Environ Care

Problem 5-2

A project engineer with EnvironCare is assigned to start up a new office in a city where a 6-year contract has been finalized to take and to analyze ozone-level readings. Two lease options are available, each with a first cost, annual lease cost, and deposit-return estimates shown below.

	Location A	Location B
First cost, $	-15,000	-18,000
Annual lease cost, $ per year	-3,500	-3,100
Deposit return, $	1,000	2,000
Lease term, years	6	9

a) Determine which leave option should be selected on the basis of a present worth comparison, if the MARR is 15% per year.

b) EnviroCare has a standard practice of evaluating all projects over a 5-year period. If a study period of 5 years is used and the deposit returns are not expected to change, which location should be selected?

c) Which location should be selected over a 6-year study period if the deposit return at location B is estimated to be $6,000 after 6 years?

Solution:

a) Since the leases have different terms (lives), compare them over the LCM of 18 years. For life cycles after the first, the first cost is repeated in year 0 of each new cycle, which is the last year of the previous cycle. These are years 6 and 12 for location A and year 9 for B.

PwA= -15,000 - 15,000(P/F,15%,6) + 1,000(P/F,15%,6)

= -15,000(P/F,15%,12) + 1,000(P/F,15%,12) + 1,000(P/F,15%,18)

-3,500(P/A,15%,18)

= $-45,036

PwB= -18,000 - 18,000(P/F,15%,9) + 2,000(P/F,15%,9) + 2,000(P/F,15%,18)

-3,100(P/A,15%,18)

= $-41,384

Location B is selected, since it costs less in PW terms; that is, the PwB value is

Numerically larger than PwA.

b) For a 5-year study period no cycle repeats are necessary. The PW analysis is

PwA= -15,000 – 3,500(P/A,15%,5) + 1,000(P/F,15%,5)

= $ -26,236

PwB= -18,000 – 3,100(P/A,15%,5) + 2,000(P/F,15%,5)

= $ -27,397

Location A is now thw better choice.

c) For a 6-year study period, the deposit return for B is $6,000 in year 6.

PwA= -15,000 – 3,500(P/A,15%,6) + 1,000(P/F,15%,6) = $ -27,813

PwB= -18,000 – 3,100(P/A,15%,6) + 2,000(P/F,15%,6) = $ -27,138

Location B now has a small economic advantage. Noneconomic factors are likely to enter into the final decision.

Comments

In part (a), the deposit return for each lease is recovered after each life cycle, that is, in years 6, 12, and 18 for A and in years 9 and 18 for B. In part (c), the increase of the deposit return from $2,000 to $6,000 (one year later), switches the selected location from A to B. The project engineer should reexamine these estimates before making a final decision.

* General Requirements: (I need your help to complete this exercise)

Answer and hand in the assignment questions in a Microsoft Word sheet and at least four sheets in the Microsoft Excel software. For example: one sheet of Microsoft Excel with 15% and 18 years computations, another with 15% and 6 years computations, the third with 10% and 18 years, and the last one with 10% and 6 years computations.

*Questions: (I need your help to complete those questions)

1. What happened in the problem when you changed the interest rate from 15% to 10%, with the least common multiple (18 years)? Did the decision changed? Did the present value quantities change? If they are different, why did they change?

 

2. What happened in the problem when you changed the interest rate from 15% to 10%, with the time study period of 6 years? Did the decision change? Did the present value quantities change? If they are different, why did they change?

 

3. Why is the best location different when using the least common multiple (18 years) and the time study period of 6 years?