Chapter 2a principles of corporate finance principles of corporate finance Lecturer Sihem Smida Sihem Smida The Time Value of Money

1- 2 Chapter Objectives  Distinguish between simple and compound interest.  Calculate the present value and future value of a single amount for both one period and multiple periods.  Calculate the present value and future value of multiple cash flows.  Calculate the present value and future value of annuities.  Compare nominal interest rates (NIR) and effective annual interest rates (EAR).  Distinguish between the different types of loans and calculate the present value of each type of loan. 1-2

1- 3 What is cash flow?  Cash flow is the money that is moving (flowing) in and out of your business in a month.  Cash is coming in: from customers who are buying your products or services. If customers don't pay at time of purchase, some of your cash flow is coming from collections of accounts receivable. Revenus, profit, rentaccounts receivable  Cash is going out: in the form of payments for expenses, like rent or a mortgage, in monthly loan payments, and in payments for taxes and other accounts payable. accounts payable. 1-3

1- 4 Time Value Terminology  Future value (FV) is the amount an investment is worth after one or more periods.  Present value (PV) is the current value of one or more future cash flows from an investment PVFV

1- 5 If we can measure the value of cash flow, we can:  Translate Rs.1 today into its equivalent in the future (compounding).  Translate Rs.1 in the future into its equivalent today (discounting). ? Today Future Today ? Future

1- 6 Simple interest  Simple interest refers to interest earned only on the original capital investment amount. –FV = original capital (PV) + interest – Interest = PV × r×t  Example : PV = 100 ; r = 10% ; t = 3 ; FV? FV = 100( ×3 ) FV = 130 FV = PV(1 + r×t )

1- 7 Exercises  Exercise 1: What will 6000$ which are deposit in an account worth after 6 months earning 12% (simple interest )per year ?  Exercise 2: You deposit 5000$ in bank, after 7months you distinguish that the amount needed is Calculate the simple interest rate?

1- 8 Interest Rate Terminology  Compound interest refers to interest earned on both the initial capital investment and on the interest reinvested from prior periods. 1-8

1- 9 Future Value of a Lump Sum  Example: You invest $100 in a savings account that earns 10 per cent interest per year (compounded) for three years. After one year: $100  ( ) = $110 After two years: $110  ( ) = $121 After three years: $121  ( ) = $

1- 10 Future Value of a Lump Sum  The accumulated value of this investment at the end of three years can be split into two components: –original principal$100 –interest earned$33.10  Using simple interest, the total interest earned would only have been $30. The other $3.10 is from compounding. 1-10

1- 11 Future Value of a Lump Sum  In general, the future value, FV t, of $1 invested today at r per cent for t periods is:  The expression (1 + r) t is the future value interest factor (FVIF). Refer to Table A

1- 12 Time Value Terminology  The number of time periods between the present value and the future value is represented by ‘t’.  The rate of interest for discounting or compounding is called ‘r’.  All time value questions involve four values: PV, FV, r and t. Given three of them, it is always possible to calculate the fourth. 1-12

1- 13 Future Value of a Lump Sum Example:  What will $1000 amount to in five years time if interest is 12 per cent per year, compounded annually?  From the example, now assume interest is 12 per cent per year, compounded monthly.  Always remember that t is the number of compounding periods, not the number of years. 1-13

1- 14 Interpretation  The difference in values is due to the larger number of periods in which interest can compound.  Future values also depend critically on the assumed interest rate—the higher the interest rate, the greater the future value. 1-14

1- 15 Future Values at Different Interest Rates 1-15

1- 16 Present Value of a Lump Sum You need $1000 in three years time. If you can earn 10 per cent per year, how much do you need to invest now? Discount one year: $1000 ( ) –1 = $ Discount two years: $ ( ) –1 = $ Discount three years: $ ( ) –1 = $

1- 17 Interpretation  In general, the present value of $1 received in t periods of time, earning r per cent interest is:  The expression (1 + r) –t is the present value interest factor (PVIF). Refer to Table A

1- 18 Present Value of a Lump Sum Example: Your father promise to give you Ryal in 10 years time. If interest rates are 12 per cent per year, how much is that gift worth today? 1-18

1- 19 Present Values at Different Interest Rates 1-19

1- 20 Future Value of Multiple Cash Flows Example:  You deposit $1000 now, $1500 in one year, $2000 in two years and $2500 in three years in an account paying 10 per cent interest per year. How much do you have in the account at the end of the third year? 1-20

1- 21 Solutions  Solution 1 –End of year 1:($1000  1.10) + $1500 =$2600 –End of year 2:($2600  1.10) + $2000 =$4860 –End of year 3:($4860  1.10) + $2500 =$ 846 $ 8306  Solution 2 $1000  (1.10) 3 =$1331 $1500  (1.10) 2 =$1815 $2000  (1.10) 1 =$2200 $2500  1.00=$2500 Total=$

1- 22 Present Value of Multiple Cash Flows Example:  You will deposit $1500 in one year’s time, $2000 in two years time and $2500 in three years time in an account paying 10 per cent interest per year. What is the present value of these cash flows? 1-22

1- 23  Solution $2500  (1.10) –3 =$1878 $2000  (1.10) –2 =$1653 $1500  (1.10) –1 =$1364 Total=$