9. Borrowing Cost

This one is gonna be pretty easy. Here, we're just gonna look at the total cost of borrowing. There are two ways to determine the total cost of borrowing. One is cash out minus cash in. It seems pretty straightforward. The amount of money that you paid out minus the amount of money that you got in would leave you with the difference, which would be the cost. That's the first method. The second method is to add up all your cash payments, take away any premium, and add any discount, and that is your total cost to borrow. What we're trying to figure out here is if you have a bond, and it sells at either a premium or a discount, how much is it actually costing you to borrow this money?

Let's take a look at two different examples. Throughout this chapter, we've been looking at, one, a bond that sells at a discount. We say that that is a $100,000 bond, three years, semiannual, coupon rate is 10%, and market rate is 12%. And then we've been looking at this other bond that sells at a premium.

We'll call that one 100,000 also. Also three-year, semiannual, 10% coupon. But in this one, we say that the market rate is 8%. So you can see the bond is the same. All that's different is what the market rate is.

For the bond at a discount, we calculated that it would sell for 95,083, leaving us with a discount of 4,917. And for the one at a premium, we calculated that it would sell for 105,242, leaving us with a premium of 5,242.

If you wanna see how we calculated this stuff, go back and watch some of the earlier videos. Now that we have these two bonds, we're gonna try to figure out what is the total cost of borrowing for each of them. Now, the two methods are cash out versus cash in and cash payments minus premium plus discount. Let's do the cash out versus cash in first.

We'll say that one is the discount and bond two is the premium. And the formula we're doing is out minus in gives us cost. On the discount, how much is our cash out? We know that we're gonna have to pay back 100,000 at the end, and it's a 10% coupon semiannual, so we end up with 100,000 times 6 periods, times coupon rate of 5%.

So we end up with 30,000 of cash payments. Six $5,000 cash payments. So our cash out is gonna be 100,000 face value at the end plus the 30,000. And our cash in is how much? How much did we sell this bond for? Well, we sold it for 95,083.

So our cash in is gonna be 95,083. So we have 130,000 minus 95,083, and that comes out to 34,917. So our total cost to borrow is $34,917. Now, you may look at this number and think, "That looks oddly familiar."

Well, our discount was 4,917, and our total cash payments out were 30,000, which is why method two is cash payments out minus premium plus discount. So let's go ahead and just do method two for the discounted bond. We have cash payments out, six payments at $5,000 for a total of 30,000 plus the discount gives us 34,917. Either method works. It's just a matter of which one you want to do. Let's see if we can do the one on the premium side.

Cash out minus cash in. Cash out is actually gonna be the same thing because it's the same bond, isn't it? 100,000, three-year semiannual, 10%. So that's gonna be the same. Cash in, however, is the 105,242, 'cause we got paid extra because our coupon rate was higher than the market rate. 105,242, that gives us 24,758. So our cost to borrow was actually less than the total amount of cash payments. We made 30,000 cash payments, but you'll have to remember we got an extra five grand up front, so it stands to reason that our cost to borrow is going to be less.

The second method is cash payments plus any discount minus any premium. And of course, that gives us 24,758. It's nice when it works, isn't it? I personally find method number one a little bit easier to remember just 'cause it's cash out minus cash in. That's pretty straightforward on how you calculate the cost of anything. Basically, what is the net amount of money that you spent? What did you lay out and what did you get, and what's the difference between the two of those? But make sure you remember both. Neither of them is very complicated. And of course, you're only gonna have premium or discount.

You're not gonna have a bond that has both a premium and a discount. But this formula here will cover any type of bond, whether a premium or a discount.