Question

Five years ago, you paid for the right to receive twelve $25,000 annual end-of-the-year cash flows. If discounting the cash flows at an annual rate of 8%, what did you pay for these cash flows back then?

Answer Options:

$128,223.20

$474,428.16

$188,401.95

$300,000.00

Answer 1

Annual cash inflow (PMT) = $25,000

No of annual cash flows (N) = 12

Annual interest rate (i) = 8% p.a.

Amount paid for above cashflows (PV) = ??

Using financial calculator or PV function in excel,

PV of cash flows (PV) = $ 188,401.95

Alternatively you can solve using PV for annuity formula,

PV = PMT x [1-(1+i)^-n / i] = 25000 x [1-(1+0.08)^-12 / 0.08] = 25,000 x 7.5361 = $ 188,401.95

{Note that question is not clear with respect to if the cash inflows would start 1 year from now or 1 year from time I paid for right. If cash inflows will start 1 year from now, PV = 188401.95 / 1.08⁵ = $ 128,223.20. I am almost sure that question means to say that cash inflows will be received from the time I paid and not 1 year from now.}

Thumbs up please if satisfied. Thanks :)