# Does a Lessee Include Residual (or only loss of residual) In Lease Calculation?

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Mattheus
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I am confused on the answer to this question. I thought that a lessee includes the present value of the lease payment plus any anticipated loss on the fair value of any guaranteed residual value. The residual value in the problem is 20K and guaranteed. I thought that as long as the fair value of the residual did not decrease, the lessee ignores it from calculating the lease acquisition. If for example the lessee guaranteed \$20K but estimated that the asset would only be worth \$10K at the end of the lease, then it would include the present value of \$10K into the balance sheet.

I answered A because the problem doesn't say that the residual will fall below \$20K at the end of the lease. B is the correct answer (adding the present value of the residual)

A company leases a machine from Leasing, Inc. on January 1, year 1. The lease terms include a \$100,000 annual payment beginning January 1, year 1. The machine's fair value is \$500,000 and the residual value is estimated at \$20,000. The company guarantees the residual value. The useful life of the machine is six years, and the lease term is five years. The implicit rate of interest is 6% and is known by the company. The following present value factors are provided:

Five Years Six Years
Present value of \$1 at 6% 0.7473 0.7050
Present value of an annuity due at 6% 4.4651 5.2124
Present value of an ordinary annuity at 6% 4.2124 4.9173

What is the value of the machine in the company's balance sheet at lease inception?

A.
\$446,510

B.
\$461,456

C.
\$520,000

D.
\$535,340

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