 1000 So the FV of all the deposits is 1081+1040+1000=3121

12. Present value of an annuity The present value of future payments is given by the following formula The present value of future payments is given by the following formula PVA= PMT ( 1-(1+i)^-n ) I Example. What is the present value of 2000 euro deposit each month for 2 years and interest rate 5%

13. Perpetuities The annuities who go on indefinitely are called perpetuities The annuities who go on indefinitely are called perpetuities The present value of a perpetuity is given by the following equation: The present value of a perpetuity is given by the following equation: PVp= PMT PVp= PMT i What is the present value of a bond which gives 100 euro coupon rate each year for an infinite years (5% interest rate ) What is the present value of a bond which gives 100 euro coupon rate each year for an infinite years (5% interest rate )