Time Value Of Money - LA 2 - Lecture 1 - PDF

Learning area 1 Time value of money Time value of money WHAT YOU NEED TO KNOW ➜ Theory concepts of what time value of money entails ➜ CALCULATIONS! ➜ How to calculate PV, FV, I/YR, N, and PMT (these acronyms will be explained shortly) ➜ You have to be able to use both a calculator (or its...

Learning area 1 Time value of money Time value of money WHAT YOU NEED TO KNOW ➜ Theory concepts of what time value of money entails ➜ CALCULATIONS! ➜ How to calculate PV, FV, I/YR, N, and PMT (these acronyms will be explained shortly) ➜ You have to be able to use both a calculator (or its app on a smart device) AND EXCEL FUNCTIONS! (Excel is super duper easy though- it gives you the formulas!) WHAT YOU NEED TO KNOW: ➜ Time value of money concepts are used extensively in finance and investments: - Calculating the value of financial instruments, - Cost of capital - Capital budgeting - Investment decisions WHAT YOU NEED TO KNOW Type of questions you can expect: ➜ Short calculations, sometimes as MCQ, counting 2 or 3 marks. Normally you have all your data and just need to enter it correctly in your calculator/excel ➜ Longer type word sums where you are provided with a scenario and have to do one or more calculations ➜ HINT: Usually when a question counts more than 4 marks, you have to do more than one calculation to get to the answer Learning outcomes ➜ Calculate present and future values for a single payment as well as an annuity ➜ Calculate the present value of a perpetuity ➜ Calculate the implicit rate applicable to a particular investment or borrowing using present and future values, a payment and a particular term (n) for said payment ➜ Differentiate between simple and compound interest Learning outcomes ➜ Calculate an effective interest rate where interest is compounded more than once per period ➜ Calculate an annual percentage rate (APR) for a given effective rate ➜ Calculate the outstanding principle amount of borrowing or the principal amount invested after a number of payments have been made Learning outcomes ➜ Calculate the new term and/or payment applicable to a borrowing or investment if a change in the rate applicable to the particular borrowing or investment takes place ➜ Define the net present value of a project and explain whether the project should be accepted or not ➜ To present the time value of money problems on a time line ➜ Be able to use both calculators and excel to calculate time value of money problems Time value of money: Introduction Time value of money: ➜ Is a fundamental concept in financial management and capital investment evaluation, ➜ Is simply a reflection of the combined influence of interest and time, ➜ and is fundamental to almost all financial decisions Time value of money: Introduction ➜ Describes the greater benefit of receiving money now rather than later ➜ Underlies financial theory why people are willing to forgo spending ➜ Interest compensates the borrower or lender for the time value of money Time value of money: Introduction ➜ R100 received today is worth more than R100 a year from now, since interest can be earned. WHY? ➜ Interest compensates for risk and uncertainty. ➜ The longer you wait to receive money, the higher the risk that you won’t receive it at all – risk!!! ➜ People want to be compensated for assuming additional risk, hence people earn interest on deferring spending of money Time value of money: Introduction ➜ Inflation – purchasing power of money. - Money loses value over time (inflation)- your purchasing power decreases. - That is why a movie ticket in the year 1999 cost only R25. Interest compensates for this loss in purchasing power. ➜ Modern financial systems allow us to keep money safe in banks - That is why it is better to deposit money in a bank than keep it “safe” under your mattress- the money under your bed will lose value as years go by Time value of money: Introduction ➜ Banks compensate us for not using the money immediately in the form of interest - Interest compensates us for assuming risk of not spending money immediately, for the loss of purchasing power by deferring spending and for assuming additional credit risk by not investing in riskless assets Risk and Return Risk and return are 2 key concepts in finance: Risk ➜ In finance, risk refers to the degree of uncertainty and/or potential financial loss inherent in an investment decision. In general, as investment risks rise, investors seek higher returns to compensate themselves for taking such risks Risk and Return ➜ Risk is the likelihood of losing your investment- if you lend money, risk is the likelihood that you won’t receive your money back from the person you lent money to ➜ Higher uncertainty of repayment = higher risk Risk and Return Return ➜ A return, also known as a financial return, in its simplest terms, is the money made or lost on an investment over some period of time. ➜ A return is normally expressed as a percentage derived from the ratio of profit to investment. ➜ The return an investor earns by investing in a company is also a cost to the company (but this is explained in more detail in the cost of capital chapter) Risk and Return Relationship between risk and return: ➜ The higher the risk assumed by the investor, the higher the return demanded by the investor: Example ➜ Mr Smith wants to invest in Company A, by lending them money at an interest rate of 6%. Since the company is likely to repay the money, the interest rate is quite low, just enough to offset inflation. ➜ Company B on the other hand is a new venture and doesn’t have a track record of repaying loans on time. Mr Smith demands 10% interest before he will lend money to company B. ➜ This increase in interest rate reflects the additional risk (the uncertainty that he will not be repaid) Mr Smith assumes by investing in Company B, rather than Company A. Risk and Return ➜ The 6% and 10% represents the return an investor can earn ➜ But it is also represents the finance cost of the company (the company pays 6% or 10% interest payments) ➜ It is expressed as a percentage. ➜ The higher risk the investor assumes, the higher return he demands on his investment. Risk and Return ➜ So why doesn’t everybody invest in “riskless” assets such as government bonds? ➜ Because lower risk assets provide a lower return- people want to make MORE money and are willing to assume higher risk of not getting their money back for the promise of making more money in the future. Time value of money ➜ PV = present value or beginning amount ➜ I/YR = interest rate/yield/return/cost (NB!) ➜ FV = future value at end of “N” periods ➜N = number of compounding periods ➜ PMT = an annuity or series of equal payments ➜ CF0 = series of uneven cash flows ➜ NPV = net present value ➜ IRR = internal rate of return Time value terms ➜ PV - The value at time = 0, in other words at the beginning of the investment period, or the time period “now”. ➜ I/YR - THE MOST IMPORTANT CALCULATION! I/YR, also called the YIELD, is the return an investor receives on an investment. Conversely, it is also the cost of capital to the company (remember return for investor is same as cost to company) Time value terms ➜ FV - Future value of an investment- the amount the investment will grow to, or is valued at some point in future ➜ N (Nper in excel) - It is the number of periods of the investment horizon (periods are not necessarily years- refer to compounding interest rate slides) ➜ PMT - Series of coupon payments (DO NOT CONFUSE WITH I/YR) Financial calculator Financial calculator ➜ Step 1 - Switch on your calculator - Press “ON” Financial calculator ➜ Step 2 - Make sure that your payment schedule is set to 1 - To do this: - Press “1” - Press the “Orange arrow” (which is the 2nd function or SHIFT key) Financial calculator - Press “PMT” (Note that “P/YR” appears in orange on the bottom of the “PMT” button) - Your payment schedule is now set at 1 payment per year - If you press 2nd function Clear all, “1 P Yr” should flash on the screen - ALWAYS KEEP P/YR AS 1! Financial calculator Step 3 You will need to set your compounding periods to 1x times a year Step 2 Step 1 Financial calculator ➜ For all calculations on the calculator, we will be following the same steps ➜ First press the amount and then tell the calculator what the input is, for example: - Press 10, then N. This tells the calculator the number of periods is 10 Financial calculator ➜ The Orange Arrow key is NB! It is the SHIFT or 2nd function Key. It will tell the calculator to calculate the input printed in orange on the bottom of each key ➜ Some of these “orange” keys we will use a lot later on, for example NPV (Net Present Value) and IRR/YR (Internal Rate of Return)  Note below CST and PRC is: IRR/YR and NPV NB for LA6!!! Orange Arrow key: SHIFT/ 2nd Function Financial Calculator APP It looks the same as the I downloaded the calculator. HP10BA Pro App Just note the CLR ALL is for my Samsung in the middle of the keypad (I have the calculator already) HP10 BA PRO is free Most important row! Clear All SHIFT C Orange arrow key: SHIFT or 2nd Function  Financial Calculator APP Step 5 Step 1 Press the key for the variable Always press you wish to calculate for the 1 SHIFT P/YR answer This is to set your compounding periods to 1x times a year Step 4 Press your N/I/YR/ PV keys to store the values Step 2 Always CLR ALL before starting a new sum. Your calculator remembers the inputs Step 3 Always type the number first before typing N/I/YR/PV etc. Future value of a single amount FUTURE VALUE OF A SINGLE AMOUNT FVn = PV (1 + I)n Where: FV = Future value at time tn PV = Present value at time t0 i = interest rate n = duration of investment Future value of a single amount Determine the future value of R100 in three years’ time if invested at 10% per annum. FV = 100 (1 + 0,10)3 = 100 (1,331) = R133.10 Future value of a single amount ➜ Calculator inputs: ➜ SHIFT CLR ALL (To clear all previous inputs) ➜ 1 SHIFT P/YR (to make sure I have set the calculator to 1 payment per year) ➜ 100 PV ➜ 10% I/YR ➜ 3N ➜ PRESS FV = -R133.10 ➜ Why is it a negative? Future value of a single amount Step 4 10 I/YR Step 2 1 P/YR Step 3 100 PV Step 5 Step 1 3N CLR ALL Step 6 Press FV Cash flow direction ➜ Why is the calculator showing a negative amount for FV? ➜ The minus indicates direction of cash flows on a financial calculator ➜ All investments are either cash inflows or cash outflows ➜ You have to tell your calculator the direction of the cash flow Cash flow direction ➜ Your answer of R133.10 is still correct ➜ In this example you invest R100, which is a cash OUT flow to you, since you have to take money out of your cash (bank) account to invest somewhere else ➜ To adjust for this, you can put your PV as –R100 ➜ Your calculator will then give you a positive answer of R133.10 as your FV Cash flow direction ➜ A positive FV of R133.10 means you receive a cash IN flow of R133.10 when the investment matures in 3 years’ time ➜ PV and FV will ALWAYS have opposite signs ➜ If you have to calculate N, I/YR or PMT, you have to input PV and FV as opposite signs, otherwise your calculator won’t give you an answer! Cash flow direction Example: ➜ How long will it take for an initial investment of R100 to grow to R133.10 at an interest rate of 10%? ➜ PV = -R100 ➜ FV = R133.10 ➜ I/YR = 10% ➜N = 3 years Future value of a single amount Future value of R100 at 10 percent Beginning Year Interest Earned Ending Amount Amount 1 R100,00 R10,00 R110,00 2 110,00 11,00 121,00 3 121,00 12,10 133,10 4 133.10 13,31 146.41 5 146.41 14,64 161,05 Total interest R61,05 Future value of a single amount COMPOUNDING MORE FREQUENTLY THAN ANNUALLY Annually Semi-annually Quarterly PV0 R100 R100 R100 i/YR 12% 6% 3% N 5 10 20 FV R176.23 R179.08 R180.61 Compounding Interest can be paid more often than just once a year ➜ You have to make certain adjustments to you calculations to account for compounding ➜ Adjustments: - N = Multiply with number of compounding periods - I/YR = Divide by number of compounding periods - PMT = Divide by number of compounding periods Compounding ➜ Annually (1 payment per year), semi-annually (2 payments per year), quarterly (4 payments a year), monthly (12 payments per year), daily (365 payments per year) ➜ Example: See next slide SIMPLE INTEREST Year 1: 5% of $100 = $5 + $100 = $105 Year 2: 5% of $100 = $5 + $105 = $110 Year 3: 5% of $100 = $5 + $110 = $115 Year 4: 5% of $100 = $5 + $115 = $120 Year 5: 5% of $100 = $5 + $120 = $125 COMPOUND INTEREST Year 1: 5%of $100.00 = $5.00 + $100.00 = $105.00 Year 2: 5%of $105.00 = $5.25 + $105.00 = $110.25 Year 3: 5%of $110.25 = $5.51+ $110.25 = $115.76 Year 4: 5%of $115.76 = $5.79 + $115.76 = $121.76 Year 5: 5% of $121.55 = $6.08+ $121.55 = $127.63 Simple and Compound interest To adjust compounding interest rates for my calculations, I have to do the following adjustments: ➜N = Multiply with number of compounding periods ➜ I/YR = Divide by number of compounding periods ➜ PMT = Divide by number of compounding periods Simple and Compound interest Example: ➜ Mr Sizwe deposits a lump sum of R10 000 at a bank at an interest rate of 12%, compounded quarterly for 5 years. ➜ PV = 10 000 ➜N = 5*4 = 20 ➜ I/YR = 12%/4 = 3% ➜ No PMT in this example ➜ FV = R18 061.111 Present value ➜ The goal is to determine the amount of money which a firm or investor would accept at present in place of a given amount at a future date. ➜ The concept and computation of PV are important to the capital investment process since most projects are expected to yield cash flows over some number of periods in future.  Present value of a single amount The present value PV of a future amount FV is the amount of money which can be invested today at a given interest rate i per period to accrue to the same future amount FV after n periods. FV PV = (1 + i ) n Present value of a single amount Determine the present value of R133,10 which is expected in three years’ time if the discount rate is 10% per annum. 133,10 PV = (1,10)3 = R1,00 Examples 1. Calculate the future value of R1 000 invested for 5 years at a compound interest of 10% per year. 2. If you invest R15 000 today and would want to receive R18 895,50 three years from now, at what compound interest rate should this amount be invested? 3. How long would it take R2 000 invested today at a compound interest rate of 9% per annum to increase to R3 077, 20? Examples 1. ➜ CLR ALL, 1 P/YR ➜ PV = R1 000 ➜N = 5 years ➜ I/YR = 10 % ➜ FV = R1 610.51 Examples 2. ➜ CLR ALL, 1 P/YR ➜ PV = -R15 000 ➜N =3 ➜ I/YR = 8% ➜ FV = R18 895.50 Examples 3. ➜ CLR ALL, 1 P/YR ➜ PV = -R2 000 ➜N = 5 years ➜ I/YR = 9% ➜ FV = R3 077.20 Future value of an annuity What is an annuity? ➜ A stream of equal (even) periodic cash flows ➜ The cash flows can be inflows or outflows ➜ 2 types: - Regular annuity (deferred payment annuity) when payment’s received at the end - Annuity due when (payment’s received upfront) / beginning Future value of an annuity ➜ An annuity comprises equal annual payments or receipts over a predetermined time period. ➜ Time line for future value of a R100 annuity after 4 years invested at an interest rate of 6% per annum: Future value of an annuity FV Annuity: calculator ➜ CLR ALL, 1 P/YR ➜ PV =0 ➜N =4 ➜ I/YR = 6% ➜ PMT = -R100 ➜ FV = R437.46 Class example ➜ Mr Y deposit R1 400 per annum at the end of each year into a bank savings account for 25 years which will earn 8% per annum. Determine the amount in the savings account at the end of the period. Class example ➜ CLR ALL, 1 P/YR ➜ PMT = -R1 400 ➜ I/YR = 8% ➜N = 25 ➜ FV = R102 348,32 Present value of an annuity ➜ The present value or discounting process is the inverse function of the approach for compound interest or future value. ➜ It represents the amount an investor will accept at present in place of given amount in future, or in the case of annuities, the series of cash flows at specific point in time ➜ Present value of a R100 annuity for 4 years if the discount rate is 6% per annum ➜ In a time line presentation: Present value of an annuity PV Annuity: calculator ➜ CLR ALL, 1 P/YR ➜ PMT = R100 ➜N =4 ➜ I/YR = 6% ➜ PV = R346.51 Class example ➜ A firm expects to receive cash inflows of R3 000 per annum for 10 years as a result of implementing a new investment project. Determine the present value of the annual cash flows if the discount rate is 8%. Class example ➜ CLR ALL, 1 P/YR ➜ PMT = 3 000 ➜ I/YR = 8% ➜ N = 10 ➜ PV = - R20 130.24 Some tips to remember ➜ Always clear all your inputs (Your calculator remembers everything) ➜ Make sure your P/YR is set to 1 per year (rather multiply the periods and divide the interest rate and payments when compounding more than once a year) ➜ Remember to make PV – and FV + when calculating N or I/YR or PMT (opposite signs, otherwise you won’t get an answer) Some tips to remember - excel ➜ Excel gives you the formulas for time value of money calculations, it is just a matter of inputting the information in the correct order ➜ Set up your information in the columns and then choose the correct cells as you input your info in the excel function Some tips to remember - excel ➜ As soon as you type the equal sign, the function you want, and the opening bracket, then excel will tell you the order of the inputs (see next slide) ➜ Alternatively, you can make use of the insert function tab for “Financial” found in the “Formulas” tab. From here you can just select the correct cells again. Some tips to remember - excel ➜ “Click-and-drag” does not work! You will make mistakes! ➜ Remember to adjust for compounding interest periods! Excel will not do this for you automatically. ➜ You can ignore “[Type]”. We assume all payments occur at year-end and hence [Type] is set at 0. You do NOT need to change this or adjust it in any way. Just ignore [TYPE]! ➜ We will discuss the calculations in excel in detail in the next lectures. Really useful links ➜ The following webpages offer really useful information on using excel for time value of money calculations: ➜ https://www.journalofaccountancy.com/issues/2018/m ar/excel-functions-calculate-time-value-of-money.html ➜ http://www.tvmcalcs.com/index.php/calculators/excel_t vm_functions/excel_tvm_functions_page1 ➜ http://www.tvmcalcs.com/calculators/apps/excel_loan_ amortization