A firm has arranged a ten-year lease, at an annual rent of $8,000. The first rental payment has to be paid immediately, and the others are to be paid at the end of each year. What is the present value of the lease at 12%?

The present value of the lease is $50,626

Explanation:

A fix Payment for a specified period of time is called annuity. The discounting of these payment on a specified rate is known as present value of annuity.

In this question the lease payment of $8,000 per year for ten years paid immediately at a rate of 12% is an advance annuity.

Formula for Present value of advance annuity is as follow

PV of annuity = P +P x [ ( 1- ( 1+ r )^-(n-1) ) / r ]

Where

P = Annual payment = $8,000

r = rate of return = 12%

n = number of years = 10 years

Placing values in the formula

PV of annuity = $8,000 + $8,000 x [ ( 1- ( 1+ 0.12 )^-(10-1) ) / 0.12 ]

PV of Annuity = $50,626

the answer is a. $209,000

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