There are trade-offs involved in every economic decisions. When considering whether or not to carry out a capital investment, it is rational for firms to estimate the expected rate of return on investment by comparing the costs of purchasing and maintaining the capital goods and the future expected profits. However, it is flawed to treat the value of a pound that is received in the future to be equal to the value of a pound received today.
One reason is that due to rising inflation, the true value of the currency will depreciate over time, and this results in a fall in the purchasing power of a pound. Rational economic agents also tend to value near term benefits more than the long term benefits because of the future uncertainties and risks. This phenomenon is described as time preference. Hence, the concept of discounting plays a significant role to address the issue raised by the change in real values of the resources at different time periods.
By taking into account the trade-off between immediate and delayed benefits, it will eliminate the problem of time preference. As there is always a time lag between purchasing the capital goods and generating revenue from the investments, this concept is particularly important in the theory of investment expenditure. Another important consideration is that the money spent on capital investment can actually be used in alternative ways, most often, by lending the resources out to earn interests.
So by engaging in a certain capital investment, firms will have to forgo these interests or alternative investment possibilities. Thus, it is vital for them to adjust the anticipated stream of future expected profits to expected present values so as to weigh the costs and benefits of an investment. This can be done by reducing the value of future profits at the discount rate to determine their worth under present valuation. Then the net present value can be calculated by subtracting the total present value of the expected future benefits by the present cost.
If the net present value is positive, firms should therefore undertake the investment. For instance, assume that the nominal interest rate is µ per year and the expected rate of inflation to be ? in all future periods. Since the expected real interest rate is equal to the nominal interest rate minus the expected inflation rate, it will be (µ – ?), and to simplify it, let it be ?. If the firm decides to lend out resources, after a year, the total amount receivable will be (1 + ?), and the year after that will be (1 + ?)2 and so n; if the firm decides to purchase the machinery and the investment is financed by borrowing, then it has to repay the total amount of loan of (1 + ?) next year, and (1 + ?)2 the year after. All these show that the value of 1 pound today is equivalent to (1 + ?) pound next year, this implies that the value of 1 pound next year is equal to 1 / (1 + ?) pound this year. The expected real interest rate, ?, is in fact equivalent to the real discount rate and 1 / (1 + ?) pound will be the real expected present value.
So the expected present value of 1 pound after two years will be 1 / (1 + ?)2 pound. It can then be generalised to the following formula: PV = FV / (1 + ?)n, where PV = present value, FV = future value, ? = the real discount rate and n = the number of period of time between the present and when the future value is expected to be received or paid. For example, suppose a firm has the opportunity to purchase a new machine which would offer ?50 profits in a year’s time and ?80 profits in two year’s time. The machine would then become worthless.
If the firm would like to carry out the investment, it has to borrow a loan of ?110 to buy the machine. The nominal rate of interest charged on the loan would be 5%. So, the expected present value of future profits would be PV1 + PV2 = ?[50 / ( 1 + 5%) + 80 / ( 1 + 5%)2] = ?120. 18. The net present value would be ?(120. 18-110) = ?10. 18, thus, the firm should invest in it. If the capital goods are known to physically depreciate at a constant annual rate of ?, then the formula can be further derived as PV1 + PV2 + … + PVk = FV / (1 + ?) + FV(1 – ? ) / (1 + ?)2 + … FV(1 – ? )k-1 / (1 + ?)k = FV[1 + x + x2+ … + xn] / (1 + ?), where x = (1 – ? ) / (1 + ?) It is always true that the nominal interest rate is positive, thus, the nominal discount rate is always positive. Each future payment is multiplied by its respective discount factor. So the higher the discount rate, the greater the denominator and the lower the expected present value of the associated future profits. The expected present value and the future value are positively related, so an increase in future value will lead to a greater present value.
There is also a negative relationship between the present value and the rate of physical depreciation of the machine. The faster the rate of a machine wears out, the less valuable it will worth, and the less stream of profits the firm expects to receive. It is vital to notice that the rationale of all these are based on the assumption that profit maximisation is the firms’ prime objective. Normally firms would pursue a capital investment only if it is profitable. However, it may be argued that due to many reasons such as imperfect information, the firms might concentrate on the alternative objectives instead.
If the objective of sales volume maximisation is adopted by the firm, then knowing that the expected present value of future profits exceeds the present cost will not give any implications of sales volume being maximised. Thus, this will decrease the extent to which the concept of discounting is important in the theory of investment expenditure. Nevertheless, underlying all of the decisions is optimisation, to a certain extent, profit maximisation would be the overall objective of the firms.
If many different investment possibilities are available to a firm, the firm can compare the net present values of these investments. The net present values have to be at least 0, otherwise the investments will be rejected. The larger the net present value, the greater the expected return can be generated from the investment. Hence, the concept of discounting allows the firm to determine which investment is more attractive than the next best alternative use of the funds in monetary terms. This makes it a key consideration in the theory of investment expenditure.
When there is a fall in expected real interest rate, with other things being equal, the real discount rate will fall to the same level. It follows from the previous formula that the denominator will be smaller, so the expected present value will be larger. The rate of return of any capital investments would then be greater. For instance, referring back to the example on the previous page, assume that the expected real interest rate now falls to 2% and the expected inflation is 0, the nominal interest rate will be 2%. The expected present value will now be: PV1 + PV2 = ?[50 / ( 1 + 2%) + 80 / ( 1 + 2%)2] = ?125. 1. This illustrates that the present value has increased by ?5. 73 due to the falling expected real interest rate from 5% to 2%. A rise in the expected future benefits of capital goods will lead to an increase in desired investment expenditure. In addition, the desired investment expenditure function is given as , with the assumptions of expected inflation being 0 and the rate of physical depreciation to be a constant. The variable i is the economy’s nominal interest rate; is the level of business optimism. It is known that i has an inverse relationship with I and as a positive relationship with I. We know that when the expected real interest rate falls, the expected future benefits of capital goods will increase. Then in general the firms will be more optimistic about the future profitability of any capital investments, so will increase. This will raise desired investment expenditure. Moreover, if the firm has a lot of cash on hand, it will have to consider whether to lend out its resources or spend them on capital investment. This decision depends on which option has a higher real rate of return.
This is done by comparing between the present value of future expected profits and the interests receivable through lending. A decline in expected real interest rate will imply that there will be a lower return in saving. Then engaging in capital investments would be a more favourable option. A further increase in desired investment expenditure will be stimulated. Furthermore, falling expected real interest rate will lead to borrowing become cheaper and more attractive, as the interests for repayment of loans will be less.
Even if the firm has to finance a capital investment by borrowing a loan, the lower real cost of borrowing will increase the expected rate of return, and this gives an incentive for the firm to undertake an investment. In conclusion, due to rising inflation, the phenomenon of time preference and the opportunity cost of engaging in a capital investment, the concept of discounting has a crucial role in the theory of investment expenditure. By using the discount rates to compute the present values of anticipated future revenue, it allows the firms to make rational comparisons between different investment possibilities in different timeframes.
In addition, the concept of discounting can logically explain why a cut in expected real interest rate will, other things being equal, stimulate investment expenditure through various ways. Notice that it causes a rise in expected rate of return in all cases. It also shows that all firms, regardless of whether they are holding sufficient funds or having to borrow the funds to undertake the capital investments, will increase their desired investment expenditure when the expected real interest rate falls.