CF 4-7A – Corporate Bond Calculations – Corporate Finance

Let's have a run through problem four, seven, a more bond calculations, lots of present values to be done. I'll do them all in my financial calculator first, and then I'll circle back and I'll just do Starshot. I'll do the first one here, um, by hand afterwards. So if you're somebody that has to do it by hand, I understand it's a little more time consuming and honestly a little more tedious, but it's doable. It's not hard. It's just, you got to take your time, but let's go through with our financial calculator calculator first, and then we will solve, uh, Starshot by hand. So we're given a bond table and we're just missing information, right? Starshot is missing. It's coupon, uh, coupon, by the way, uh, is what drives the PMT, right? That's the regular payment. Is this the coupon? It's the interest payment. So as I'm thinking about my financial calculator, I'm sort of, I translate coupon into PMT. Their maturity is all about the number of periods. Price is the present value. How much would you pay for this bond today? And yield is our discount rate or our IY in our financial calculator. So we're asked to fill in the missing information. Starshot's missing the coupon. So Starshot, uh, we'll call this company one, company two, company three, Starshot's company one. It's missing the PMT, uh, company two ascendancy is missing the PV, the, uh, price and company three is missing the yield. So that's sort of what we're going to solve for. The starred things are what's missing everything else we should know about these companies. So it's always like one thing missing in these finance questions and here it's very plain that one thing is missing. We can compute it. Uh, so let's start with the first company, Starshot, the number of periods here, 10 years. So that's 20 compounding periods, our IY 6.5% per year. That's 3.25 per six months because these are semi-annual coupon payments. So we've got to convert everything into semi-annual data. So 10 years, that's 26 months periods, 6.5% per year is 3.25 per six months. Uh, PV is the price and the price, the price is quoted as a percentage, right? So we're, uh, the company's asking a thousand dollars or giving a thousand dollar face value for his bonds to buy it. You got to pay 92% of the face value. You have to pay $927 and 30 cents to buy $1,000 bond. You got to pay 92% of the full price. I put it in as a negative spat all over my computer screen here. I put it in as a negative, uh, because, uh, it's a negative cashflow. You're buying a bond. So, uh, the PMT will come out as a positive. That's the positive cashflow from the bond. And the FV also will come out as a positive. That's, you know, the lump sum coming back to at the end and the lump sum at the end here is a thousand dollars. We don't know what the regular coupon payment is going to be. Let's solve for it. 20 goes in as our N 3.25 goes in as our IY negative 927.3, 927.3 negative goes in as our PV PMT. We don't know. A thousand goes in as our FV and we compute PMT and I get 27.4997. Uh, I'm going to just call that 27.5. Now that is our payment every six months. So annualized 27.5 times two is $55 in interest per year, 55 per year. Well, on a thousand dollar bond. Uh, $55 in interest per year is five divided by a thousand point 0.55. It's 5.5%. So our coupon would be quoted as 5.5%. 5.5 is the answer for part one, Starshot coming to ascendancy. Okay. Coupon is 7.5. So we're just working backwards from what we just did on Starshot. It's a thousand dollar bond. 7.5% is $75 in annual coupon. Divide by two, we get 37.5. That's what's going to go into our calculator as the PMT. Oops. I'm kind of jumping ahead here, but it is 37.5. Let's look at the N, the number of periods for that second bond. It's 30, 15 years, semi-annual payments. That's 30 payments. Our IY 7.2, that's going to go in as 3.6 half. Our FV is a thousand. That one actually took care of itself quickly. I'm alarmed at how quickly that went, because I think I must have skipped a step. I try to explain every step in detail. I might not have done the job there, but hopefully you're doing your best to keep up. I'm sorry in advance if I skipped a step there. It felt like I was quick to get to the calculator. 30 goes in as F. 3.6 goes in as IY. We don't know our PV. Uh, 37.5 goes in as the PMT. A thousand goes in as FV. And then we compute, uh, what do we compute in PV? 1027.25, 1027.25. It shows up as a negative number here because that's a negative cashflow. All right. I'll switch it back to a positive number. Now we're saying what percentage, the face value of the bonds, $1,000 to buy one. You got to pay a little bit more. So it's like we're paying 102%. So I was just divide by the face value. And then that number is my percentage. So 1.02 is the same as 102.72%. So 102.72 and you know, whatever, however many decimals your professor wants to go to, I would seeing this one was three. I was like, okay, I'll go for three. That's as many as we're going to need. 102.725. That's the percentage of the face value of the bond. You got to pay to buy a bond. Okay. Last one, a number of periods for bond. Number three is 20 silver line ventures. So 20, uh, years rather is 40 semiannual periods. Our PV is 117.468. So, uh, we have to pay a $1,174.68. If we want to buy one of these bonds, I'll put that in as a negative. Our regular payment amount is based on the coupon. Again, looking at the third bond here, 9.2. So $1,000 times 9.2% is 92 bucks a year. Divide by two is 46 bucks every six months. And a thousand goes in as our FV. Let's crunch the numbers. 40 goes in as N. 1174.68 negative goes in as PV. 46 goes in as PMT. A thousand goes in as FV. And now I compute IY. Where are you? IY. There you are. 3.75. Now remember to get it into the table, 3.6 was 7.2 in the table. 3.25 was 6.5 in the table. Well, 3.75 is 7.5 in the table. And there we have it. We've solved them. Uh, our PMT for the first one is 5.5 or our coupon rather. Our price for the second one is 102.725 and our IY for the third one was 7.5. Congratulations. You made it, you got to the end. As I promised though, I'm going to come back and I'm going to do the first one by hand. You can do the first two of these by hand. The third one, I don't think so. IY is just torturous to do by hand. It was even like 7.5. Yeah, you could get there, but you know, when it's 7.325 or something like this, it's trial and error to calculate IY is a pain. You can do it in two seconds in a financial calculator, but we'll do a Starshot company by hand. To do it by hand, you have to break the bond down into its component parts. Uh, there's the present value of an annuity. Those recurring payments will take the present value of those. And we'll also take the present value of the lump sum, the thousand dollars at the end of the bond. And that combines to give us the present value of the bond. So this question we're missing the coupon, right? The regular payment to the regular cashflow of the bond. That's what we're looking for. And that is right here. So, uh, that's what we're solving for. We should have every other component of this. And we do, we have the present value of the bond. The bond price is 92.73% of a thousand dollars. So the PV of the bond is nine to 7.30. The C is what we're solving for. We'll multiply that by bracket. There went a little wonky one minus one over one plus R. So it's one plus our yield. But remember a yield is given annually. We need to divide it by two. So it's, uh, 3.25%. So it's 1.0325 to the power of T the number of periods, which is 20 semiannual periods to the power of 20, uh, all divided by 0.0325. Brackets were way overkill. Let's make them a little smaller. Oh, much more beautiful. Add that to our FV, our future value of our bond, which is a thousand divided by 1.0325 to the power of 20. Okay. So I'm going to solve for, uh, I've already got my left here. I'm going to leave C I'm going to solve for what's in the brackets. I'm going to solve this one. So let's solve. So solving for what's in the brackets, uh, 1.0325 to the power of 20. Equals 1.8, nine, five, one over X 0.5, two, seven, five, one minus that minus one equals 0.47 divided by 0.0325 divided by 0.0325. I get 14.54. Okay. So 14.54 C times 14.54 plus a thousand divided by 1.035, 1.0325. So that's when he is 1.0325 to the power of 20 equals one over X times a thousand equals 527.47 equals 927.3. So 927.3 equals C times 14.54. Now we're just in like algebra mode. Uh, we'll subtract 527.47 from 927.3, 927.3 minus 527.47. I get 399.83 equals 14.54 times C divide both sides by 14.54. So this number divided by 14.54 equals our payment. Uh, C equals 27 point. I'm going to call this it's 27.4986. We're going to call this 27.5. And remember that every, uh, six months, so double it to get annualized. And we end up with a payment of 55. And this number is looking very familiar to me. Uh, 55 divided by a thousand gives us a coupon rate of, uh, 5.5%. So that's the number that would go in our table. And that is the number we got earlier in the question. So there we've done it. We've done it by a calculator. But we can also do it by hand. And the payment's hard to do by hand. PV, uh, the price is easier to do by hand. And then the yield is very, very difficult to do by hand, but we won't worry about that. Okay. We have solved this, uh, in our calculator and now we've solved it by hand. Hope this video helped. And if you made it to the end, for goodness sakes, I hope you'll hit me with one of those sweet, sweet likes. All right. Have a great day. Bye bye.