Question

Angel is planning to purchase an additional two hectares of water holdings on 28 May 2019. Angel plans to pay for the water rights by making a series of $15,000 payments every three months to the seller. The first $15,000 payment occurs on 28 May 2020 and the final $15,000 payment occurs on 28 May 2022. Assuming interest rates are 6% p.a. compounded quarterly, what is the equivalent value of the water rights on 28 May 2019?

Answer 1

Quarterly Payments = $ 15000, APR = 6 % per annum compounded quarterly or (6/4) = 1.5 per quarter, First Payment occurs on 28 May 2020 and the last one happens on 28 May 2022.

Number of Quarterly Payments = 9 and Equivalent Annual Rate = EAR = [1+(0.06/4)]^(4) - 1 = 0.06136 or 6.136 %

Value of Quarterly Payments on 28 May 2020 = 15000 + 15000 x (1/0.015) x [1-{1/(1.015)^(8)}] = $ 127288.876

Equivalent value of Water Rights on 28 May 2019 = PV of Quarterly Payments on 28 May 2019 = 127288.876 / (1+EAR) = 127288.876 / (1.06136) = $ 119929.572