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# Determining the present value of the lease

On January 1, 2010, Hershey Co. leased a machine for 5 years at an annual rental of \$64,000, payable on the date of signing the lease and each December 31 thereafter. The machine has an estimated useful life of 8 years and no salvage value. Hershey Co. has an option to purchase the machine for \$1at the end of the lease. The market value of the machine is not known. Hershey's incremental borrowing rate is 8%.
a) What is the present value of the lease?
b) What is the impact of the lease on 2010 income statement and year-end balance sheet?

#### Solution Preview

a) What is the present value of the lease?

- The first thing that we need to find out it by what rate the machine is depreciated at. The depreciation rate can also be known as the discounting rate for the machine and is the rate that reduces the machine's value on an annual basis, thus giving the machine a different annual valuation.

- The present value of the lease is today's value of the future discounted factor that the machine will have earned for the owner.

Future value of cash flows is:
Yr 1: 64,000
Yr2 : 64,000 * (1.08^1) = 69,120
Yr 3: 69,120 * (1.08^2) = 80,621.57
Yr 4: 60,621.51 * (1.08^3) = 101,559.96
Yr5: 101,559.96 * (1.08^4) = ...

#### Solution Summary

This solution provides assistance determining the present value of the lease in the example below.

\$2.19