Question

A security company offers to provide CCTV coverage for a parking garage for ten years for an initial payment of $45,000 and additional payments of $25,000 per year. What is the equivalent annual annuity of this​ deal, given a cost of capital of 4%​?

Answer 1

Equivalent Annual Annuity =$30,548.09

Step-by-step explanation:

The equivalent annuity is the annual cash cash flows that is the same in value to the present value of the total cost associated with providing the CCTV coverage.

Equivalent Annual Annuity = Total PV of cost /Annuity factor

To determine the total prsent value of cost associated with CCTV would sum the present value of the additional payment for 10 years and the initial cost.

Initial cost - 45,000

Additional payment = 25,000

PV of additional payment = A× 1-(1+r)^(-n)/r

= 25,000 × 1- 1.04^(-10)/0.04 = 202,772.39

Total PV of cost = 202,772.39 + 45,000 = 247,772.39

Total PV of cost = 247,772.39

Equivalent Annual Annuity = Total PV of cost /Annuity factor

Annuity factor = 1-(1+r)^(-n)/r = ( 1- 1.04^(-10)/0.04) = 8.1109

Equivalent Annual Annuity =247,772.39 /8.1109 = 30,548.09

Equivalent Annual Annuity =$30,548.09