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 an additional $$20,000$ in residual value is expected to be owed at the end of the lease term. 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 $6\%0\mathrm{.}74730\mathrm{.}7050$

Present value of an annuity due at $6\%4\mathrm{.}46515\mathrm{.}2124$

Present value of an ordinary annuity at $6\%4\mathrm{.}21244\mathrm{.}9173$

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

Note: Please provide detail explanation on each step of calculation.