LA 2 Time value of money (Lecture 2).pdf

Learning area 1 Time value of money Lecture 2 Some calculator/app tips ➜ Always make sure that your calculator is set to 1 P/YR - 1 Shift (orange arrow/button) P/YR ➜ Always make sure your calculator is set to END mode - Shift BEG/END - The display should read END ➜ If you change...

Learning area 1 Time value of money Lecture 2 Some calculator/app tips ➜ Always make sure that your calculator is set to 1 P/YR - 1 Shift (orange arrow/button) P/YR ➜ Always make sure your calculator is set to END mode - Shift BEG/END - The display should read END ➜ If you change the compounding periods on your calculator REMEMBER TO CHANGE IT BACK WHEN YOU ARE DONE! Some calculator/app tips ➜ If you change the number of compounding periods on your calculator to 2 P/YR, 4 Y/R or 12 P/YR: - Input annual I/YR - Multiply N by number of compounding periods - Divide PMT by number of compounding periods Some calculator/app tips ➜ Always remember to CLR ALL before starting a new question ➜ PV and FV will ALWAYS have opposite symbols - To calculate N, I/YR, PMT, you need to input [– PV] and [FV] - PV is generally a negative as this represents a cash outflow at the beginning of the investment horizon - The minus does NOT indicate a negative amount. Rather, it indicates direction of the cash flow Some calculator/app tips ➜ For the I/YR, input the annual rate (or adjusted for compounding periods) as a whole number without the % - Example: 10 I/YR - Do NOT include the % symbol or divide by 100 ➜ For the most part excel has the same inputs as the calculator/app: - The few exceptions will be discussed in the excel lectures What is a sinking fund? ➜ Money you set aside for a specific upcoming expense. ➜ A sinking fund has a clear purpose attached to it— whether it's to save for a vacation, down payment on a home, or a big-ticket splurge. ➜ In business, a sinking fund is a fund established by an economic entity by setting aside revenue over a period of time to fund a future capital expense, or repayment of a long-term debt. Sinking fund ➜ A loan of R20 million is to be redeemed in 15 years’ time. A sinking fund is foreseen for this purpose. Annual instalments can be invested over the 15 year period at 10% per annum. What amount should be invested annually? Sinking fund ➜ FV = R20 000 000 ➜N = 15 ➜ I/YR = 10% ➜ PMT = R629 475,54 Bond Amortisation ➜ Please note the difference between bond amortisation and bonds (or debentures) which are financial instruments! ➜ Bonds are debt financial instruments issued by large corporations, financial institutions and government agencies that are backed up by collateral or physical assets. ➜ Debentures are debt financial instruments issued by private companies, without collateral or physical assets to back them up ➜ Study the additional study material to understand the formulas and to be able to calculate the interest paid or capital amount due after a certain period – similar to examples done in class. Bond Amortisation ➜ A loan of R15 000 at 18% p.a. compounded semi- annually from a financial institution, is to be repaid by equal semi-annual payments over the next three years. The first payment is due 6 months hence. What is the payment? Bond Amortisation ➜ C ALL, 1 P/YR ➜ PV = R15 000 ➜ N = 3*2 = 6 ➜ I = 18%/2 = 9% ➜ PMT = R3 343.80 ➜ Amortisation schedule: Amortisation schedule ➜ Keep same inputs ➜ 2nd function AMORT ➜ 1-1: ➜ = R1 993.80 (Principal) ➜ = R1 350 (Interest) ➜ = R1 3006.20 (Balance) ➜ 2nd function AMORT ➜ 2-2: … ➜ TIP: If you want to take a shortcut to eg. Period 5, you can use the following keys: ➜ 5, INPUT, 2nd function AMORT  Amortisation schedule Step 1 Step 2 15 000 PV SHIFT AMORT 9 I/YR 6N PMT = R3 343.80 Step 4 Step 3 To go to end of year 2: Press the “=“ sign Press 4 (2x2 periods) PRIN: Principal repaid INPUT Press “=“ again SHIFT INT: Interest paid AMORT Press “=“ again “=“ BAL: Balance outstanding Amortisation schedule Amortisation schedule ➜ An amortisation schedule tells us several things: - What is the total amount of interest paid over the duration of the loan - What each payment consists of - The balance outstanding at the end of a specific period ➜ In the previous example we calculated that each payment will be R3 343.80. In other words, if you borrowed money to buy a car, that will be the payment you make to the bank. Amortisation schedule ➜ In the first period, this payment of R3 343.80 consists of R1 350 of interest and R1 994 of the principal amount that is repaid. ➜ Compare this to the 5th period, where you pay R529 interest and R2 814 of the principal Amortisation schedule ➜ You pay more interest at the beginning of the duration of the bond ➜ Each payment will consist of the principal amount you repay plus a portion of interest. ➜ Since the payment is fixed at R3 343, your first interest payment is calculated as - [R15 000*0.09 = R 1 350], ➜ Hence the principal repayment becomes - [R3 343 – R1 350 = R1 994] Amortisation schedule ➜ Because of the repayment, your interest is calculated in the next period as - [(R15 000 – R1 994)*0.09 = R1 170] - This is continued for the rest of the payment schedule - The interest decreases as the principal amount outstanding decreases - Your payment remains constant Amortisation schedule ➜ Be careful when compounding and payments are semi- annually or quarterly. The schedule gives you number of payment periods and not years! ➜ Remember the example says over 3 years, but compounded semi-annually ➜ Hence, if you want to know total interest paid after 1 year, you have to add [R1 350 + R1 170] = R2 520. ➜ The total payment per year is R3 343*2 = R6 686 ➜ NB!!! This is a trick question in the test/exam! Make sure you read carefully whether they ask for period or year! Nominal and effective interest rates ➜ The nominal interest rate is the stated or contractual rate of interest charged by a lender or promised by a borrower. ➜ The effective interest rate is the rate actually paid or earned. ➜ In general, the effective rate > nominal rate whenever compounding occurs more than once per year. ➜ Effective r = (1 + nominal r/n)ⁿ - 1 ➜ NB! We always use nominal rates in questions, unless the question asks you what the effective rate is! Nominal and effective interest rates ➜ Assume a financial institution is offering 18,5% p.a. compounded monthly, on fixed deposits of R10 000 or higher for 1 year. What is the effective rate, r, per annum? ➜ In one year, R1 at r% (effective) p.a. will amount to 1 + r, ➜ and at 18,5% p.a. compounded monthly will amount to (1 + 0,185/12)^12 Nominal and effective interest rates ➜ Setting (1 + r) = (1 + 0,185/12)^12 ➜ r = (1 + 0,185/12)^12 -1 ➜ = 1,2015212 – 1 ➜ = 0,2015212 ➜ = 20,15%. Nominal and effective interest rates Using your calculator: ➜ Enter the nominal rate and press SHIFT, then NOM%. ➜ Enter the number of compounding periods and press SHIFT, then P/YR. ➜ Calculate the effective rate by pressing SHIFT, then EFF%. ➜ REMEMBER TO SET YOUR CALCULATOR BACK TO 1 P/YR!!! Basic patterns of cash flow ➜ The cash inflows and outflows of a firm can be described by its general pattern. ➜ The three basic patterns include a single amount, an annuity, or a mixed stream: Present value of a mixed stream ➜ Using Tables:  A mixed stream of cash flows reflects no particular pattern  Find the present value of the following mixed stream assuming a required return of 9%. Present value of a mixed stream ➜ C ALL, 1 P/YR ➜ Cf0 =0 ➜ Cf1 = 400 ➜ Cf2 = 800 ➜ Cf3 = 500 ➜ Cf4 = 400 ➜ Cf5 = 300 ➜ I/YR = 9% nd ➜ NPV (2 function PRC) = R1 904.76 The principle of equivalence ➜ A comparison of the financial merits of two or more alternative investment opportunities with different cash flow patterns can only be meaningful if the amounts for each alternative respectively, are reduced to a specific point in time. ➜ The principle of equivalence is explained in the next table: The principle of equivalence The principle of equivalence ➜ The only difference is the time framework of the annual cash flows as the total undiscounted cash flows are the same. ➜ On the basis of time value of money – B would be preferable to A (due to higher return in the earlier years) ➜ Compare B to C? What do you think? The principle of equivalence ➜ Although cash flow initially on B is higher than C, C nets a higher total cash flow. ➜ BUT: According to NPV, then B will be preferable to C, NPV of B > NPV of C. ➜ B and C can now be compared on the “basis” of the principle of equivalence. Questions 1. Our company considers buying an asset for R3 350. The investment is very safe, you will sell the asset in 3 years for R4 000. You know you could invest the money at 10% elsewhere with very little risk. Is this an acceptable investment? 2. Investment X offers to pay you R2 000 per annum for 4 years while Investment Y offers to pay you R2 500 per annum for 3 years. Which one of these cash flow streams has the highest present value if the discount rate for each is 5% and 20%? 3. It is estimated that your company will generate R27 000 per annum each year for the next 8 years from a new information data base. The computer system needed to set up the data base will cost R180 000. If you borrow the money to buy the system at 7% per annum, can you afford the new system? Solution 1 Option A: Buy asset for R3 350 and sell for R4000. Profit = R650 Or PV = 3 350 FV = 4 000 n =3 i/yr = 6,09% Option B: PV = R3 350 n =3 i/yr = 10% FV = R4 458.85 Solution: option B will be more profitable. Solution 2 Solution 2 Investment X: ➜ PMT = R2 000 ➜ N = 4 years ➜ I = 5% ➜ PV = R7 091.90 Investment Y: ➜ PMT = R2 500 ➜ N = 3 years ➜ I = 20% ➜ PV = R5 266.20 Solution 3 PV = R180 000 N = 8 years i/yr = 7% PMT = R30 144.2 Cash flow of R27 000 will not be sufficient to fund the re- payment of the loan. Homework ➜ Case study on click-up