CORPORATE FINANCE-I Lecture# 2 & 3: TIME VALUE OF MONEY Faculty: Prof. Kulbir Singh (Imt-nagpur) 12/28/2010

Introduction  Consider the following situations:  You expect a liability of Rs.100,000 in 5 years and you wish to know how much you should set aside today to meet the liability.  Your car dealer offers you two schemes – A & B. Under the first scheme, you can borrow the entire amount at an interest rate of 15%. Under the second scheme, the car dealer gives a discount of 10% on the sticker price but the interest charged on the amount borrowed would be 19%. You have to decide on the scheme.  You come across advertisements inserted by 2 banks in a daily. Bank A offers 13% interest per annum on deposits. Bank B offers 12% semiannual interest. You have to choose between these banks 12/28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 2

Basis for Time Value of Money Inflation. Preference for Current Riskiness of the cash flow 12/28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 3

Future Value and Compound Interest Let us suppose you deposited Rs.1000 in Global Trust Bank for one year and the bank pays 13% interest. Interest = 0.13 x 1000 = Rs.130 Amount at the end of 1 year = Principal + Interest = Rs.( ) = Rs In general, Value of investment after 1 year = Initial investment x (1+r) where ‘r’ is the interest rate in decimal form. 12/28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 4

Future Value and Compound Interest Now, if you wish to keep the balance in the bank, the principal for the second year would be Rs.1310 (and not 1000) and interest would be paid on this amount. Interest for the second year = 0.13 x 1310 = Rs Amount at the end of second year = Rs.( ) = Rs An investment of Rs.1000 grew to Rs.1310 in one year and Rs in two years. The amount available at the end of the investment horizon is called future value and the process of multiplying the investment is called compounding. Note: interest earned in the first year also earned interest in the second year. 12/28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 5

Future Value and Compound Interest In general, The term (1 + r) n is called Future Value Interest Factor or FVIF. It is the value of Re.1 interest at r % after n years. 12/28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 6 Future Value of an amount, FV = Amount (1 + r) n

Future Value Interest Factor (FVIF) The Value of Re.1 for different interest rates and time periods is readily available in the form of a table – Future Value Interest Factor Table (See Table A-1 at the end of the book). A section of the table is reproduced in Exhibit /28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 7

FVIF To find the value of Re.1 at 10 % for 5 years. Similarly try 12 % and 4 years. Now find the future value of Rs.282 at 10% for 3 years. Future Value = A(1 + r) n = 282 * FVIF 10,3 = 282 x = Rs /28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 8

Future Value of a series You invest Rs.500 today, Rs.1000 at the end of 1 st year and Rs.1500 at the end of 2 nd year. You are required to find the future value at the end of 2 nd year. Assume 8% interest. The future value of this series is nothing but the sum of future values of each cash flow as shown below: 12/28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 9

Future Value of a series Future Value = FV of Rs FV of Rs Note that 1500 itself is the future value of the Cash flow occurring at the end of 2 nd year. FV = 500 (1.08) (1.08) = 500 x FVIF 8, x FVIV 8, = Rs.3163 What would happen to the future value if the cash flow were to occur at the beginning of the year? Beginning of year 1 is same as year 0 (that is today) and beginning of year 2 is same as end of year 1. The cash flow would be: 12/28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 10

Future Value of a series FV = ( )(1.08) 2 + (1500 x1.08) = Rs /28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 11

Types of Cash Flows Cash flows can exhibit different patterns. Different periodic amounts & the series had a finite life. A series of periodic flows of equal amounts is called an Annuity and a series of periodic flows of equal amounts but with an infinite life is called a perpetuity. Thus investing or receiving Rs.500 as dividends forever is a perpetuity. 12/28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 12

Future Value of an Annuity You require Rs.250,000 at the end of 5 years to buy a Car. Assume that this is the price that would prevail 5 years from now for the model you have in mind. You wish to invest a fixed (constant) sum every year to accumulate Rs.250,000 at the end of 5 years. The series of cash flows is shown below: 12/28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 13

Future Value of an Annuity 12/28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 14

Future Value of an Annuity To make our life simple, the value of FVIFA for various r & n are presented in the form of a Table (See Table A-2 at the end). A section of the Table is shown in Exhibit /28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 15

Present Values 12/28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 16

Present Values The process of bringing a cash flow to the present is called discounting and the rate of interest is called discount rate. The discount rate is a rate at which present and future values are traded off. The term [1/1 + r) t ] is called Present Value Interest Factor or PVIF. 12/28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 17

Present Values The value of [1/1 + r) n ] for various combinations of r and n is given in the present value interest factor table (see Table A-3) at the end of the book. A section of the Table is reproduced in Exhibit /28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 18

Present Value of a Series Consider the same cash flows again. The present value of this series is the sum of present values of each of these cash flows. 12/28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 19

Present Value of an Annuity The present value of an annuity ‘A’ receivable at the end of each year for a period of n years at an interest rate of r is given by: 12/28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 20 The term in the bracket is called Present Value Interest Factor of an Annuity or PVIFA. It is the present value of an annuity of Re.1 for the given values of r and n. The values of PVIFA (K, n) for various combination of r and n are given in Table A-4 at the end of the book. A section is shown in Exhibit 2-4.

Present Value of an Annuity 12/28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 21 The term in the bracket is called Present Value Interest Factor of an Annuity or PVIFA. It is the present value of an annuity of Re.1 for the given values of r and n. The values of PVIFA (K, n) for various combination of r and n are given in Table A-4 at the end of the book. A section is shown in Exhibit 2-4.

Present Value of an Annuity 12/28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 22 On December 31, you buy a car for Rs.200,000 paying 20% up front and agreeing to pay the balance in 5 equal annual installments. The rate of interest is 15%. Amount payable = 0.8 x 200,000 = Rs.160,000 PVA n = A [ PVIFA r,n ] A = [ 160,000 / 3,352 ] = Rs.47,732.70

Present Value of an Annuity 12/28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 23 Sometimes annuities grow at a constant rate. Retirement and pension benefits, for example, increase every year with a cost of living adjustment. The present value of a series of growing annuity can be estimated using the following equation: For eg., if A = Rs 6600, r=5%, n=30 periods, g=3.5%, PV = Rs 154,251

Loan Amortization 12/28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 24 Assume that you have borrowed Rs.10 lakh from a financial institution at an interest rate of 14% per annum. The loan is to be cleared in equal annual installments. Annual installment = Rs 10,00,000 / PVIFA(14,5) = Rs.10,00,000 / 3,433 = Rs.291,290 This installment contains interest and principal components. The principal is retired partially every year and the interest is paid on the outstanding balance. The loan amortization schedule is presented in Exhibit 2-5.

Loan Amortization 12/28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 25

Effective and Nominal Rates 12/28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 26 How should we compare interest rates that are quoted for different periods? A car dealer offers 2 schemes – A & B. Under the first scheme you have to pay an interest of 12% compounded monthly and under the second scheme you have to pay an interest of 12% compounded annually. You are required to choose between the two. The trick is to convert both of them into same basis. There is a simple formula to do this :(1 + annual rate) = (1 + monthly rate) 12 For the first scheme, the annual rate is 12%. So the rate per month is 12/12 = 1%. Substitute in the above equation (1 + annual rate) = ( ) 12 Annual rate = 12.68%

Effective and Nominal Rates 12/28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 27 From the numerical it must be clear that the shorter the compounding period, the higher will be the interest rate. The rate quoted on an annual basis (12%) is the simple annual rate and the rate that considers more frequent compounding is called effective rate (12.68% in the above example).

Perpetuity 12/28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 28 Some investments make a regular income forever. Let’s suppose the dividend per share of Company X is Rs.2. It is expected to remain at this level forever (the firm is a going concern). If the appropriate discount rate is 13%, ……..the present value of this perpetual stream = (Rs.2/0.13) =Rs In general, PV of a Perpetuity = Per Period Amount/Discount Rate

Perpetuity 12/28/2010Faculty: Prof. Kulbir Singh (IMT-Nagpur) 29 If an amount to grow at a constant rate forever it is called a growing perpetuity. The present value of a growing perpetuity can be estimated using the following formula. If an amount to grow at a constant rate forever it is called a growing perpetuity. The present value of a growing perpetuity can be estimated using the following formula.