APPENDIX TO “DETERMINANTS OF MINING
INVESTMENT: A CASE STUDY OF ZIMBABWE”
Lyman Mlambo, Institute of Mining Research, University of Zimbabwe
Theoretical Literature Review on Determinants of Investment
The following two sections briefly look at the main theories of investment. It is from theories of investment that we identify the major factors that determine investment. The two theories 1looked at here are Keynes’ theory and the accelerator model.
2Keynes’ Theory of Investment
Pentecost (2000, p.119) identifies two main components to the theory: (1) the role of expectations; and (2) supply price of capital goods. He views the value of a piece of capital equipment as the net present value of income that will be derived from the use of that equipment, that is, income over and above its purchase cost. That is, value or demand price of machine (V) is given by:
nmRI3ttNPV！？ (1) ；；tt;；;；1？i1？it！！m？10t
where n = the whole life of the piece of equipment
m = the whole investment period (that is the time it takes to set up the investment equipment).
This may be one year or more.
i = discount rate (normally, the rate of interest)
R = net receipts from use of machine in period/year t.
A net present value of zero indicates that the project is not profitable, while any positive NPV shows that the project (or having the asset) is profitable.
It can be observed that the first term in the RHS is the total income/net receipts from the use of the equipment over its lifespan (n), and that the second term is the total cost of having the equipment operational or its purchase price or cost.
The rate of discount which ensures that NPV is equal to zero, or that total net receipts over the asset life equals the cost of the asset, is of great interest and it is called the internal rate of
return (IRR). It is what Keynes calls the marginal efficiency of capital(MEC) and is actually
the expected rate of return from a capital asset (Shapiro, 1974). IRR is the discount rate that ensures that net receipts cover the initial cost.
The market interest rate is a measure of the cost of loanable funds hence may be used to discount future money to present value because it represents the time value of money. A lower interest rate will mean that future receipts of a project are not heavily discounted, and
1 Two other theories are identified in the literature – neo-classical theory and Tobin’s Q-theory (see
Dzawanda 1994 and Pentecost 2000). However, apparently what we get from the neo-classical theory is the emphasis on the importance of real rate of interest in the calculation of user cost. From Tobin the emphasis is on the financial market as an alternative investment to investment in real markets. 2 Based on Pentecost (2000), NEPC Handout, and Shapiro (1974). 3 This formulation is from NEPC Investment Profitability Analysis’ handouts. For a more detailed treatment of this theory read Pentecost (2000) and Shapiro (1974)
when their present value is compared with initial project costs, the NPV will be higher than with a higher rate of interest.
Therefore, a comparison of the MEC to the current market rate of interest, r, indicates
whether or not an investment may be profitable. It would be profitable if r < MEC and vice versa. That is, if the interest rate in the market is lower that the one that would give a profit of zero, then investment profitability is positive. Thus, once MEC is given, r determines whether
or not the good will be purchased though it does not determine the MEC of that good (Shapiro, 1974, p.163).
IRR (MEC) may be computed by a trial and error method (where one tries several discount
rates until the appropriate one is found) or some short-cut method (adhoc method) (NEPC
Handout on Investment Profitability Analysis).
Anything that makes the businessman expect more income flow from use of a capital good, assuming the capital good does not change its price, will raise its MEC. Also a fall in the price of the capital good (by reducing costs hence increasing NPV) with expected income unchanged will raise its MEC. A decrease in r affect MEC though it would make the purchase of the good more profitable if r falls below MEC from a position of MEC<r (Shapiro, 1974, p.163).
If a firm has a given set of possible investment projects and assuming it has the money available or can borrow to invest, each year it will invest in the projects whose MEC are higher than the current market rate of interest. As the market rate of interest falls, ceteris
paribus, new additional projects with lower MECs are undertaken. The optimal level of capital stock in any given year is that where the least (last) profitable of all the projects has MEC equal to the current of interest, otherwise, the capital stock is not optimal. When MEC = rate of interest there is no need for net investments (Shapiro, 1974, pp.164-165).
Therefore, all things the same, a change in either interest rate or MEC affects net investment. When interest rate falls more projects will be undertaken and vice versa. When MEC falls (due to change in business conditions) less projects will be undertaken at the same rate of interest (many projects become less profitable) and vice versa.
The Keynesian investment function can then be summarised by:
I！；？；i (2) 01
；where captures exogenous shifts in (business) expectations (Pentecost, 2000, p.124). Thus, 0
both MEC and interest rate affect investment.
The Accelerator theory of investment
The flexible accelerator model assumes the existence of an equilibrium, optimal, desired, or
long-run stock of capital required to produce a given output for a given technology, rate of interest, and so forth (Gujarati (1988, p.519).
Further derivation follows equation (3).
*K！；Q (3) t1t
*KQwhere is desired mining capital stock in period t, and is current mining output in tt
4The capital adjustment process is defined by the following equation:
*;；K？K！，K？K (4) tt？1tt？1
where , being , is the coefficient of adjustment. ，0，，：1
*;；K！，K？1？，K (5) ttt？1
Substituting (3) into (5) and simplifying gives:
5;；K！，；Q？1？，K (6) t1tt？1
The net investment function as strictly based on relationship (4) becomes:
nK？K！I！，；Q？，K (7) tt？1t1tt？1
(If we assume that replacement investment in period t is a positive proportion of previous 6period’s level of capital, gross investment is given by (See Dzawanda 1994):
gI！K？K？(K (8) ttt？1t？1
g;；I！K？1？(K (9) ttt？1
Substituting (7) into (8):
g;；I！，；Q？(？，K (10) t1t？1t？1
Lagging (10) once and multiplying the result by (1？)we get: (