![]() ![]() We will not work with Annuity Due situations in this text, however it is relatively simple to do so by making a simple adjustment to your calculator. Note that there is a variation referred to as an “Annuity Due” that assumes cash flows come at the BEGINNING of the period. With annuities, we assume cash flows come at the end of each period. Also, bond valuation is partially modeled as an annuity since we receive a fixed coupon payment each year. Simple retirement analysis can be structured as an annuity. For instance, calculating a mortgage payment on a home is an annuity. Many financial situations can be modeled as an annuity. Assuming a 5% discount rate, what is the most you would be willing to pay for that investment today? ANNUITIESĪn annuity is a sequence of equal, periodic cash flows. You are offered an opportunity to make an investment today that will pay you $100,000 in 20-years. Once we know what those future cash flows are worth to us today, we can evaluate the investment. Present value will be an important concept in valuation because most investments are structured in a manner that we pay a set amount today to receive cash flows in the future. The reason for this is that if we invested $3899.59 today and let it compound for 5 years at 9%, it would grow to $6000 at the end of the 5th year. Alternatively, we would be willing to pay $3899.59 or less to receive $6000 in 5 years, but we would NOT be willing to pay any more than $3899.59. In other words, we are indifferent between receiving $3899.59 today and receiving $6000 in 5 years – they both are worth the same to us. Thus, $6000 received in 5 years is only worth $3899.59 today (assuming a 9% discount rate). Assuming a 9% discount rate, what is this worth to you today?Īgain, we can ignore the negative sign in the answer (since the only non-zero cash flow that we entered was the $6000 Future Value). You are going to receive $6000 in 5 years. ![]() EXAMPLE TWO – Present Value of a Single Cash Flow The solution to this and other practice problems can be found at the end of this tutorial. You are investing $400 today and want to know how much you will have after 45 years if you earn a 9.5% rate of return over the 45-year time period. We will reintroduce this in a little bit. In our example, we only entered 1 non-zero value for a cash flow (the $10,000 PV), so the sign doesn’t matter. Specifically – IF YOU ENTER NON-ZERO VALUES FOR TWO OR MORE OF THE CASH FLOW KEYS (THE CASH FLOW KEYS IN THE 5-KEY APPROACH ARE THE PV, PMT, AND FV KEYS), YOU MUST BE CAREFUL OF CASH FLOW SIGNS. ![]() However, there are certain problems where this is important. In a problem like this you can just ignore the negative sign in front of the $15,007.30. If you receive $10,000 today, the only way for the problem to “balance out” is for you to give back $15,007.30 at the end of the 6th year. Because you entered the Present Value (PV) as $10,000, the calculator assumed you were receiving $10,000. The calculator needs to keep track not only of the dollar amounts, but which way the money is flowing. This is due to the way the calculator “thinks” when it is solving TVM problems. Notice that the answer came out negative instead of positive. Thus, you will have $15,007.30 at the end of the 6th year. In this example we are not using an annuity, so we are going to set the Annuity Payment to zero. The 7% rate of return means you have a 7% interest rate. You have 6 years, so the number of time periods is 6. Since you are starting with $10,000, that is your present value. You are investing $10,000 today and want to know how much you will have after 6 years if you earn a 7% rate of return over the 6-year time frame. EXAMPLE ONE – Future Value of a Single Cash Flow To solve, you just press the key representing what you are trying to find. The order that you enter the variables doesn’t matter as long as you enter the four that you know first, and then solve for the fifth. To do this, you must use the “+/-“ key on your calculator instead of the “–“ key. Sometimes you will need to enter a negative value. For example, if we want to put in 10 periods, we would enter this as 10 N. When entering values into your financial calculator you press the value you are entering first, then the key. PMT ⇒ This key refers to the Annuity Payment PV ⇒ This key refers to the Present Value Sometimes this interest rate is referred to as a discount rate or rate of return. I/Y ⇒ This key refers to the interest rate (do not enter as a decimal ⇒ 10% would be 10 not 0.10). N ⇒ This key refers to the number of periods Most of TVM analysis on your Financial Calculator can be done with the 5-key approach. ![]()
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