Annual Worth Analysis

The least common multiple (LCM) of lives need

not be used when evaluating two alternatives by

the annual worth method because, if inflation and

deflation effects are neglected,

• a. the assumptions for annual worth analysis are different

  from those for the present worth method.

• b. cost and revenue estimates never remain the

  same over more than one life cycle.

• c. the annual worth value used to evaluate the

  alternatives is determined over a large number

  of life cycles.

• d. the annual worth over one life cycle is assumed

  to be the same for all succeeding life cycles.

An automation asset with a high first cost of

$10 million has a capital recovery (CR) of

$1,985,000 per year. The correct interpretation

of this CR value is that

• a. the owner must pay an additional $1,985,000

  each year to retain the asset.

• b. each year of its expected life, a net revenue

  of $1,985,000 must be realized to recover the

  $10 million first cost and the required rate of

  return on this investment.

• c. each year of its expected life, a net revenue

  of $1,985,000 must be realized to recover the

  $10 million first cost.

• d. the services provided by the asset will stop if

  less than $1,985,000 in net revenue is reported

  in any year.

The MARR is 6% per year.The annual worth of vendor 2 cash flow estimates is closest to

• a. $67,000.

• b. $43,370.

• c. $ -43,370.

• d. $63,370.

Of the following three relations, the correct one(s)

to calculate the annual worth of vendor 1 cash

flow estimates is (note: All dollar values are in thousands)

Relation 1: AW₁= -200(A/P,6%,10) + 70 +25(A/F,6%,10)

Relation 2: AW₁= [-200 - 50(P/A,6%,10) +120(P/A,6%,10) +

25(P/F,6%,10)](A/P,6%,10)

Relation 3: AW₁= -200(F/P,6%,10) + 25 +(-50 + 120)(A/P,6%,10).

• a. 1 and 3.

• b. 1.

• c. 1 and 2.

• d. 3.

The AW values for the alternatives are as listed.

The vendor(s) that should be recommended are

AW₁ = $44,723

AW₂ = $43,370

AW₃ = $40,000

• a. 1 and 2.

• b. 3.

• c. 2.

• d. 1.

If a revenue alternative has a negative AW value

and it was correctly calculated, it means one or

more of the following:

1. The equivalent annual worth of revenues does

not exceed that of the costs.

2. The estimates are wrong somewhere.

3. A minus or plus sign of a cash flow was entered

incorrectly into the Excel PMT function.

4. The alternative should have a longer life so revenues

will exceed costs.

• a. 1

• b. 2

• c. 3

• d. 4

Estimates for one of two process upgrades are:

first cost of $40,000; annual costs of $5000 per

year; market value that decreases 5% per year to

the salvage value of $20,000 after the expected life

of 10 years. If a 4-year study period is used for AW analysis at 15% per year, the correct AW value is

closest to

• a. $-15,000.

• b. $-11,985.

• c. $-7,600.

• d. $-12,600.

The perpetual annual worth of investing $50,000

now and $20,000 per year starting in year 16 and

continuing forever at 12% per year is closest to

• a. $4200.

• b. $8650.

• c. $9655.

• d. $10,655.

You graduated with an MS degree in engineering and have a great job. Next month you start an automatic draft from your paycheck of $1000 each month, placing it into a mutual fund retirement account. You plan to continue at this rate

for 20 years then stop making deposits. Assume

a return of 6% per year compounded monthly

is a good expectation for all years. If you retire 10 years after the last deposit and the first retirement

benefit is withdrawn at the end of the first

month of year 31, the equivalent monthly worth of each retirement payment to you and your heirs forever is closest to

• a. $3290 per month.

• b. $2820 per month.

• c. $4200 per month.

• d. $4180 per month.

If the present worth PW of a perpetual investment

and the interest rate are known, the AW value is

determined using the relation(s)

Relation 1: AW = PW divided by i

Relation 2: AW = PW times i

Relation 3:AW = PW times the (AP,i%,∞) factor

• a. 1 only.

• b. 2 and 3.

• c. 2 only.

• d. 1 and 3.