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Ball Ltd. purchased land and constructed a service station, at a total cost of $ 450,000. On January 2, 2019, when construction was completed, Ball sold the service station and land to a major oil company for $ 500,000, and immediately leased it back from the oil company. Fair value of the land at the time of the sale was $ 50,000. The lease is a 10-year, non-cancellable lease. Ball uses straight-line amortization for its other assets. The economic life of the station is 15 years with zero residual value. Title to the property will revert back to Ball at the end of the lease. A partial amortization schedule for this lease follows:
-What is the interest rate implicit in the amortization schedule presented above?
A) 12%
B) 10%
C) 8%
D) 6%

Question

Use the following information for questions.
Ball Ltd. purchased land and constructed a service station, at a total cost of $ 450,000. On January 2, 2019, when construction was completed, Ball sold the service station and land to a major oil company for $ 500,000, and immediately leased it back from the oil company. Fair value of the land at the time of the sale was $ 50,000. The lease is a 10-year, non-cancellable lease. Ball uses straight-line amortization for its other assets. The economic life of the station is 15 years with zero residual value. Title to the property will revert back to Ball at the end of the lease. A partial amortization schedule for this lease follows: 
-What is the interest rate implicit in the amortization schedule presented above?
A) 12% 
B) 10% 
C) 8% 
D) 6%

Quizplus · Accepted Answer

The interest rate implicit in the amortization schedule presented above is 10%. This can be calculated by finding the annuity factor (8.513) and dividing the annual lease payment ($60,213) by the annuity factor, which results in a present value of $514,221. This represents the present value of the lease payments plus the fair value of the land, which was sold at the time of the leaseback. Then, the difference between the present value and the fair value of the property ($514,221 - $50,000 = $464,221) represents the present value of the building, which was sold at the time of the leaseback. Dividing the present value of the building by the total cost of the property ($464,221 / $450,000) results in an annual effective interest rate of 10.04%, which is rounded to 10%.

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