Your client, Motor Leasing Corporation, leases trucks and automobiles, both by fleet (with each vehicle on a separate lease) and individually. For internal purposes, the company computes interest earned on leases on a straight-line basis; for statement purposes, it makes an adjustment to accrue additional interest income by the “rule of 78s,” contending that the average vehicle lease life is 48 months. One of your major audit objectives is to determine that the amount is computed accurately.

The most critical part of the “rule of 78’s” adjustment is average vehicle lease life, which the client contends is 48 months. There is no way of directly establishing the lease life of a vehicle on the road, but it can be estimated by observing the time period of terminated leases.
You decide to determine the average life of all leases terminated during the past two years, and to compare the average to the 48-month period as a test of its reasonableness. The number of vehicles leased and the rate of turnover have
remained reasonably stable over the past several years.
You decide your approach will be as follows:
(1) Select a preliminary sample of 50 leases, using a random number table.
(2) Calculate the confidence limits of the average life of all leases on the basis of the preliminary sample in order to

(a) obtain data for computing the final sample size, and

(b) gain a preliminary indication of the reasonableness of the client’s assumption.
(3) Determine the final sample size and select the sample. Evaluate the final sample to determine whether the client’s figure is accurate within ± 2.0 months.
You determine the population characteristics to be as follows:
• There are 20,000 leases currently active.
• There are 18,000 leases terminated during the two-year period.
• Data concerning the leases terminated are available on an EDP listing consisting of 300 pages with 60 leases (lines) per page. The lease identification numbers are not consecutive, and the listing is in sequence by lessee, not by lease ID number.

Required :

a. Determine and describe how you will identify and select the preliminary sample.

b. Indicate the evaluation method you will use and whether you will make an interval estimate or a hypothesis test. Specify precision and reliability or Alpha and Beta risks and materiality you consider appropriate.

c. Assume you have selected the preliminary sample, reviewed the leases, and summarized the sample data as follows:

(i) Determine the confidence limits of the average life of all leases from the results of the preliminary sample, using the assumptions you made in part b.
(ii) Describe the results of this evaluation in terms of the apparent reasonableness or unreasonableness of the client’s assumption of the average lease life.
(iii) Calculate the final sample size, given the results of the preliminary sample results, population facts, audit decisions that were stated in the problem, and judgments you have made.

Transcribed Image Text:

Size of preliminary sample Sum of the audited values Sum of the squares of the audited values (squared before summing) 50 leases 2,331 lease-months. 115,341