Handbook of Civil Engineering Calculations

Calculation Procedure:

1. Establish a basis of comparison for the investments
   To establish a basis of comparison, assume that each investment pays an annual dividend
   and that the invested capital remains intact until the venture terminates. (Although these
   assumptions are not realistic, they are entirely valid for comparative purposes.)


2. Calculate the annual dividend under each plan
   Thus, for plan A, the annual dividend = $200,000(0.141) = $28,200. Compute the divi-
   dends for the other plans in the same manner.


3. Construct a dividend-investment diagram
   Use the same procedure as for Fig. 7. Plot the points representing the sets of values asso-
   ciated with the five plans.
   Draw a line through the origin of the dividend-investment diagram with a slope of 12
   percent. Determine which point is most distant from this line. This point corresponds to
   the most profitable rate of return. Study of the plot shows that plan B should be adopted.
   Related Calculations: To compare these five plans algebraically, assume that
   the firm has a total available capital of $460,000 (the investment required under plan E)
   and that the amount remaining after investment in one of the five plans will be allocated
   to another investment yielding an annual dividend of 12 percent.
   Next, calculate the total annual dividend corresponding to each plan.

Plan Dividend, $

A 200,000(0.141) + 260,000(0.12) = 59,400

B 270,000(0.138)+ 190,000(0.12) = 60,060

C 340,000(0.125)+ 120,000(0.12)= 56,900

D 410,000(0.116) + 50,000(0.12) = 53,560

E 460,000(0.123) =56,580

Since plan B yields the highest total dividend, it is the best choice.

RELATIONSHIP BETWEEN BEFORE-TAX

AND AFTER-TAX INVESTMENT RATES

A corporation is investigating a proposed investment under which it will receive annual
dividends and recover its capital when the venture terminates in 12 years. Since the ven-
ture is highly speculative, the firm wishes to earn a minimum of 15 percent on its capital
as calculated after the payment of taxes. If income from the investment will be taxed at 56
percent, what must be the minimum rate of return as calculated before the payment of tax-
es?

Calculation Procedure:

Compute the minimum acceptable before-tax investment rate
Use the relation ib = ij(\ — t), where ib and ia = before-tax and after-tax investment rates,
respectively; t = tax rate. Thus, ib = 0.15/0.44 = 34.1 percent.