A security company offers to provide CCTV coverage for a parking garage for 10 years for an initial payment of $50 000 and additional payments of $20 000 per year. What is the equivalent annual annuity of this deal, given a cost of capital of 6%?
A)-$14 720
B)-$20 000
C)-$26 793
D)-$19 720

Question

Quizplus · Accepted Answer

To calculate the equivalent annual annuity, we need to find the constant annual payment over 10 years that would have the same present value as the initial payment and the 10 annual payments.

The present value of the initial payment is simply $50,000.

The present value of the 10 annual payments can be calculated using the formula for the present value of an annuity:

PV = PMT x [1 - (1 + r)^-n] / r

where PV is the present value, PMT is the annual payment, r is the cost of capital, and n is the number of years.

Plugging in the values, we get:

PV = $20,000 x [1 - (1 + 0.06)^-10] / 0.06 
PV = $154,678.29

So the total present value of the deal is:

$50,000 + $154,678.29 = $204,678.29

Now we can use the formula for the equivalent annual annuity:

EAA = PV / [(1 - (1 + r)^-n) / r]

Plug in the values and solve for EAA:

EAA = $204,678.29 / [(1 - (1 + 0.06)^-10) / 0.06] 
EAA = $26,793.25

Therefore, the equivalent annual annuity of the deal is -$26,793.25 (negative sign indicates the payment). The closest answer is C, which is -$26,793.

A Security Company Offers to Provide CCTV Coverage for a Parking