# Degree of Leverage Problem 2 523 Corporate Finance

##### Degree of Leverage Problem 2

Corporate finance onenote practice problem in this presentation we’re going to work a practice problem in onenote it’ll be the second practice problem that will be similar in nature we’re going to be focusing in on the degree of leverage calculations degree of operating leverage degree of financial leverage and the combined leverage in the case where we have

An increase in the volume the sales volume what will be the impact or the effect of an increase on our leverage calculations get ready it’s time to take your chance with corporate finance here we are in onenote if you would like to follow along in one note you’re not required to do so but if you have access to it and would like to we are in the 523 degree of

Leverage problem 2 in the practice problems section closing this back out we’re gonna have our information up top we’ll read through the information and then we’ll have a smaller component of that information as we go through the practice problem so we have our sales price per unit is going to be 55 the fixed costs are going to be the 500 000 variable cost so

We’re going to break this out in a little bit more detail in that we’re going to give us how many uh pounds it takes for one unit which is often the case you might see this in something like cooking or something like that where you’re trying to say well you know how much is it going to take of a certain resource in order to make one unit of something well you

Have to break that down to the pounds and whatnot so we have the cost per pound is going to be 35 cents it’s going to take 45 pounds in our case to make one unit of these 55 units they’re going to account we’re going to calculate the break-even point in units then we’re going to calculate the degree of operating leverage we will do so at two different levels of

Sales one selling twenty thousand and then selling the thirty five thousand we’re going to assume that the annual interest is thirty thousand and then we’re going to calculate the degree of financial leverage as well as the combined leverage with that information comparing and contrasting what will happen when there’s an increase in basically the sales volume in

This case from 20 000 units to 35 000 units first let’s start with the breakeven point useful to have the breakeven point to then consider how far away we’re going from the breakeven point as we produce more units so we’re gonna we’re gonna usually we’re gonna be increasing hopefully we’re increasing the unit production away from the breakeven point anything under

The breakeven point would of course result in a loss so we’re gonna have the even point uh units now notice we’re not talking about the the 20 000 units when we think about the break-even point we’re just figuring the break-even points so this so ignore the 20 000 uh units here this is simply the break-even point so we’re gonna have the fixed costs are going to

Be the 500 000 then we have the contribution margin in units which will be then the unit price of the 55 that’s how much we’re going to sell them for the variable cost is going to be a little bit more tricky because now we have the pounds that we need and the unit price per pound so we’re going to take that 0.35 unit price per pound times the 45 pounds we need

For one unit it’s going to give us the 15.75 which is about 16. so notice we rounded out the pennies here which would be kind of nice to see the pennies but note there’s rounding there so the 15.75 minus the 55 which would give us the 39.25 so it’s about 39 really it’s 39.25 if we then took our fixed cost of 500 000 divided by the 39.25 that’s going to give us

About 12739 so once again that’s the break-even point in units and we’re thinking about the unit production levels of twenty thousand and thirty five thousand those both being over the break even point of twelve thousand uh seven thirty five so we’re just basically thinking about going further away from the break-even point uh at this point if we went below the

Break-even point in terms of units of production that would result in a loss so now we want to think about the contribute the degree of operating leverage at the first level of production that being the 20 000 units as opposed to the 35 000. so our degree of operating leverage we have two calculations for it in essence we have three ways we can express the first

Calculation and then the second calculation being the percent change in operating income percent change in sales we’ll think about the second one later that can be a useful way to think about it one because it’s just nice to know different ways to calculate one thing because that’s better understanding of it but also uh that might be useful if you if you’re

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Outside the company and you don’t have the contribution margin because you don’t have a contribution margin income statement you just have the normal income statement but if you’re internal to the company you may have the contribution margin income statement when making decisions and calculating your leverage calculations so we’ll do that one here we’ll do the

Top one and we’ll look at this percent change calculation in a future presentation so then we’re going to take our information calculate the degree of operating leverage at the 20 000 units first calculating the uh contribution margin we’re gonna have the numerator and denominator we’ll calculate the numerator first and kind of like a tax return type of format

To break it out in detail we’re gonna end up with on the right hand side both the numerator and the denominator at which time we will divide them so then we’re going to say that the units sold are now the 20 000 20 000 units sold that’s going to be basically x here in our calculation the contribution margin per unit is going to be the 55 sales price and then

The 16 about on the cost because remember the cost was actually the uh 0.35 times 45 which is 15.75 so the 55 minus this the 15.75 so this minus the 55 would give us about 39.25 which would be more exact 39.25 and then if we took the 20 020 000 times the 39.25 we’re going to get the 785 000 contribution margin so that’s going to be our numerator then so now we

Have our numerator the denominator we can say think of as operating income or contribution margin minus fixed cost which is basically the operating income we can calculate it this way as well taking that same contribution margin minus the fixed cost which is what we will do here so we have the con we have the then the contribution margin minus the fixed costs the

Contribution margin picking up that same number because we just calculated it then we have the fixed costs now being in our practice problem the 500 000 so the 500 000 so the contribution margin minus the fixed cost will be the 280 000 and then if we were to divide those two out we would then be taking the 780 000 numerator divided by the 285 000 denominator

Getting about 2.75 again there’s going to be rounding always rounding involved in these types of calculations that’s the degree of operating leverage obvious remember that as the leverage goes up that means that there’s going to be more risk but there could also be more benefit if if there’s an increase there could be a multiplier effect which would increase

Uh good times possibly and could have a multiplier effect if there’s a decrease why because we’re we’re calculating the risk related to the fixed costs so the fixed costs are risky because uh they don’t change with the level of production so if you were to have a decline then in sales volume then you’re going to have then the fixed costs will remain the same

They’re not going to decline and that’s kind of a problem whereas the variable cost would decline and if you have an increase in sales volume you don’t have to pay any more fixed costs which is nice and that could make create a multiplier effect on on an increase so now we want to think about what would happen then if we move from 20 000 units to 35 000 units of

Sales of production well now we’re moving further away from the break-even point so we’re not below the break-even point so typically if you’re in the in the positive and you’re moving upwards in terms of of production if the fixed costs would remain the same then you would expect that the degree of operating leverage to go down why because as you go up the sales

Will go up the variable costs will go up in proportion to the sales and when you think about the breakout then between the fixed costs and the variable costs it’s leaning towards the variable costs which are the non-riskier ones which fluctuate with the with the production level so as you start to lean toward towards the cost structure being being heavier on

The variable costs the degree of leverage the degree of leverage uh will go down with regards to the risk of the fixed costs or you can also just think of it as the fixed costs themselves are less as related to the sales and the fixed costs are what are risky so if the sales are going up and there and the fixed costs are less material related to the the increase

In the sales then you would think you would have less risk you would think that the leverage would be going down let’s test it out we’re going to then say that we are going to be calculating this for the 35 000 now same calculation for the degree of operating leverage but now using the 35 000 units we’re then going to have the contribution margin the numerator

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Calculated as the units sold which is now 35 000 and then the contribution margin per unit which is going to be the unit price of 55 times the 16 which was really i believe if we do this the unit cost was really 45 times .35 or 15.75 so then if we subtract those two out we’re going to get the 39 or really really we get the uh so i’m going to subtract those two

Out we’ve got the 55 minus the 15.75 was it was 39.25 and then if we take that times the uh the units that were sold times the 35 000 we get about 1 million 373 750 that’s going to be our numerator up top and then the denominator is going to be basically the operating income or contribution margin minus the fixed cost contribution margin we already have so we’re

Pulling that number over the fixed cost then being the 500 000 given in the data so then if we subtract those two out we’re getting our denominator of the 873 750 then we can divide these two things out being the 1 million 373 75 divided by the 873 750 that’s going to give us our 1.57 so 1.57 that of course now being smaller than what it was before at the 2.75

So we can see that the increase in the sales volume does indeed increase the degree of operating leverage so then let’s go on down and say well let’s create our income statement and then calculate the degree of financial leverage based on that so to do that we’ll we’ll make a little income statement it’s going to be a contribution margin based income statement

Sales minus variable cost being contribution margin as opposed to sales minus cost of goods sold being gross profit so we’re going to say these sales then being the units sold we’re going to start off the 20 000 units we’re going to have the unit sales price at the 55 that giving us the 1 million 100 000. we then have the variable costs variable cost at the units

Sold 20 000 the unit variable cost is the 16 which i think is really the 15.75 if if we calculate that out it’s the 0.35 times the 45 multiplying that out so that 16 is rounded gives us variable cost of the 315 000 the total sales minus the total variable cost is going to give us that contribution margin of the 785 000 contribution margin and then we’re going

To subtract out the fixed costs which were given at the 500 000 that will then give us the earnings before interest and taxes which is basically operating income from this point on down you’re basically at the same kind of format from your contribution margin income statement the thing we’re using here and the regular type of income statement so then we’re going

To say subtract out the interest which was given to us at the 30 000 and that will give us then earnings before taxes and then if you were to subtract out taxes which we don’t have that would give you the earnings after taxes so we’re stopping here at the earnings before taxes so now we’re going to calculate the degree of financial leverage based on our income

Statement we have just constructed we’re going to be using this calculation the second one earnings before interest and taxes divided by the earnings before taxes we also have a percentage calculation up top this one is you might want to look it over but it’s less useful than the the interest calculation of the percent calculation i mean for the operating income

Because these two numbers whether you’re using internal statement a contribution margin income statement or a normal income statement will typically be on it or something you can derive from the income statement so i’ll be focusing in on this formula then and we’re just going to be picking up them the earnings before interest and taxes which we have now calculated

To be the 285 thousand we’re going to divide that by the earnings before taxes that being the 255 000 the difference then of course being the interest of the 30 000 we’re kind of measuring the effect of debt now which is what most people think of when they think of leverage if we divide those two out then we’re going to be getting the 1.25 so like the other or all

Leveraged calculations as that goes up that would mean that the leverage would be going up risk would be going up but you also have that multiplier effect that could be a benefit in good times could be a problem in term term times of a decline what would happen then to the degree of financial leverage if you were to increase the sales volume from twenty thousand

To thirty five thousand again we’re moving up away from the break even we’re already past the break even at the twenty five thousand so sales are going to be increasing then what what would be the what would you expect to happen well that means that the amount of interest is going to stay the same unless we took out more debt so if we didn’t take out more debt

To do that the interest is going to be remaining the same and we’re going to have the earnings basically going up in relation to the interest so that means the risk related to the kind of the interest the result of the debt it should be going down so as we have an increase in the sales volume the interest as related to it becomes less significant less material

You would then expect then the degree of financial leverage to be going down let’s see if that is indeed the case now we’re going to be creating our income statement contribution margin income statement at the new volume of 35 000 units that’s going to be the sales being the units sold 35 000 unit price now 55 that’s that’s the same price times the new units

That gives us the sales of the 1 million 925 variable costs then being the units at the 35 000 times the variable cost which i believe are actually 15.75 about 16 that’s going to give us the variable cost of the 551 250 if we subtract out the sales minus the variable cost we get the contribution margin 1 million 373 750 fixed costs remain the same 500 000 the

Earning before taxes then uh is going to be the contribution margin minus the fixed cost the 875 750 the interest has not changed still at the 30 000 and that this is where our key component is so this number has now increased this number remains the same the earnings before taxes now has increased and so that’s what we have if we then take that that formula or

That income statement and we apply our calculation for the degree of financial leverage the earnings before interest and taxes divided by the earnings before taxes we get earns before interest and taxes picking up that 873 750 divided by the earnings before taxes picking up the 843 750 that then gives us our our calculation if we divide those two out at the 1.07

Which does indeed result in a lower calculation than we had before it was 1.12 now we’re at the 1.04 which would make sense given the fact that that our income is basically going up no loan happened therefore the leverage the interest related to it should be going down so then let’s look at our combined uh our combined leverage which would be combining the two

Of them which we can do a couple different ways we can multiply the two leverage formulas together or you can do our calculation contribution margin divided by the earns before taxes to get to the same number let’s start off with our 20 000 units to do that if we take our contribution margin up top we’re going to say contribution margin 785 000 this is at the 20

000 units our original 20 thousand the earnings before taxes is going to be the 255 thousand that’s going to give us dividing that out about 3.08 you can also calculate that by taking the degree of operating leverage which we found for the 20 20 000 units the first and multiplying that times the degree of financial leverage at the 20 000 units and you’ll get that

3.08 as well and then if we go on down and we do it uh for the second volume being the 35 000 units we have our income statement for the 35 000 units if we calculate our combined leverage we could do that two ways once again we can calculate it in terms of the contribution margin which is the 1 million 373 750 and we can take the earnings before interest and

Taxes which was the 843 750 dividing those two out we get the degree of combined leverage the 1.63 which could also be found by multiplying out the degree of operating leverage at the 35 000 times the degree of financial leverage the 1.57 times the 1.04 and that will bring us to the same spot so obviously the the combined leverage at the 1.04 is lower than what

It was at the less units at the 1.12 and that’s because both the components of it both the degree and operating leverage and the degree of financial leverage went down when there’s an increase in the units that are being sold the degree of operating leverage goes down because there was no change to the fixed cost the fixed cost now being less relevant compared

To the total cost or to the sales and therefore less risk there that leverage ratio went down the interest related to the financing did not change because we didn’t take out any more debt therefore it’s going to be decreased as well with relation to the sales volume so when you combine them together the combined the combined leverage ratio should be lower as well

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Degree of Leverage Problem 2 523 Corporate Finance By Accounting Instruction Help \u0026 How To