Tough question

[1947]

A firm's annual revenue grows twice as fast as its costs. In 2007 it operated at a $1000 loss, it broke even in 2008, and in 2009 its revenues were 44% higher than in 2007. If the firm's revenues and costs grew at a constant rate over this period, what was its profit in 2009?

A $700
B $1000
C $1300
D $1600
E $2000

[Mike@Magoosh]

Hi, there. I'm happy to help!

First of all, let's consider the revenues. "in 2009 its revenues were 44% higher than in 2007." That's a 44% increase, which means

(2009 rev) = 1.44*(2007 rev)

Well, if we assume a constant rate of growth, a constant percentage, that means the multiplier would be constant each year
(2008 rev) = r*(2007 rev)
(2009 rev) = r*(2008 rev) = (r^2)*(2007 rev)

BIG IDEA: to figure out the single year percent increase from multiple years, you don't take a root of the multi-year percentage, but rather a root of the multi-year muliplier.

r^2 = 1.44
r = 1.2

So the revenue grows 20% a year. That means costs grow at 10% a year.

We know it operated at a $1000 loss in 2007, which means (2007 rev) = (2007 costs) - 1000

(2008 cost) = (2008 rev)
1.1*(2007 cos) = 1.2(2007 rev)
1.1*(2007 cos) = 1.2[(2007 costs) - 1000]
1.1*x = 1.2*(x - 1000)
1.1x = 1.2x - 1200
1200 = 0.1x
12000 = x

The cost in 2007 were $12,000.
The cost in 2008 were 10% greater, #13,200, which were also the revenue in 2008.

Cost in 2009 = 13200*1.1 = 14,520
Revenue in 2009 = 13200*1.2 = 15,840

(2009 profit) = (2009 rev) - (2009 cost)
= 15840 - 14520 = $1320

Hmm. This is close to C, but not exact. I was interpreting growth as a percent growth, and "twice as fast" as double the percent, but now I wonder if that's what the author of the question had in mind. If it's not, then I would argue the question is not clearly written.

I hope that's helpful. Let me know if you have any further questions.

Mike

[niketdoshi123]

it broke even in 2008

Shouldn't this mean that the firm was still at loss in 2008. But

(2008 cost) = (2008 rev)

I am confused!!!

[GMATGuruNY]

A firm's annual revenue grows twice as fast as its costs. In 2007 it operated at a $1000 loss, it broke even in 2008, and in 2009 its revenues were 44% higher than in 2007. If the firm's revenues and costs grew at a constant rate over this period, what was its profit in 2009?

A $700
B $1000
C $1300
D $1600
E $2000

Another approach is to guess and check.

Revenues:
An increase of 44% over 2 years implies an increase of 20% each year.
To illustrate:
100 + .2(100) = 120.
120 + .2(120) = 144.
Percent increase = (144-100)/100 = 44%.

Costs:
Since the revenues grow twice as fast as the costs, the costs increase 10% each year.

Since the loss in 2007 is $1000, the revenues and costs in 2007 are almost certainly multiples of 1,000.

Case 1: Revenues in 2007 = 10,000.
Since the loss = 1000, the costs = 11,000.
2008:
Revenues = 10,000 + .2(10,000) = 12,000.
Costs = 11,000 + .1(11,000) = 12,200.
In order to break even, the revenues needs to increase just a bit.

Case 2: Revenues in 2007 = 11,000.
Since the loss = 1000, the costs = 12,000.
2008:
Revenues = 11,000 + .2(11,000) = 13,200.
Costs = 12,000 + .1(12,000) = 13,200. Success!
2009:
Revenues = 13,200 + .2(13,200) = 15,840.
Costs = 13,200 + .1(13,200) = 14,520.
Profit = 15,840 - 14,520 = 1320.

The closest answer is C.

[1947]

Hi, there. I'm happy to help!


Well, if we assume a constant rate of growth, a constant percentage, that means the multiplier would be constant each year
(2008 rev) = r*(2007 rev)
(2009 rev) = r*(2008 rev) = (r^2)*(2007 rev)

Thanks Mike for pointing out that constant rate of growth means multiplier would be constant each year. Instead I was interpreting that a constant would be added each year i.e.
(2008 rev) = r+(2007 rev)

[Mike@Magoosh]

it broke even in 2008

Shouldn't this mean that the firm was still at loss in 2008. But

(2008 cost) = (2008 rev)

I am confused!!!

Dear niketdoshi123

Let's say a company's revenues for a given year are R and their costs for the same year are C.

If C > R, they operate at a loss --- they run a deficit of (C - R)

If C = R, then they break even --- no loss, no profit

If C > R, they operate at a profit, and P = R - C

In this problem, 1947 said "it broke even in 2008", which means in 2008, there was no loss, no profit, and the revenues were exactly equal to the costs. That's why I concluded from that:

(2008 cost) = (2008 rev)

Does this make sense now? Please let me know if you have any further questions.

Mike

[Mike@Magoosh]

Thanks Mike for pointing out that constant rate of growth means multiplier would be constant each year. Instead I was interpreting that a constant would be added each year i.e.
(2008 rev) = r+(2007 rev)

You are quite welcome. Best of luck to you, and please let me know if you have any further questions.

Mike

[1947]

Thanks Mike for pointing out that constant rate of growth means multiplier would be constant each year. Instead I was interpreting that a constant would be added each year i.e.
(2008 rev) = r+(2007 rev)

You are quite welcome. Best of luck to you, and please let me know if you have any further questions.

Mike

why would the constant rate of growth means multiply by a constant and not add a constant ?