An alumnus has decided to donate to the colleges Excellence

An alumnus has decided to donate to the college’s Excellence Fund and
has offered the college any one of the following three plans:

Plan A: $60,000 now
Plan B: $16,000 per year for 12 years beginning 1 year from now
Plan C: $50,000 three years from now and another $80,000 five years from now

If the college can earn 12% per year on its ready-assets account and the inflation rate is expected to be 11% per year, which plan should the college accept?

Solution

nominal interest rate = 12%=0.12

inflation=11%=0.11

realinterest rate, r = nominal interest rate-inflation = 0.12-0.11 = 0.01

Plan A: Present value of donation = $60000

Plan B:Present value of an annuity = A(1-(1+r)^-n)/r

PV of Plan B = 16000*(1-1.01^-12)/0.01 = $180081

Plan C: PV of plan C = 50000/1.01^3 +80000/1.01^5 =$124646

Plan B has highest PV so the college shoud accept Plan B.