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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