Question

	Shaun is considering an investment in a financial instrument that will pay him $800 at the beginning of each year for 5 years. Using a discount rate of 6.0%, determine what this expected stream of cash flows is worth to Shaun today assuming annual discounting of cash flows. (The answer is $3,572.08, but I am unsure how to arrive at this solution. Please provide a thorough explanation. Thanks!

Answer 1

Amount to be invest at the BEGINNING of each year = PV of Annuity = P*[1-{(1+i)^-n}]/i

Note: For the purpose of calculation (so that formula can be applied), it will be considered that amount will be received for 4 years at the end of each year starting from 1 year from now, and we will also add an additional annuity that will be received today. Effectively, we have a total of PV of next 4 installments and today’s installment.

Where, P = Annuity = 800, i = Interest Rate = 0.06, n = Number of Periods = 5-1 = 4

Therefore, Present Value = PV of next 4 installments+Today's Installment = [800*{1-((1+0.06)^-4)}/0.06]+800 = 2772.08+800 = $3572.08