Question

Find the best investment and financing program using the Dean Model.

Dean Model Exercise Initial investment Project Option Amount Interest rate 400 19.1% 200 11% 2 200 18.5% 300 10% 3 100 300 12% 4 100 6.5% 200 15% 5 50 13% Find the best investment and financing program using the Dean Model

Answer 1

Dean Model is simultaneous analysis of investment and financing options. Mathematically the model can be formulated using the variables and parameters below:

Objective function:

$\sum Aj1* Xj +\sum Di1* Yi \Rightarrow Maximize$ called as compounded Value (CV)

with $\sum Aj0* Xj +\sum Di0* Yi = 0$

here Xj is extent of investment projects (here 1 to 5)

and Yj is the extent of financing options (here 1 to 4 for A to D)

and Aj1 and Di1 are the net cashflows associated with each project in time 1 and 0 for O subscripts

Let us consider the below provided data:

Invesment Options	Initial invesment	IRR	Rank	Capital Flow at year 1
1	400	19.10%	2	476.4
2	200	18.50%	3	237
3	100	22%	1	122
4	100	6.50%	5	106.5
5	50	13%	4	56.5

Financing options	Amount	Interest	Rank	Capital flow at year 1
A	200	11%	2	222
B	300	10%	1	330
C	300	12%	3	336
D	200	15%	4	230

The capital flow for first yearin invesments and financing is calculated using following function= initial investment/amount *(1+ IRR or interest) and rank is derived on the basisof IRR and interest. (lower interest better and Higher IRR is better)

Hence the objective function stands for year 1 as:

476.4*x1 + 237* x2 + 122* x3 + 106.5* x4 + 56.5* x5 - 222* y1 - 330* y2 - 336* y3 - 230* y4 >>>>> Maximize

with for year 0 (initial values)

-400*x1 -200* x2 -100* x3 - 100* x4 - 50* x5 + 200* y1 + 300* y2 + 300* y3 + 200* y4

1. Eliminating invesmentes and financing options

invesment options and financing options can be eliminated first on the basis of graph plotting on the accumulated manner and in ranking order.

invesments options	financing option	Initial invesments	interest rate of financing	IRR of projects
3	2	50	10%	22%
3	2	100	10%	22%
3,1	2	150	10%	19.10%
3,1	2	200	10%	19.10%
3,1	2	250	10%	19.10%
3,1	2	300	10%	19.10%
3,1	2,1	350	11%	19.10%
3,1	2,1	400	11%	19.10%
3,1	2,1	450	11%	19.10%
3,1	2,1	500	11%	19.10%
3,1,2	2,1,3	550	12%	18.50%
3,1,2	2,1,3	600	12%	18.50%
3,1,2	2,1,3	650	12%	18.50%
3,1,2	2,1,3	700	12%	18.50%
3,1,2,5	2,1,3	750	12%	13%
3,1,2,5,4	2,1,3	800	12%	6.50%
3,1,2,5,4	2,1,3,4	850	15%	6.50%
	2,1,3,4	900	15%
	2,1,3,4	950	15%
	2,1,3,4	1000	15%

From the above accumulated numbers it is clear that invesment option 4 and financing option 4 (D) are completely out of picture as at this point the interest fall above IRR of projects.

hence options left for invesments are 1,2,3 and 5. and financing options left are 1,2,3.

The possible combinations of invesments with these options are as follows with their compounded values:

			proportion of funding type			Compounded value
Strategy Number	invesments considered	invesments required	1	2	3
1	1	400	50%	100%	0%	35.4
2	2	200	0%	67%	0%	17.22
3	3	100	0%	33%	0%	12.11
4	5	50	0%	17%	0%	1.5
5	1,2	600	100%	100%	33%	49.512
6	1,3	500	100%	100%	0%	46.4
7	1,5	450	75%	100%	0%	36.4
8	2,3	300	0%	100%	0%	29
9	2,5	250	0%	83%	0%	18.5
10	3,5	150	0%	50%	0%	13.5
11	1,2,3	700	100%	100%	67%	59.624
12	2,3,5	350	25%	100%	0%	30
13	3,5,1	550	100%	100%	17%	46.9
14	1,2,5	650	100%	100%	50%	49.9
15	1,2,3,5	750	100%	100%	83%	59.9

Hence from the above options , strategy number 15 is the best option as it has highest Coompounded Value of 59.9

hence best option with dean model is investment in 1,2,3,5 with funding from A, B and C (83.33%).