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
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 β, then the formula can be further derived as
PV1 + PV2 + ... + PVk = FV / (1 + α) + FV(1 - β ) / (1 + α)2 + ... + FV(1 - β )k-1 / (1 + α)k = FV[1 + x + x2+ ...+ xn] / (1 + α), where x = (1 - β ) / (1 + α) 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