FIN 17 Calculating Present Value of a Lump Sum

Let's have a look at problem three, three, a, uh, present value question. Your grandfather makes you an offer. They say I'll give you a hundred thousand dollars today or $200,000 in 10 years. Assume you wish to use a discount rate of 8%. Are you better off or worse off if you take the money today and by how much in today's dollars? Okay. Uh, so there's a, I think a quick, easy way to solve this, but the issue is actually the second part. The first part should be easy. Cause you can just go, okay. If he gives me a hundred thousand dollars today, I can go, well, I can invest that at 8%. So times 1.08 to the power of 10. And I can say a hundred thousand dollars today. Times 1.08 raised to the power. Oops. 1.08 raised to the power of 10 times a hundred thousand. Uh, you can see, uh, I make $215,892 and 50 cents. Uh, I should take the a hundred thousand dollars today, right? A hundred thousand dollars today in 10 years is worth whoops. Uh, two 15, eight 92. I'm clearly better off to take the a hundred grand today than to take 200 grand in 10 years, but in a $15,000 better off in 10 years. How much better off am I in today's dollars? Well, the way we would get at that is to take this $200,000 and discount it back to today. So how would you go about doing that? Well, the present value times 1.0 in this case, 1.08 to the 10 equals the future value, right in this scenario. So the present value times 1.08 to the 10 equals $200,000 to discount it back. You just divide by 1.08 to the 10. So I'm going to take 1.08 to the power of 10, 2.159. And I'm going to divide 200,000 divided by 2.159. And that's going to give me how much that $200,000 is worth today. Again, 200,000 divided by 1.08 to the 10. So 200,000 divided by 2.159. To do that, just to keep all the decimals, you can go one over X in your calculator to divide 1 divided by 2.15 and then multiply that by 200. That discounts the money to today. I get 9, 2, 6, 3, let's call it 9, 2, 6, 3, 9. So $200,000 today is worth 92,639. I'm being offered $100,000 today, or I can take something that's worth $92,000 today. I should obviously take the $100,000. Now what's the difference? It's a difference of 7,361. So you are $7,361 better off if you take the $100,000 today. So that is the answer to the question. Showing you how to do this in the financial calculator. Let's think of our inputs here. The number of periods here is, what is the number of periods? 10. Our interest rate is 8%. Our present value is what we're solving for. Our PMT is zero. Uh, our, we don't have to worry about a payment at the beginning. And our future value here is positive $200,000. So what is that in today's dollars? Uh, okay. Clear second function, clear TVM, second function, clear work. Okay. Making sure everything's clear. Uh, 10 goes in as N. Eight goes in as IY. Uh, zero goes in as PMT and 200 goes in as FV. And now I compute PV and I get 9, 2, 6, 3, 9, 9, 2, 6, 3, 9. And in other words, I'd have to give up $92,000 today. That's why it's negative. I'd have to give up $92,000 today to get $200,000 back in 10 years. Uh, so I'd rather get the $100,000 right now. And you can see the numbers do indeed match up. There we have it. We've solved 3, 3, A. As always, thanks for watching. Bye-bye.