An alumni wants to establish a scholarship that covers the full cost of tuition

Question

An alumni wants to establish a scholarship that covers the full cost of tuition for one high achiever each year in perpetuity. The university, on the advise of the Finance Department has opted to begin awarding it in 5 years. This year, the estimated full cost of studies for one student is $27,950 and is expected to grow annually at a 3% inflation rate. If the scholarship is invtest to earn a nominal rate of 6%, how much must the donor contribute today to fund the scholarship?

a) $937,221.07

b) $603,894.27

c) $742,294.46

d) $831,293.87

Explanation / Answer

Year

1

2

3

4

5

6

Cost of Studies (last year *103%)

$    27,950.00

$ 28,788.50

$ 29,652.16

$ 30,541.72

$        31,457.97

$ 32,401.71

PVF (6%) = 1/(1+0.06)^5

               0.74726

Terminal Value = Year 6 Cost / (6% -3%)

$ 1,080,057.01

Present value = Terminal value * PVF

$      807,083.40

Hence amount required is

$ 807,083.40

Year

1

2

3

4

5

6

Cost of Studies (last year *103%)

$    27,950.00

$ 28,788.50

$ 29,652.16

$ 30,541.72

$        31,457.97

$ 32,401.71

PVF (6%) = 1/(1+0.06)^5

               0.74726

Terminal Value = Year 6 Cost / (6% -3%)

$ 1,080,057.01

Present value = Terminal value * PVF

$      807,083.40

Hence amount required is

$ 807,083.40

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