Latest / VoraPrep Audio — Professional Licensure & Certification Exam Prep / [CFA Level I] CFAQM: Rates, Returns, and Time Value of Money Fundamentals
Transcript
- Hey, welcome to VoraPrep Audio. Thanks for tuning in. Let’s picture this, because you will absolutely see a version of this on your exam. You’re a junior analyst, and your boss drops three investment proposals on your desk. One pays a big lump sum in five years. Another one is a steady stream of payments for ten years. The last one is just a mix of uneven cash flows. They all have different risks, so they all need different discount rates. Your job? Figure out which one is the best deal. To do that, you have to master one of the most fundamental ideas in all of finance: the time value of money. All it really means is that a dollar today is worth more than a dollar tomorrow. Why? Because you can invest that dollar today and it can start earning more money for you. A dollar today is like a seed. You can plant it, and it grows. A dollar you get a year from now is just a dollar. It hasn't had time to grow yet. The interest rate is what tells us how fast that seed can grow. When you see an interest rate on the exam, you need to look closely. The stated rate, or nominal rate, is the number they advertise—like "8% per year." But what really matters is how often it compounds. If it compounds quarterly, you need the periodic rate. That’s just the stated annual rate divided by the number of periods. For example, 8% per year compounded quarterly is 2% per quarter. To really compare different investments, you need the Effective Annual Rate, or EAR. This is the true rate you earn after factoring in all the compounding. An account that pays 8% compounded quarterly gives you a slightly higher return than one that pays 8% compounded annually. The EAR is what lets you make that apples-to-apples comparison. The formula is one plus the periodic rate, raised to the power of the number of periods, all minus one. Let's cover a few other key terms. The discount rate is the rate you use to find out what future cash flows are worth today. It's your required rate of return. Think of it as the minimum you need to earn to make an investment worthwhile, after considering inflation and risk. The core skill here is moving money back and forth through time. When you move money forward, you're calculating its Future Value, or FV. When you bring future money back to today, you're calculating its Present Value, or PV. You’ll see a lot of questions about annuities. An annuity is just a series of equal payments. The key distinction is timing. If payments happen at the end of each period, like a car loan, that's an ordinary annuity. If payments happen at the beginning of the period, like rent, that's an annuity due. An annuity due is always worth a little more. That's because each payment gets an extra period to earn interest. And a perpetuity? That's just an annuity that goes on forever. The single most important rule here is the cash flow additivity principle. It sounds complicated, but it's not. It just means you can't add cash from year one to cash from year five. That's like adding pesos and yen without converting them to a common currency. The result is meaningless. You have to bring all cash flows to a single point in time. This could be the present, or some point in the future. Only then can you add or subtract them. When a time value of money question appears, use this mental checklist. First, identify the type of cash flow. Is it a single payment? A neat annuity? Or a mix of unequal cash flows? This tells you which calculator functions to use. Next, figure out what you know and what you need to find. Your financial calculator has five main keys. There's N for the number of periods. I slash Y for the interest rate per period. PV for present value. PMT for the annuity payment. And FV for future value. The question will give you most of these values. You just solve for the one that's missing. Next, and this is critical, check the compounding frequency. If it's anything other than annual, you must adjust your inputs. For a 5-year loan with quarterly payments, N isn't 5. It's 5 times 4, which is 20. And the interest rate isn't the annual rate. It's the annual rate divided by 4. You must adjust both N and I slash Y. If you’re dealing with an annuity, double-check your calculator mode. Most calculators default to END mode, for ordinary annuities. If the question says payments are at the beginning of the period, you have to switch it to BEGIN mode for an annuity due. Finally, you solve. But be careful with your signs. Money leaving your pocket—an investment—should be a negative number. Money coming into your pocket should be positive. If you mix them up, you’ll get an error or a wrong answer. Let's try an example with uneven cash flows. This is where the additivity principle is key. Say an investment pays you 100 dollars in one year, 200 in two years, and 300 in three years. The discount rate is 8%. What's the present value of this entire stream? You can't just add 100, 200, and 300. That's financial malpractice. You have to discount each payment back to today. So, you take the 100 dollars and divide it by 1.08. You take the 200 dollars and divide it by 1.08 squared, since it's two years away. And you take the 300 dollars and divide it by 1.08 to the third power. This gives you about 92 dollars and 59 cents for the first payment. 171 dollars and 47 cents for the second. And 238 dollars and 15 cents for the third. Now they're all in today's dollars. So now you can add them up. The total present value is 502 dollars and 21 cents. That’s the cash flow additivity principle in action. Now, let's cover the common traps. The number one mistake is the compounding frequency. It's easy to get excited, see a 6% annual rate compounded quarterly for 5 years, and forget to adjust. You must remember to adjust. N becomes 5 times 4, which is 20. And I slash Y becomes 6 divided by 4, which is 1.5. Always adjust both. The second trap is mixing up an annuity due and an ordinary annuity. Forgetting to switch your calculator to BEGIN mode for a "payment at the start of the year" problem is an easy way to lose points. The third trap is the sign convention. Your calculator thinks in terms of cash inflows and outflows. If you invest 10,000 dollars, that's an outflow. Enter it as a negative PV. The future value you get back will be a positive FV. Be consistent. Let’s try a couple of practice questions. Get your calculator ready if you can. First question: An investor deposits 10,000 dollars today into an account that pays 6% annual interest, compounded quarterly. How much will they have in 5 years? Okay, let's set it up. The number of periods, N, is 5 years times 4 quarters per year. So N is 20. The interest rate per period, I slash Y, is 6% divided by 4. That's 1.5. The present value, PV, is the 10,000 dollars you're depositing, so we make that negative 10,000. There are no other payments, so PMT is 0. Now, compute FV. You should get 13,468 dollars and 55 cents. Let’s do one more. What's the present value of an ordinary annuity that pays 500 dollars at the end of each year for 8 years, if the discount rate is 7%? Okay, this is an ordinary annuity, so your calculator should be in END mode. N is 8. I slash Y is 7. The payment, PMT, is 500. There's no lump sum at the end, so FV is 0. Now, compute PV. You should get negative 2,980 dollars and 60 cents. The negative sign just means that's what you'd have to pay today to receive that stream of future payments. Here are the key takeaways. First, always adjust N and I slash Y for the compounding frequency. Second, know the difference between END mode and BEGIN mode for annuities. Third, use your sign conventions correctly for cash inflows and outflows. And finally, never add cash flows from different time periods until you bring them to a common point in time. Practice these on your calculator until it becomes muscle memory. VoraPrep is a full exam-prep app — lessons, practice questions, and an AI tutor in one place. Get started at Vora Prep dot com.