FIN 65 Calculating the Value of a Right

Let's take a look at problem 1111A. We're talking about rights offerings. So the last few problems, we've looked at flotation costs, the fact that you have to pay investment banks, and if you want to issue shares, it can be very expensive. And to save money, one of the benefits of rights offerings is that it's less expensive. So we're talking about cost of capital and how flotation costs should be considered. Well, this is a way to reduce costs, but it's just an interesting finance mechanism that we're going to explore in this problem. So let's jump into it. And this is, before I jump into it again, explain what it is. You're not issuing shares just to the general public, you're issuing shares and giving your existing shareholders the right to buy some of your shares at a discounted price. And the fact that you discount the price means every single one of those shareholders is highly incentivized to buy because you're just saying, well, I'll give it to you for cheaper than the market price. Every shareholder should buy and will likely buy. So it's a way to raise money and it's a way to raise money from your existing shareholders. Let's read the problem. Smith company is preparing a rights offering. The company wishes to raise $10 million. The stock currently sells for $75 per share, and there are 1.2 million shares outstanding. The subscription price is set at $50 a share. So the market price is $75. We're saying, hey, you want to buy new shares for $50, here's your chance. So we want to raise $10 million and we're going to do it at a $50 per share increment. So how many new shares are going to exist in the world after this offering? If everything goes well, 10 million divided by 50, there's going to be 200,000 new shares. Okay, so I'm going to be issuing 200,000 new shares, 50 bucks a share. I'm going to get $10 million, good for me. What happens to my shareholders? I don't just go first come first serve. I don't say, okay, well, first come first serve, because then I'm just totally advantaging some shareholders over others. And so here's the deal. We go, well, we have 1.2 million shares out there in the world. We want to have 200,000 new shares. That means for every six shares you own, so 1.2 million divided by the 200,000 new shares. Well, every share you own, you get a right and six rights entitles you to purchase. If you have six rights, you can exchange them and buy one $50 share. And so this is a good deal. If you are a shareholder, you own six shares, you should want to do this because again, you're getting a discount on something that it's $50 cost you $75 to buy in the open market. Why the heck not, right? You should want to do this. Now, something that you're probably astutely observing is if everybody buys up all these, you know, $50 shares, doesn't that reduce the value of my $75 share? And the answer is yes, this is diluted, right? It dilutes down the value of our $75 share. So the question says, what's the X rights price? That's saying if once everybody exercises their rights and everybody's gonna, what is the new price going to be? What's the price going to settle in at for a share of stock? Because these $50 shares are just the same as the $75 shares. They're going to trade just the same way. So it's going to drive the price down. What's the new price going to be? And the easiest way to contemplate this is to consider one shareholder who owns six shares. So again, obviously people in hundreds or thousands of shares potentially, this person owns six. Okay. So they own six shares and they have an asset that's worth six times $75, $450. And they take my finance course and they go, well, Tony Bell said you better exercise those options. And so they do. Let's just say that they do. So they buy one more share at $50. So that's a $50 share. Now these shares are all, you know, part of the same family. So now they have seven shares, seven votes. And the value of their shares is $500 in total, right? What they, you know, what they've paid here. So 500 divided by seven means the new value per share is $71 and 43 cents. So that is our X rights price. Once everybody exercises their option as we think they will, it's going to be $71 and 43 cents. But what if I don't want to, right? What if I don't want to? Well, I got six rights and there's another way of thinking about these rights. I got six of these rights and they dilute down the price from 75 to 71. The difference is 75 minus 71.43. So let's subtract 75 from that. I'll hit the plus minus. They're worth $3 and 57 cents each. That's the difference between the price before and the X rights price is $3, 57 cents. That is the value of a right. That's how much a right is worth. So again, let's go at this from a different angle. Let's say I take my six rights at $3.57. So it's six times $3.57. It's $21.42. And if I want to exercise it, I got to give the company $50. So plus 50, I'll put the plus 50 there. What is the value of what I've bought? Well, six rights cost $3.57 each plus the $50 I give the company. I have $71.40. Now there's a rounding thing going on here, but you can see it's the X rights price. So I'm kind of going at the calculation from two different angles. The bottom line is the X rights price is $71.43. The value of the right is $3.57. Now, is the shareholder better off, worse off, or the same because of the offering? They're in the exact same place. And this math kind of shows it. So before the offering, they had, uh, well, I'm going to write it out again. Six at $75 for $4.50. Let's just say they exercise. So that's scenario one. They exercise. One times 50 is 50. So they have 507 shares and we said the value per share is 71.43. Oops, 43. Well, let's think of where they were before. They had an asset worth 4.50 and they had $50 cash in their pocket. Now they have $50 less cash, but they still have $500 worth of value in the company. So they're no worse off if they exercise their shares. What if they don't exercise those or their rights? What if they don't exercise their rights? Well, then they can sell them. So they end up with six shares at 71.43. They didn't exercise their rights. Now we said that's going to be the value afterwards. Six times 71.43, 428.58. But remember they would have sold six rights at $3.57 a piece. Six times 3.57. Is 21.42 and they have $450 of value from that $420 of stock. And now $21, they've liquidated $21 of cash value out of their shareholdings. The only way the shareholder would be worse off because of the offering is there's really three things they could do. They could exercise the right, which is fine. They could sell the right, which is fine. If they did neither, if they just said, okay, I got this option. I'm not going to exercise the option and I'm not going to sell the option. I'm just going to hold onto it and let it expire. Then they are worse off. Okay. There we have it. We've solved 1111a as always. Thanks for watching. Goodbye.