A lease on an office building calls for a payment of $3,500,000 today and annual payments of $5,000,000 for 40 years. The first of the annual payments will be payable 30 months from now when the building becomes ready for occupancy. Using a discount rate of 9% compounded semiannually, calculate the present value of the lease.

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The present value of the lease can be calculated using the formula for the present value of an annuity and the present value of a single sum. The $3,500,000 payment today is already in present value terms, so it does not need to be discounted. The $5,000,000 annual payments for 40 years, starting 30 months from now, need to be discounted back to present value using the given discount rate of 9% compounded semiannually. The effective semiannual rate is 4.5% (9% annual rate divided by 2), and there are 80 semiannual periods in 40 years. The first payment is 30 months (or 5 semiannual periods) from now, so we calculate the present value of an annuity due (since the payments start in the future). The present value of the lease is the sum of the present value of the $3,500,000 immediate payment and the present value of the annuity of $5,000,000 payments for 40 years, discounted at a 9% annual rate compounded semiannually. The correct calculation leads to the present value of approximately $49,704,495.

A Lease on an Office Building Calls for a Payment