which has a vertical offset of $500. Therefore, the firm should allocate $4000 to plan A
and $4000 to plan B.
Related Calculations: Alternatively, calculate the total dividend corresponding
to every possible division of the available capital. For example, if $1000 is allocated to
plan A and $7000 to plan B: Dividend under plan A = $300; dividend under plan B =
$3000(0.15) + $4000(0.10) = $850; total dividend = $1150. Using this technique, we find
the maximum total dividend to be $1450; this occurs when the capital is divided equally
between two plans. Thus, the previous findings are verified.
This procedure and the previous one show two methods of establishing the optimal di-
vision of available capital, i.e., computing the rate of return on an incremental investment
and computing the total dividend. The latter represents a more straightforward approach,
particularly where both alternative investments yield a variable rate of return.
ALLOCATION OF CAPITAL TO THREE
INVESTMENTS BY DYNAMIC
PROGRAMMING
A syndicate has $600,000 available for investment; and three investment plans, A, B, and
C, are under consideration. Under each plan, the amount that can be invested is a multiple
of $100,000 and the investors receive annual dividends and recover their capital when the
venture terminates at the expiration of 5 years. The annual dividends corresponding to the
various levels of investment are shown in Table 7. The investments can be combined in
any manner whatever. Devise the most profitable composite investment.
Calculation Procedure:- Identify the most profitable combination of plans A and B
and determine the corresponding annual dividend if $600,000
is placed in this combination
The problem of identifying the most profitable combination of all three plans can be
solved by dynamic programming. By this technique, the most profitable combination will
be formed in stages, starting with combinations of A and B, identifying the most prof-
itable ones, and then expanding these to include C.
TABLE 7
Annual dividend, $
Amount
invested, $ Plan A Plan B Plan C
100,000 25,000 10,000 15,000
200,000 44,000 32,000 31,000
300,000 63,000 60,000 48,000
400,000 80,000 91,000 56,000
500,000 89,000 93,000 79,000
600,000 95,000 94,000 102,000