Chapter 8 48 Financial Planning Handbook PDP
The Financial Planner's Toolkit As a financial planner, you will be doing a lot of mathematical calculations for your clients. Doing these calculations for a large number of years is very tricky and difficult if you do not use the correct tools. It is recommended that you use either computer spreadsheet software like MS Excel or a financial calculator to do these calculations. Basic Concepts of Time Value of Money Money today is more valuable than money in future. This is because when you forego spending money at present, you can earn interest on it. Interest can be considered to be the rent for money. When you give your house to somebody to live in, you get some money as rent. Similarly, when you deposit your money with somebody, you get interest as rent. Interest is expressed as a rate or percentage. The amount of interest that you receive is determined by multiplying the time for which you deposit the money with the rate of interest and with the amount of money that you deposit. So the future value of your money is calculated as below: Future Value = Original Amount Deposited + Interest on the original amount The original amount that you deposit is referred to as the Principal. Since it is the amount that you have at present, it is also known as the Present Value. Therfore the generalized formula for calculating interest is:, FV = PV + PV x R x T Or FV = PV(1+R)T FV = Future Value PV = Present Value R = Rate of Interest T = Time period Interest can be calculated in two ways: Simple Interest This is when interest is calculated on the principal amount only. SI = PV x R x T, SI = Simple Interest R = Rate of Interest T = Time period PDP Financial Planning Handbook 49
Compound Interest This is when the earned interest is also deposited alongwith the principal and you also receive interest on interest. To illustrate, if you deposit Rs. 100 for 2 years at an interest rate of 8% p.a., then after one year, the interest you will earn would be: 100 x 8% = Rs. 8 For the next year, you will not only earn interest on Rs. 100 but also on the interest that you earned in the first year Rs. 8 i.e. you will earn interest on Rs. 108. 108 x 8% = Rs. 8.64 The generalized formula for calculating future value at compound interest can be stated as below: FV = PV(1+ R) T Let us now look at various scenarios where you may be required to calculate present value and future value. A Single Cash Flow Future Value of a Single Cash Flow The future value of a single cash flow with simple interest is given by: FV = PV(1+r)t, FV = Future Value PV = Present Value r = Rate of Interest t = Time period The future value of a single cash flow with compound interest is given by: FV =PV (1+r) t, FV = Future Value PV = Present Value r = Rate of Interest t = Time period MS Excel The Excel FV function can be used to find out the future value of a single cash flow. The FV function is: = FV(RATE,NPER,PMT,PV,TYPE), RATE is the interest rate for the period; NPER is the number of periods; PMT is the equal payment or annuity each period; PV is the present value of the initial payment; and TYPE indicates the timing of the cash flow, occuring either in the beginning or at the end of the period. 50 Financial Planning Handbook PDP
The PMT and TYPE parameters are used while dealing with annuities. Note: The initial payment is a cash outflow, while the future value is a cash inflow for the investors. Accordingly, we need to treat the initial payment as negative in value. Suppose that a firm deposits Rs. 22,000 for eight years at 12 per cent rate of interest. How much would this sum accumulate to at the end of the eight year? F 8 = PV x (1+i) n = 22,000 x (1+0.12) 8 = Rs. 54,471.19 In column B7 we write the formula: =FV (B4,B3,0,-B2,0). FV of Rs. 54,471.19 is the same as calculated above. Financial Calculator Use [ ] [ ] to select Set:, and then press [EXE] Press [2] to select End Use [ ] [ ] to select n, input 8, and then press [EXE] Use [ ] [ ] to select I%, input 12, and then press [EXE] Use [ ] [ ] to select P/Y, input 1, and then press [EXE] Use [ ] [ ] to select PV, input 22,000, and then press [EXE] Use [ ] [ ] to select FV Press [SOLVE] to perform the calculation Present Value of a Single Cash Flow The present value of a single cash flow is given by: PV = FV / (1+r) t, FV = Future Value PV = Present Value r = Rate of Interest t = Time period MS Excel We can find the present value of a single cash flow in Excel by using the built-in PV function: = PV (RATE, NPER, PMT, FV, TYPE) PDP Financial Planning Handbook 51
The function is similar to FV function except the change in places for PV and FV. We use the values of parameters as given in the following illustration: Suppose that an investor wants to find out the present value of Rs. 25,000 to be received after 13 years. Her interest rate is 9 per cent. We enter in column B5 the formula: = PV (B4,B3,0,-B2,0). We enter negative sign for FV; that is B2. This is done to avoid getting the negative value for PV. You can also find the present value by directly using the formula l PV = FV x (l + i) n Financial Calculator Use [ ] [ ] to select (1) Set:, and then press [EXE] Press [2] to select End Use [ ] [ ] to select (2) n, input 13, and then press [EXE] Use [ ] [ ] to select (3) I%, input 9, and then press [EXE] Use [ ] [ ] to select P/Y, input 1, and then press [EXE] Use [ ] [ ] to select (6) FV, input 25,000, and then press [EXE] Use [ ] [ ] to select PV Press [SOLVE] to perform the calculation Future Value of an Annuity An Annuity represents a series of equal payments (or receipts) occurring over a specified number of equidistant periods. Ordinary Annuity Payments or receipts occur at the end of each period. 52 Financial Planning Handbook PDP
Annuity Due Payments or receipts occur at the beginning of each period. The future value of an ordinary annuity is given by: FVA = Future Value of Annuity A = Annual Payment Amount i = interest n = number of years The future value of an annuity due is given by: FVADn = FVAn (1+i) FVADn = Future Value of Annuity Due FVAn = Future Value of Annuity A = Annual Payment Amount i = interest n = number of years PDP Financial Planning Handbook 53
MS Excel The Excel FV function for an annuity is the same as for a single cash flow. Here, we are given value for PMT instead of PV. We will set a value with negative sign for PMT (annuity) and a zero value for PV. We use the values for the parameters as given in the following illustration: Suppose that a firm deposits Rs. 3,000 at the end of each year for six years at 3 per cent rate of interest. How much would this annuity accumulate at the end of the sixth year? F 6 = 3,000 (FVA 6, 0.03 ) = 3,000 x 6.4684 = Rs. 19,405.23 In column C6 we write the formula: = FV (B5,B4,-B3, 0, 0). FV of Rs. 19,405.23 is the same as in the illustration. Instead of the built-in Excel function, we can also directly use the formula below to find the future value: We can enter the formula and find the future value. We will get the same result. Financial Calculator Use [ ] [ ] to select (1) Set:, and then press [EXE] Press [2] to select End Use [ ] [ ] to select (2) n, input 6, and then press [EXE] Use [ ] [ ] to select (3) I%, input 3, and then press [EXE] Use [ ] [ ] to select P/Y, input 1, and then press [EXE] 54 Financial Planning Handbook PDP
Use [ ] [ ] to select (4) PV, input 0, and then press [EXE] Use [ ] [ ] to select (5) PMT, input 3,000, and then press [EXE] Use [ ] [ ] to select FV Press [SOLVE] to perform the calculation Annuity of a Future Value (Sinking Fund) In the previous example, we had seen that Rs. 3,000 deposited for a period of 6 years at 3% accumulates to Rs. 19,405. However, if we wish to calculate the opposite that is the value of annual payments that will accumulate to Rs. 19,405 in 6 years at 3%, then the formula is given by: FVA = Future Value of Annuity A = Annual Payment Amount i = interest n = number of years MS Excel The Excel function for finding an annuity for a given future amount is as follows: = PMT (RATE, NPER, PV, FV, TYPE) We use the values for the parameters as given in the following illustration: Suppose that a firm earns Rs. 19,405 at the end of for five years at 6 per cent rate of interest. What is the annuity (PMT) of this value? In column B6 we write the formula: = FV (B5,B4,B2,-B3,0). Note that we input both FV and PV and enter negative sign for PMT. The value of PMT is Rs. 3,442.38. Instead of the built-in Excel function, we can enter formula: and find the value of the sinking fund (annuity). We will get the same result. PDP Financial Planning Handbook 55
Financial Calculator Use [ ] [ ] to select (1) Set:, and then press [EXE] Press [2] to select End Use [ ] [ ] to select (2) n, input 5, and then press [EXE] Use [ ] [ ] to select (3) I%, input 6, and then press [EXE] Use [ ] [ ] to select P/Y, input 1, and then press [EXE] Use [ ] [ ] to select (4) PV, input 0, and then press [EXE] Use [ ] [ ] to select (6) FV, input 19,405, and then press [EXE] Use [ ] [ ] to select PMT Press [SOLVE] to perform the calculation Shridhar invests Rs. 1 Lakh at the end of each year, in the retirement fund corpus. LICL has promised a return of 10% pa. How much has his retirement corpus grown to in 20 years time. Present Value of an Annuity The present value of an ordinary annuity is given by: PVA = Present Value of Annuity A = Annual Payment Amount i = interest 56 Financial Planning Handbook PDP
The present value of an annuity due is given by: PVAD n = PVA n (1+i) PVAD n = Present Value of an Annuity Due PVA n = Present Value of Annuity A = Annual Payment Amount I = interest n = number of years MS Excel The Excel PV function for an annuity is the same as for a single cash flow. Here we have to put in the value for PMT instead of FV: Suppose that an investor wants to find out the present value of an annuity of Rs. 10,000 to be received for 5 years. The interest rate is 9 per cent. We enter in column B5 the formula: = PV (B4,B3,-B2,0,0). We enter negative sign for FV; that is B2. This is done to avoid getting the negative value for PV. You can also find the present value by directly using the formula: PDP Financial Planning Handbook 57
Financial Calculator Use [ ] [ ] to select (1) Set:, and then press [EXE] Press [2] to select End Use [ ] [ ] to select (2) n, input 5, and then press [EXE] Use [ ] [ ] to select (3) I%, input 9, and then press [EXE] Use [ ] [ ] to select P/Y, input 1, and then press [EXE] Use [ ] [ ] to select (5) PMT, input 10,000, and then press [EXE] Use [ ] [ ] to select PV Press [SOLVE] to perform the calculation Perpetuity A perpetuity is an infinite annuity. In a perpetuity, the annual cash flows continue forever. The present value of a perpetuity is given by: PV = a/r PV = Present Value a = Annual Payment Amount r = interest rate The concept of perpetuity finds application in case of stock valuation. Stocks are valued at present value of their expected earnings. For example, suppose a company is expected to earn Rs. 5 every year. If the discount rate is 10% then the value of the stock would be: Price of Stock = PV of earnings = 5/0.10 = Rs. 50 Growing Perpetuity The present value of a perpetuity that grows at a constant rate of g% is given by: PV = a/(r-g) 58 Financial Planning Handbook PDP
PV = Present Value a = Annual Payment Amount r = interest rate g = growth rate of annual payments To illustrate, a company expects to earn Rs. 5 per share in this year and expects its earnings per share (eps) to grow at a rate of 6% every year. If the discount rate is 10%, then the current price of the share would be: Price = 5 / (10-6) = 5/0.04 = Rs. 125 This formula also enables us to understand the PE Ratio in terms of the growth rate of earnings. PE Ratio = Price per share / Earnings per share Or P 0 = Current Stock Price e 0 = Current Earnings per share g = earnings growth rate r = discount rate Different Periods of Compounding The future value depends a lot on the way the interest is compounded. Interest may be compounded once a year or more frequently like semi-annually, quarterly, monthly or even daily. In such cases, the future value is given by: PDP Financial Planning Handbook 59
FV n = Future Value after n periods r = rate of interest per period n = number of periods m = number of times of compounding per period PV 0 = Present Value at start of period 0 Exercise: Let us see the effect of compounding at different periodicity: Comparison of different compounding periods for Rs. 1000 invested for 2 Years at an annual interest rate of 12%. Annual FV 2 = 1,000(1+ [.12/1]) (1)(2 = 1,254.40 Semi FV 2 = 1,000(1+ [.12/2]) (2)(2) = 1,262.48 Qrtly FV 2 = 1,000(1+ [.12/4]) (4)(2) = 1,266.77 Monthly FV 2 = 1,000(1+ [.12/12]) (12)(2) = 1,269.73 Daily FV 2 = 1,000(1+[.12/365]) (365)(2) = 1,271.20 Therefore, you can see that although the stated rate of interest is 12% in each case, the results are significantly different. The stated rate is also known as Annual Percentage Rate, APR. The Effective Annual Rate, EAR, is the rate if there was compounding only once per period; it is true effective rate. The relation between APR and EAR is given by: If the compounding period is made infinitely small, it is known as continuous compounding. The EAR for continuous compounding is given by: Yield or IRR Calculation MS Excel Excel has built-in functions for calculating the yield or IRR of an annuity and uneven cash flows. The Excel function to find the yield or IRR of an annuity is: = RATE (NPER, PMT, PV, FV, TYPE, GUESS) GUESS is a first guess rate. It is optional; you can specify your formula without it. 60 Financial Planning Handbook PDP
In column C6 we enter the formula: = RATE (C5, C4, C2, 0, 0, 0.10). The last value 0.10 is the guess rate, which you may omit to specify. For investment with an outlay of Rs. 20,000 and earning an annuity of Rs. 5,000 for 8 years, the yield is 18.62 per cent. The Excel built-in function IRR calculates the yield or IRR of uneven cash flows: IRR (VALUES, GUESS) The values for the cash flows should be in a sequence, starting from the cash outflow. GUESS is a first guess rate (arbitrary) and it is optional. In the worksheet, we have entered the cash flows of an investment project. In column B4 we enter the formula: = IRR (B3:G3) to find yield (IRR). Note that all cash flows in year 0 to year 5 have been created in that sequence. The yield (IRR) is 27.43 per cent. You can also use the built-in function, NPV, in Excel to calculate the net present value of an investment with uneven cash flows. Assume in the present example that the discount rate is 20 per cent. You can enter in column B5 the NPV formula: = NPV (0.20, C3:G3) +B3. The net present value is Rs. 21,850. If you do not enter +B3 for the value of the initial cash outflow, you will get the present value of cash inflows (from year 1 through year 5), and not the net present value. Financial Calculator Use [ ] [ ] to select (3) I%, input 20, and then press [EXE]. Use [ ] [ ] to select Csh=D.Editor x, and then press [EXE]. This displays the DataEditor. Only the x-column is used for calculation. Any values in the y-column and FREQ-column are not used. -40,000 [EXE] (CF0). 15,000 [EXE] (CF0). 25,000 [EXE] (CF0). 30,000 [EXE] (CF0). 17,000 [EXE] (CF0). 16,000 [EXE] (CF0). Press [ESC] to return to the value input screen. Use [á] [â] to select NPV: Solve. Press [SOLVE] to perform the calculation. Use [á] [â] to select IRR: Solve. Press [SOLVE] to perform the calculation. Impact of Tax and Inflation In the previous examples, we have considered the rate of interest without adjusting for tax or inflation. In real life both of these factors reduce the real rate of return that an investor gets. PDP Financial Planning Handbook 61
Exercise 1. Naina is 22 years old. She has recently started her work. Naina is working with an educational institute and she has been trained to counsel students. Day in and day out, she talks to young people about the careers and goals and where they want to be in life. This set her thinking in terms of her future. Her aspiration levels increased and she herself wanted to study further. She knew her potential and she was getting educated on the job market and her areas of interest. After doing the initial research, she concluded that she wanted to study abroad. However, as is well known, a 22 year old doesn t have a lot of money in her kitty. Also she knew that her parents could not take the burden of such a loan. She decided that she would need to plan for fulfilling this dream of hers. She calculated the amount to be Rs. 15 Lakhs. She wanted to have saved up Rs. 15 Lakhs in 8 years time. The average market return is about 10%pa. How much would she need to invest to get Rs. 15 Lakhs in 8 years? Also, if Naina invests in yearly installments rather than a one time proposition, how much will she have to invest each year, so that she will have Rs. 15 Lakhs corpus at the end of 8 years at a 10% rate of return. 2. Let us assume that an investor invests Rs. 1000 at 12% for a period of one year. Let us assume inflation to be 6% and the tax rate to be 30%. The real return that the investor gets is calculated as below: Amount Invested Rs. 1000 Rate of Interest 12% Time Period 1 year Interest received Rs. 120 Tax Rate 30% Amount payable as tax Rs. 36 Amount after tax Rs. 84 Inflation Rate 6% Amount Lost due to Inflation Rs. 60 Interest after tax adjusted for inflation Rs. 24 Effective Rate 2.4% Therefore the formula for finding the real rate of return is: Real Rate = I(1-T) R I = interest rate received T = tax rate R = rate of inflation 62 Financial Planning Handbook PDP