4.3 Age-efficiency and age-price schedules, economic depreciation, and the user cost of capital (continued)

Figure 1 shows the age-efficiency and age-price schedules for the linear, ‘one-hoss-shay’, and geometric efficiency patterns. The age-price schedules are calculated from the age-efficiency schedules assuming rental prices grow at a constant 2% and that the discount rate is 6%. When using the linear and ‘one-hoss-shay’ age-efficiency schedules the economic life of the asset is assumed to be five periods. Figure 1 illustrates the linear age-efficiency schedule produces a non-linear age price schedule and the ‘one-hoss-shay’ age-efficiency schedule produces a linear age-price profile. The geometric age-efficiency schedule produces an identical age-price schedule.

Figure 1 – Age-efficiency and age-price schedules

Once the age-price schedule is obtained from the age-efficiency schedule, economic depreciation () can then be derived as follows:

(20)    

Equation (20) shows that economic depreciation is calculated by summing the loss in value of the -vintage investments between two consecutive periods.

The real net capital stock, which is the logical base for the economic depreciation rate, is calculated by summing the value for each investment after adjusting for economic depreciation (using the age-price schedule):

(21)    

The economic depreciation rate in period is then calculated by taking the ratio of economic depreciation to the real net capital stock, that is:

(22)    

To summarise, Figure 2 shows the link between the age-efficiency schedule, the age price schedule and economic depreciation. It also serves to highlight the point that the loss in productive capacity of an asset cannot be determined independently of the depreciation pattern. Figure 2 also shows the relationship between productive capital stocks and real net capital stocks.

Figure 2 – Age-efficiency schedule, age price schedule and economic depreciation

4.4  Numerical example of the net capital stock and economic depreciation

Table 7 presents information to construct the economic depreciation rate for the asset (), which is needed to construct the user cost of capital (). Based on the linear age-efficiency schedule presented in column (4) of Table 6, column (1) of Table 7 displays the corresponding age-price schedule. The age-price schedule is calculated assuming a discount rate of 6% and that the rental price grows at a constant 2%. To calculate economic depreciation for the asset () it is first necessary to trace the loss in the value of each investment in the asset over time. This is presented in columns (2) to (7) of Table 7. Economic depreciation () is calculated by summing the loss in value of each investment between two consecutive periods. For example depreciation in is equal to the loss in value of the initial investment () between and (67.5 – 41 ≈ 26.5) plus the loss in value of the investment made in (109.1 – 73.6 ≈ 35.5), which equals 61.9.

Table 7 – Net capital stock and depreciation

	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
	1.00	100.0							100.0
	0.67	67.5	109.1					32.5	176.6	0.2
	0.41	41.0	73.6	115.4				61.9	230.0	0.3
	0.21	20.8	44.7	77.9	112.5			86.6	255.9	0.3
	0.07	7.0	22.7	47.3	75.9	112.5		103.0	265.4	0.4
	0.00	0.0	7.6	24.0	46.1	75.9	114.7	111.7	268.4	0.4

The base used to calculate the depreciation rate is the net capital stock. This is calculated by adding the age-price weighted investment for each period and is reported in column (9) of Table 7. The economic depreciation rate () is displayed in column (10) of Table 7.