CF 3-16A – PV of an Annuity – Corporate Finance

Let's take a look at problem 316, a present value of an annuity problem. You can see I've got the formula ready to go. We'll solve it first with a formula, then we'll solve it with our fancy financial calculator. But before we can do any solving, let's do some reading. You won a $50 million lump sum lottery prize. Wouldn't that be nice? Knowing that you're not good with money and are likely to waste it, you decide to buy an annuity, which will pay $100,000 per year for the next 40 years, starting one year from now. Your logic is that even if you blow the rest of the money, having a guaranteed $100,000 per year would be sensible. The current interest rate is 4% annually. So it says how much money do you need to deposit into an annuity today in order to meet your $100,000 per year for the next 40 years? And this is a very straightforward annuity problem. So we see the formula there. We'll start by solving with the formula, then use our financial calculator. We see the formula. Present value of an annuity equals the recurring cash flow, which in this case is $100,000, times, and then this big bracketed, ugly mathematical thing, 1 minus 1 over 1 plus the required rate of return, or the interest rate in this case, 4%. So 1.04 to the power of T, how many years? 40 years. So 1.04 to the 40th power, all divided by the rate of interest or required rate of return. There we are. So that's what we're calculating. PV equals 100,000 times that big messy bracket. Okay, let's deal with the bracket. So we deal with our exponent first, 1.04 to the power of 40, 4.8. Okay, 1 divided by 4.8, I use this 1 over X button, I get 0.2. 1 minus 0.2, it's going to be 0.8, well, 0.792 or 0.793. So I go, I do minus 1 equals, and then I hit the plus minus button, there it is. So now I've got the numerator complete, I divide by 0.04, and now I've resolved the entire piece of the brackets. 19.79 is the annuity factor here, 19.793. So I'm going to go 100,000 times 19.793, and that's going to give me my answer, so I just multiply that number by 100K, and I get 1.979277. So I won $50 million, congratulations to me. If I wanted to lock in 100 grand a year for the next 40 years, basically the rest of my life, that's how much money I need to set aside right now. So that is the PV of the annuity, we've answered the question. So that's all you need, great. If you want to see it done in the calculator, stay tuned, here we go, let's put it in the calculator. So I'll just start with the N, it's 40 years, so 40 goes in as my N. My IY, 4, 4% annual interest, so I put 4 in as my IY. My PV is what we are solving for, my PMT is how much we're going to be receiving on a regular basis, $100,000 is the PMT, and the future value will be zero, we're dripping this thing down to zero. So let's compute the present value, and you can see there negative 1979277, and that does indeed match with what we had figured, 199, 1979277. Okay, we've solved the problem two ways, I hope the video helped, and if it did, I hope you'll give me a thumbs up. All right, thank you so much for watching, see you in the next video, bye-bye.