Question

Shaun’s uncle, Mike, has won a lottery prize. He was given a the choice of receiving a lump sum of R 1 million today, or receiving five equal payments of R 250 000 per annum, with the first payment being received today. His required rate of return is 12% per annum. Mike asked Shaun to evaluate his two options in order to determine which option will be more beneficial to him. /

Answer 1

Since under second option payment is received in annuities of 5 periods and first is received today, so we need present value of annuity due, using the prescribed formula for PVA due

PVA due = A(1-(1+r)^-n)(1+r)/r

Here, A = 250000, r = 0.12, n = 5

Putting the values in formula

PVA due = 250000 (1-(1+0.12)^-5)(1+0.12)/0.12

PVA due = 250000 x 4.037349

PVA due = 1,009,337.25 or 1,009,337 rounded

Present value of first option is 1,000,000

Since under second option there is additional benefit of R 9,337, so second option is more beneficial.