Question

In 2009, Internationale Uutstanding University (IUU) had an enrollment of 26,123 Undergraduates, each of whom paid $6,359 per year in tuition. In 2010, enrollment was 26,761 students, and tuition was raised 2.0%. In 2011, IOU received $186.8M in revenue from student tuition, and enrollment was 26,445 students. In 2012, it is estimated that tuition will be $7,003 and IOU needs to receive 6.2% more total revenue from tuition than in 2011. ADMISSIONS What will be the compounded annualized growth rate (CAGR) of tuition for 2009 to 2012? 1 OOO 0.00% CAGR (%) PS1 1 2 3 4 5 6 7 8 My Folder CALCULATED VARIA aar = 0.0335 (3.35% 2012 enroll = 28,331 2012rev = 198.4 11g = 0.089 (8.9%) 11t = $7,064 10t = $6,486 growth = 638

Answer 1

The formula to compute CAGR is:

$CAGR = (\frac{Value @end}{Value @beginning})^\frac{1}{n} - 1$

Where,
Value @ end = Total Tuition revenue in 2012
Value @ beginning = Total Tuition revenue in 2009
n = number of years (2009 to 2012) i.e 4

Computation of Total Tuition revenue in 2009:
Number of students = 26123
Tuition per student = 6359
Therefore, Total Tuition revenue = 26123 * 6359 = 166116157

Computation of Total Tuition revenue in 2012:
Total revenue of 2011 = 186.8 million
Increased revenue % in 2012 = 6.2%
Therefore, Total Tuition revenue = (186800000 + (6.2%*186800000)) = 198381600

Therefore, substituting these values in the CAGR formula:

$CAGR = (\frac{198381600}{166116157})^\frac{1}{4} - 1$

$CAGR = (1.1942)^\frac{1}{4} - 1$

or 4.54%