Handbook of Civil Engineering Calculations

After weighing the risks involved, the firm decides that the minimum acceptable rate of
return on project A is 10 percent; on project B, 12 percent. Evaluate these investments by
the premium-worth method. If both investments are satisfactory, determine which is more
satisfactory.

Calculation Procedure:

1. Compute the present worth of the dividends
   from both investments
   The present generally refers to the date on which the investment is made. Where the pres-
   ent worth is greater than the sum invested, the excess is termed the premium worth. Such
   a result signifies that the true investment rate exceeds the minimum acceptable rate.
   For any year, PW = (dividend, $)(PW factor for 10 percent and the number of years in-
   volved). Thus, for project A:

Year P W

1 $10,000(0.9091 ) =$9,09 1

2 15,000(0.8264 ) = 12,396

3 25,000(0.7513 ) = 18,783

4 20,000(0.6830 ) = 13,660

5 10,000(0.6209) = 6,20 9

Total $60,139

Then the premium worth - $60,139 - 57,500 = $2639.
By using a similar procedure, the present worth of project B at 12 percent is as fol-
lows:

Year PW

1 $15,000(0.8929) =$13,394

2 25,000(0.7972)= 19,930

3 30,000(0.7118)= 21,354

4 20,000(0.6355)= 12,710

Total $67,388

Then the premium worth = $67,388 - $63,000 = $4388.

2. Determine the relative values of the investments
   Since both investments satisfy the minimum requirements, determine their relative values
   by computing the premium-worth percentage (i.e., the ratio of the premium worth to the
   capital invested). Thus, for project A the premium-worth percentage is $2639(100)/
   $57,500 4.6 percent. For project B the premium-worth percentage is $4388(100)/$63,000
   = 7.0 percent. Thus, project B is the more attractive because it has a higher premium-
   worth percentage.