Lecture VI: Multiple Investment Problem
I.
Multiple Investments
A. Optimal Replacement Models
Feldstien, M. S. and M. Rothschild. “Towards an Economic Theory of Optimal
Replacement.” Econometrica 42(3) (May 1974).
Leatham, David J. and Timothy G. Baker. “Empirical Estimates of the Effect of Inflation
on Salvage Values, Costs and Optimal Replacement of Tractors and Combines.”
North Central Journal of Agricultural Economics 3(2) (July 1981).
Perrin, R. K. “Asset Replacement Principles.” American Journal of Agricultural
Economics 54(1) (Feb. 1972).
B. Bussey Chapter 8
1. The question of joint investment analysis arises because projects
are mutually dependent in some fashion. The most common type
of mutual dependence is probably mutual exclusion {such as the
tractor replacement models.} One common form of mutual
exclusion occurs with credit rationing which is a violation of
perfect market assumptions.
2. Two approaches are common in the choice among multiple
investments
a. A method of ranking investments in a decreasing order of
attractiveness using NPV, benefit/cost ratios (B/C), and
IRR. Then selecting the investment until capital is
depleted.
b. The second, related formulation is an integer programming
formulation.
3. Ranking
a. It should be obvious from the proceeding lectures that NPV
and IRR can give different rankings. This difference is
called the ranking-error problem. This problem is related
to the reinvestment assumptions of each selection criteria.
b. Methodology
i.
Compute NPV and ANPV for each investment.
Define any dependencies.
ii.
List in ascending order of capital use {assuming
capital rationing problem}. Projects may be
lumped. For example, a firm may want to build
a building and buy a truck. Physically these are
not mutually exclusive, they could occur at the
same time. If the firm is considering a capital
expenditure greater than the two together, then
the combined investment including both the
truck and the building could be compared with
the more extensive investment. Alternatively,
each investment could be analyzed in turn.
iii.
Select investments until capital is used up.
Table 1. Multiple Project Cash Flows
Project
Investment
Annual Cash
Years of
Flows
Life
F
-12,000
4,281
5
G
-10,000
4,184
5
H
-17,000
5,802
10
Table 2. Net Present Value and Annualized Net Present
Value
Project
Net Present
Annualized Net Present
Value
Value
F
2,350.58
701.21
G
4,025.42
1,200.84
H
12,118.89
2,414.71
Table 3. Ranking Investments Alternatives
Project
Required
Annualized Net
Investment
Present Value
G
-10,000
1,200.84
H
-17,000
2,414.71
F, G
-22,000
1,902.05
G, H
-27,000
3,615.55
F, G, H
-39,000
4,316.76