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Welcome back, in this lesson, we'll be talking about discount in premium.

This is a situation that's very typical when bonds are issued.

That they're seldom issued exactly at the face value,

instead there's a discount or a premium.

So why is there a discount or premium?

Well, it's because they're issued at market value,

either by an auction, maybe a negotiated rate or according to a benchmark.

And because rates change almost daily, many bonds are issued at a discount or

a premium to the planned interest rate.

We may have a planned interest rate, but

it may have moved on them between the time the plan was made and

the bonds were structured, and the time the bonds are actually issued.

The result is a discounted premium.

When you have a discount or a premium, this changes the interest rate.

And the FASB requires that you change the effective rate,

so that it will represent a level rate on the sum of the face value of the debt,

plus or minus the premium or discount.

Plus premium minus discount, and minus expense at the beginning of each period,

so that that amount reflects what you've actually borrowed.

Why does a discount or a premium change the interest rate?

Well, a discount means that the cash proceeds

are less than the face amount of the bonds.

That means, I'm going to pay interest on the face amount of the bonds,

but I didn't receive that much.

It's like I borrowed less than the face amount, but

I'm paying interest on the face amount.

That means that my effective interest rate is higher than

the stated interest rate on the bonds, because the same

amount of interest is attributable to a lower amount of debt.

If there's a premium,

that means the cash proceeds are greater than the face amount of the bonds.

Again, I'm still paying the same amount of interest on the face amount,

but I received a higher amount.

That means that the effective interest rate is lower.

So a discount or a premium will change the effective interest rate.

If it's a discount, the effective interest rate will be higher.

If it's a premium, the effective interest rate will be lower.

In both cases because the cash interest that I'm paying is based

upon the face amount, whereas that's not the amount l actually received.

The difference between the periodic costs using the interest method,

using the effective rate.

And the nominal interest,

the amount that's on the cash that I'm paying out each month,

will be an amortization of the discount or the premium.

That's a mouthful, but we'll take a look at it in a real example and

it should make it a little easier to understand.

Okay, for an example, we're going to use Padre Pizza again.

Now they're issuing $10 million of bonds on January 1st, 2016,

that'll mature in 8 years.

So the bonds will mature on 12/31/2023.

They have a stated interest of 8%,

but they were sold to yield 7.75%.

The bonds, again, pay interest semi-annually.

So were the bonds sold at a discount or a premium?

Well, if they're going to pay interest at 8% but

they were sold to yield 7.75%,

that means that the yield on the bonds is less than the stated interest rate.

So the investor paid a premium to get the bonds.

So what is the price paid for the bonds?

That's a net present value problem, let's take a look.

You can the present value of a semi-annual annuity for

16 periods at 7.75%, again, adjust it for the fact that it's semi-annual.

And the present value of 10 million that you'll receive at the end of

the 16 periods.

So the present value of the 10 million at the end of 16

periods discounted at the 7.75% annual adjusted for.

We're going to use semi-annual to be consistent with both.

It's $5,442,813,

the 400,000 interest, this one's paying 8%.

So it'll pay 400,000 semi-annually for 16 periods.

Discounted at 7.75%, adjusted for semi-annual,

so it's 180/360 or 1/2, is 4,704,193.

The total proceeds then would have been $10,147,000.

The result here, well, I left off $6, but you get the idea.

The bonds then are sold at a premium over the stated value of $147,006.

So on issuance, we'll have a journal entry to show the cash we've received,

the premium on the bonds, and the bonds payable.

The bonds payable here, usually these are combined, the bonds payable and

the premium, into a single account, which will be the carrying value.

I separated them here to make it clear what the separate amounts are.

Now that bond premium of $147,006 will be amortized

to provide a constant effective interest rate.

So for each period,

the interest expense will be the effective rate times the carrying value.

And the difference between the cash paid and

the interest expense will be the amortization of the premium.

So to show you an example, if the interest expense will be the stated rate,

7.75% times 180/360, times the carrying value, which includes the premium.

The face value of the bonds plus the premium, the cash we received, so

the interest expense for the first period will be 393,196.

Well, I'm actually going to pay out 400,000.

I subtract my interest expense of 393,196.

I have amortization of the premium of 6,804.

So my new carrying value of the debt will be

$10,147,006- 6,804.

I've just amortized premium, equals 10,140,202.

I'm going to repeat this every period, why?

Because at the end of the term of the bonds, that carrying value,

which is the face amount of the bonds plus the premium I received,

is going to be 10 million.

You'll see, let's go to Excel and we'll take a look at how this mathematics works.

In this segment, we're going to show how it varies when you're given

the yield as opposed to being given the price for

which the bonds have been sold, it's actually easier.

So this is the same spreadsheet that we just prepared for our previous exercise.

Again, we've put all of our variables into a table,

10 million, 16 periods, 8%.

We've calculated the interest that will be paid, and now the carrying value

is the amount that's going to be calculated, not the yield.

So we don't have to use the Goal Seek to come down and

calculate this effective rate, that's given now in the problem.

So instead, that effective rate is going to go into

calculating our net present value of the interest,

and the net present value of the principle at the end of bond issue term.

We total those up now at this effective yield,

which we're given in the problem, that it's been sold at.

And we now know that the carrying value,

the total present value is going to be $10,147,006.

Now in real life, you're going to have to probably combine these two techniques,

because you may get a yield, but it's going to be adjusted for issuance costs.

But in this problem, we kept it simple.

We can assume that the issuance costs are zero.

We'll relax that constraint soon, soon enough.

So here, You can see the same thing.

The total present value comes down to the carrying value.

Again, I'm calculating the interest at the effective rate times the carrying value,

and that just carries on throughout the entire life of the instrument.

Again, I can tell I got the right answer at the bottom because my

final amortized amount is equal to the amount that I'm going to pay at the end.

Here's my journal entries.

Again, they trace exactly from my amortization table,

Including the amortization of premium, which is 6,804 in the first period and

12,034 in the final period, And my final payment the bond.

Okay, so let's do the journal entries for June 30th based on that math.

We're showing the interest expense, as we calculated it,

of $393,196 on June 30th.

The premium on the bonds, which decreases the carrying value of the bonds,

and there's my cash for 400,000.

And the cash will always be the same, but

the interest expense is going to change every period.

So the new carrying value is 10,133,135 in Period Two.

How did we get that?

We take the beginning carrying value, we subtract the amortization

of premium during the second period, get a new carrying value.

Now notice the amortization in the second period of 7,068 is

more than the amortization that we had in the first period.

What's happening?

Well, the amortization is increasing at an increasing rate.

So the interest expense, therefore, decreases every period for

which the bonds has been issued at a premium at an increasing rate.

So graphically, you can see that the interest expense starts out at 393,000.

It's decreasing at a increasing rate, and

it will only be about 388,000 at the end of the period.

Just a reminder, here's the amortization schedule that we prepared before.

You can see how the interest is declining over the period of the loan,

the amortization is increasing each period.

At the end of the period, the carrying value is 10 million.

And when we make our final payment of 10 million, the balance will be 0.

So at maturity, the same entry we've had before, bonds payable and cash.

The bond premium has been fully amortized.

So what if the bonds are issued at a discount?

Well, the mathematics is identical.

The only difference is,

the interest rate will now be higher than the stated interest rate.

The effective interest rate will be higher than the stated interest

because my stated interest is on a face value that's a higher

number than the amount that I actually received.

My carrying value being lower, that means my effective interest rate is higher.

My interest expense will be greater than the cash paid, but

that discount will amortize the exact same way over the period,

and at the end of the bond term, it will still be zero.

So is it required to amortize the bonds with this effective rate?

Well, yes the FASB does put that as a requirement, but

they do permit an alternative that you can use other methods of amortization.

If the results that you get are not, quote, materially different, unquote,

from those that would result from using the interest method.

So could you use straight-line?

Well, maybe you could, maybe you could if it's not materially different.

So when would that be?

Well, let's take a look at our problem here.

The premium that we have could be amortized straight-line

if the difference is immaterial.

So in our example, $147,006 of premium

could be amortized equally over each of the 16

semi-annual periods when you make interest payments.

So if I take $147,006 and divide it by 16,

I get $9,188 per period.

So the interest expense per period would be 400,000

of cash payments minus $9,188 of straight-line

amortization of the premium, equals 390,812.

And you'll have the same entry every period,

because it's a straight-line amortization.

FASB does require the use of the effective yield for

amortizing bond discount and bond premium.

But what if it's just a small amount of bond discount or bond premium?

And by small, I mean, relative to the amount of the bond issue.

It is permitted to use other methods if the difference is not material, so

you could theoretically do it straight-line.

Let's take an example.

We're going to go back to our issue that was issued for 10,200,000,

which we've already calculated out, the discount and the premium.

It's the same example, only now,

we're going to take that the amount of the premium of 200,000.

And we are going to divide it by the number of periods,

or 16, and we get a semi-annual amortization of that premium of 12,500.

What could be easier?

Now, notice that my premium is not changing every period.

It's staying the same all the way down to the bottom.

Again, I can see that I've calculated this correctly when my carrying value comes,

well, to zero at the end when I've paid off the bonds, but

it's calculated straight-line.

I have the same amount of interest every period, I'm going to recognize

the same amount of period until the end, at which point I pay off the bonds.

So an allowed alternative if the difference is not material.

In other words, if the discount or the premium is relatively small,

relative to the amount of the bond issue.

What will the journal entry look like?

Well, very similar, except that each period now, when I pay interest,

I'll have the same entry.

And I will amortize the bond premium straight-line over the period,

and the amount of premium that will be left at maturity again will be zero.

Now when can you use this?

Well, it really means it's going to be possible to use this if the discounted

premium is relatively small compared to the face value of the bonds.

So if I have $10 million of bonds, and I issue them at a discount

of a million dollars, it's probably not going to be an immaterial difference.

But if I issued them at $9,990,000, and

I only have $10,000 of premium to amortize over the period.

It probably wouldn't be materially different if I do it straight-line,

as opposed to using the interest method.

So you can tell ahead of time whether you may be

able to use the straight-line method to amortize premium or

discount by looking at it to see whether the discount or

premium is relatively small or de minimis.

So that wraps up our initial discussion of the accounting for premium or a discount.

And remember, you're going to adjust the interest rate you use to recognize

interest expense, by increasing it for a discount or decreasing it for a premium.

And you'll amortize the discount or premium that way by taking the difference

between your calculated interest expense and the cash payment.

And use that to amortize the discount over the period of the bonds, so

that at the end, the remaining discount or premium is zero, and

you pay off the face value of the bonds.

So we've added another layer of complexity here by going into discount and premium,

but don't worry, there's more fun to come.

Bonds: Discount and Premium

Accounting Analysis II: Measurement and Disclosure of Liabilities

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