7-59: One aspect of obtaining a college education is the prospect of improved fu

Question

7-59: One aspect of obtaining a college education is the prospect of improved future earnings in comparison to non-college graduates. Sharon Shay estimates that a college education has a $28,000 equivalent cost at graduation. She believes the benefits of her education will occur throughout 40 years of employment. She thinks that during the first 10 years out of college, her income will be higher than that of a non-college graduate by $3000 per year. During the subsequent 10 years, she projects an annual income that is $12,000 above the level of the non-college graduate. If her estimates are correct, what rate of return will she receive as a result of her investment in a college education?

Explanation / Answer

PW of Cost = PW of Benefits

$28,000     = $3,000 (P/A, i%, 10) + $6,000 (P/A, i%, 10) (P/F, i%, 10)

                              + $12,000 (P/A, i%, 20) (P/F, i%, 20)

Try i = 12%

$3,000 (5.650) + $6,000 (5.650) (0.3220) + $12,000 (7.469) (0.1037)= $37,160 > $28,000

Try i = 15%

$3,000 (5.019) + $6,000 (5.019) (0.2472) + $12,000 (6.259) (0.0611)= $27,090 < $28,000

Performing Linear Interpolation:

i* = 15% - (3%) [($28,000 - $27,090)/($37,160 - $27,090)] = 15% - (3%) (910/10,070)   = 14.73%

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