Now it begins; quantitative methods is worth the price of admission! I intend for these posts to be helpful to not only CFA candidates, but also to MBAs looking to brush up on their quant skills (aka poets). Before you go any further, however, you MUST invest in a financial calculator. I use the HP-12C (Hewlett Packer); it is one of only two calculators recognized by the CFA Institute (the other being the Texas Instruments BAII Plus). The majority of calculations will involve no more than 5 buttons that are nicely placed next to one another on the very top of the calculator:
n (number of time periods)
i (interest rate per period)
PV (present value)
PMT (payment for a series of cashflows)
FV (future value)
Mastering time-value questions helps to build the foundation for more difficult calculations, such as "internal rate of return (IRR)" and "net present value (NVP)," which are critical for classes in Finance and Private Equity.
The simplest of time-value questions might ask you "what $1,000 invested today in a CD for 5-years compounded annually at a rate of 3.00% would be worth at maturity?" All you need to do is type $1,000 (press "PV"), type 5 (press "n"), type 3 (press "i"), and then press "FV" and within seconds it will give you the correct answer of $1,159.27. Of course this problem could have been made more difficult by telling you that the interest compounds monthly (rather than annually), but this only requires the slightest of adjustments (i.e. adjust the number of periods for "n" from 5 to 60 (5x12 months) and for "i" from 3.00% to 0.25% (3/12 months).
They can also ask you the question in reverse by requiring you to choose between two payment options by calculating PV. For example, say "you won the lottery and your two options are to either receive a lump sum of $1,000,000 today, or receive $2,000,000 at the end of 10 years with a interest rate of 4.00% compounded annually over that period. Which is the better option?" Begin by figuring out the PV of the future lump sum by typing 10 (press "n"), type 4 (press "i"), and type $2,000,000 (press "FV"). Then press PV and you will discover that it is worth $1,351,128.24 in today's dollars, and therefore the better option. Of course, good luck, postponing your purchase of a Ferrari for 10 years! With practice you an easily master time-value questions. After all, I majored in Political Science (minor in Philosophy) in college and now look at me crunch out these numbers!
You can also solve for the number of periods ("n"), or interest rate ("i"), provided you are given the PV and FV, as well as a third variable. For example, you may be asked the question: "What is the yield to maturity (YTM) on a corporate bond that was bought for $980 and pays a semi-annual 5.00% dividend, which will mature in 10 years at a face value of $1,000?" To solve: type 20 (press "n" 10 year bond x 2 annual dividend payments), type -$980 (press "PV" negative sign to signify outflow), type $1,000 (press "FV positive sign to signify inflow), type $25 (press "PMT" signifies semi-annual 5% dividend inflow based on $1,000 par value). Once you've input these 4 variables, press "i" and after about 10 seconds (btw this is a harder calculation) the calculator will tell you that the answer is 2.63%, which you must then multiple by 2 to get the annual rate (after all, we were working with semi-annual payments), giving you a final YTM answer of 5.26%. Predictably, the YTM is greater than the 5.00% dividend rate, because the bond was bought at a $20 discount ($1,000 - $980), which must be included into the overall investment return. In contrast, if the bond was bought at a premium to face value, say $1,020, then the YTM would have been lower than the dividend rate. One last point, to avoid future aggravation for why your HP-12C is not processing properly, you MUST follow the convention of using the negative sign to signify cash outflows (money-out), and the positive sign to signify cash inflows (money-in). Otherwise, in the previous example, you would have seen the "ErroR" sign if you used positive signs for PV, PMT, and FV. Again, this will be critical later when accounting for cashflows when solving for "IRR" and "NPV."
Continuing with the trend of asking increasingly difficult (but solvable) questions, see if you can answer this final question: "Your oldest child is currently 22 years old and just completed their undergraduate degree, when she mentions to you, that in 6 years (after they gain some work experience) she would like to study for an MBA at Oxford University. Currently, tuition for the Oxford MBA is £31,000, and has been steadily rising at 5% per year. How much money money do they need to invest per month now to have enough money to pay for the MBA assuming an annual 9% investment return?" You must first calculate the FV of the price of tuition, by typing £31,000 (press "PV"), type 72 (press "n" 6 years x 12 months), and type 0.417% (press "i" 5.00% inflation rate divided by 12 months). The FV is £41,819.55. Now start the second calculation by storing the £41,819.55 (press "FV"), type 72 (press "n"), and type 0.75% (press "i" 9% investment rate divided by 12 months). Once you press "PMT" you will see that you need to invest £440.17 each month in today's pounds for 6 years to afford tuition at tomorrow's inflation adjusted price. Stayed tune for more MBA boot-camp!
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