Kensington Ltd decides to lease some equipment from Piccadilly Ltd on the following terms: $$\begin{array} { | l | r | l | }
\hline \text { Duration of lease } & 15 \text { years } & \
\hline \text { Life of leased asset } & 17 \text { years } & \
\hline \text { Unguaranteed residual } & \$ 5,000 & \
\hline \text { Lease payment } & \$ 6,000 & \text { at lease inception } \
\hline \text { Annual lease payments (in arrears) } & \$ 4,500 & \text { per year (15 payments) } \
\hline
\end{array}$$ If the interest rate implicit in the lease is 8%,what is the fair value of the equipment at the inception of the lease (rounded to the nearest dollar)?

Question

Kensington Ltd decides to lease some equipment from Piccadilly Ltd on the following terms: $$\begin{array} { | l | r | l | } 
\hline \text { Duration of lease } & 15 \text { years } & \
\hline \text { Life of leased asset } & 17 \text { years } & \
\hline \text { Unguaranteed residual } & \$ 5,000 & \
\hline \text { Lease payment } & \$ 6,000 & \text { at lease inception } \
\hline \text { Annual lease payments (in arrears) } & \$ 4,500 & \text { per year (15 payments) } \
\hline
\end{array}$$ If the interest rate implicit in the lease is 8%,what is the fair value of the equipment at the inception of the lease (rounded to the nearest dollar)?

Quizplus · Accepted Answer

The fair value of the equipment at the inception of the lease can be calculated by discounting the lease payments and the unguaranteed residual value back to their present value at the lease's inception, using the interest rate implicit in the lease (8%). This includes the initial lease payment of $6,000 (which does not need to be discounted as it is made at inception), the annual lease payments of $4,500 for 15 years, and the unguaranteed residual value of $5,000 at the end of the lease term. The correct calculation leads to a fair value of approximately $46,094.

Kensington Ltd Decides to Lease Some Equipment from Piccadilly Ltd