Question

What is the present value (at t=0) for a stream of 28 quarterly cash flows of $800 each, starting exactly 2 years from now? The APR is 12%, compounded semi-annually.

Answer 1

Effective Interest Rate or EAR = [{1+(APR/n)}^n]-1

Where, APR = Annual Interest Rate or Nominal Rate, n = Number of times compounded in a year

Therefore,

For Semi Annual,

EAR = [{1+(0.12/2)}^2]-1 = 0.1236

For Quarterly,

0.1236 = [(1+i)^4]-1

1.1236 = (1+i)^4

i = (1.1236^1/4)-1 = 0.02956

PV at 1.5 years from now = PV of Annuity = P*[1-{(1+i)^-n}]/i

Where, P = Annuity = 800, i = Interest Rate = 0.02956, n = Number of Periods = 28

PV = 800*[1-{(1+0.02956)^-28}]/0.02956 = 800*05577/0.02956 = $15093.343319

PV Today = PV at 1.5 years/[(1+Quarterly Interest Rate)^3] = 15093.343319/[(1+0.02956)^3] = 15093.343319/1.091327 = $13830.26