determine which of the points, A to H, is most distant from line OJ. Do this by scaling the
vertical offsets or by drawing lines through these points parallel to OJ.
Point G, which has a vertical offset of $520, is the most distant one. Therefore, $7000
is the appropriate sum to invest in plan A because of the following: (a) When the invest-
ment is extended from some lower level, such as $5000, to the stipulated level, the rate of
return on this incremental investment, which is represented by the slope of line EG, ex-
ceeds 10 percent, (b) If the investment is carried beyond G, the rate of return on this in-
cremental investment, represented by the slope of line GH, is less than 10 percent. Hence,
this firm should allocate $7000 to plan A and $1000 to plan B.
Related Calculations: As an alternative, construct the following tabulation to
determine the total annual dividend corresponding to every possible division of the capi-
tal. Study of this table shows that the maximum dividend of $1320 accrues when $7000 is
allocated to plan A and $1000 to plan B.
Investment, $ Dividend, $
Plan A Plan B Plan A Plan B Total dividend, $
8000 ... 800 800
1000 7000 300 700 1000
2000 6000 540 600 1140
3000 5000 720 500 1220
4000 4000 900 400 1300
5000 3000 950 300 1250
6000 2000 1020 200 1220
7000 1000 1220 100 1320
8000 ... 1300 ... 1300ALLOCATION OF CAPITAL TO TWO
INVESTMENTS WITH VARIABLE RATES
OFRETURN
Suppose that the dividend under plan B in the previous procedure is 15 percent of the first
$3000 invested and 10 percent of the excess. Determine the optimal division of the $8000
investment between the two plans.
Calculation Procedure:
- Construct a dividend-investment diagram
Use Fig. 7 and draw line OK having a slope of 10 percent and line KL having a slope of
15 percent, where K has an abscissa of $5000. The ordinate of each point on the line OKL
represents the prospective plan B dividend that is forfeited by allocating part of the in-
vestment capital to plan A. The optimal division of the investment capital is that for
which the excess of plan A dividends over forfeited plan B dividends is the maximum. - Determine the investment allocation
Find which of the points from A to His most distant from the line OKL. This is point D,