Question

Your client can buy an annuity that pays her $3,000 monthly for 5 years. The first payment will be received two years from today. If your client requires a return of 7% EAR, what’s the most she should pay for this annuity?

Answer 1

We want to find the value of the cash flows today, so we will find the PV of the annuity, and then bring the lump sum PV back to today. The annuity has 60 payments (i.e 5 yrs x 12months), so the PV of the annuity is:

PVA = $3,000{[1 – (1/1.00583)⁶⁰] / 0.00583} = $151,520.42 (where rate = 7% / 12 = 0.583%)

Since this is an ordinary annuity equation, so it is the PV at t = 2. To find the value today, we find the PV of this lump sum.

The most she should pay for the annuity is the value today:

PV = $151,520.42 / 1.07² = $132,343.80