Annuities Overview

1. Annuities Overview

Another application of discounted cash flows is to value annuities. Now, an annuity is a fixed amount of money paid or received at equal time periods for a fixed number of years. Common examples of annuities include mortgage payment when buying a house, retirement and camp, and the form of fixed cash flights, other types of loans that she is also lines, we can use Excel to introduce the ideas behind annuities. Let's say that you had the opportunity to invest in a three year annuity, which is promising to pay you 1000 at the end of each of the three years. The annuity is also promising to give you an 8% return, what should you pay for the annuity today? We can use DCF to work out the answer. So the annuity payments 1000, that's the amount that you get at the end of its year, the annuity is promising to give you an 8% return, so that's the rate. And it's a three year annuity. So let's complete DCF table just below, we've got three cash flows because they are three year annual annuity, so time is one, two, three. The future value where you're always receiving 1000, so I can absolutely reference that and then just Ctrl+D to fill down. Now I need to find the discount factor for each of the three years, and remember the discount factor equals one over, open[one plus the discount rate, which I will absolutely reference by pressing a four] raise to the power of n which I'll leave as a relative reference so that when I select the result and highlight the column and Ctrl+D fill down, what's happening here is that the discount rate is always 8%, but n is changing to reflect the year that we are in thus changing the discount factor. So what's the present value of a 1000 payment received one year from today if you're getting a 8% return, while the present value is 925.93? What's the present value of a 1000 payment in two years from today if it's giving you an 8% return or their future value times discount factor means that present value is 857.34. Finally, what's the present value of a 1000 payment, three years from today that's promising to give an 8% return. Well, we take our future value multiplied by the discount factor, and we see that same 193.83. So if we sum those present values that tells us the price which would pay today in order to receive 1000 each of the next three years and generate a 8% return.

2. Let's practice!

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