Question 15.14: Depreciation and Inflation Copper River Valves is evaluating...

Since the operating costs are stated in year-0 dollars, the first cost will be as well. Then, which values are affected by f, the inflation rate? The first cost is at time 0, so it is not affected. However, the depreciation deduction is affected, and it has a differential inflation rate found using Equation 15.3 of f_{Δdepr.} = −6.54%. The annual $45K in operating cost is best assumed to have no differential inflation. Thus, the easiest way to include inflation is to convert the depreciation deduction from nominal to year-0 dollars.

1+f_{\Delta item} = \frac{1+ f_{item}}{1+f}                          (15.3)

From Exhibit 12.7, manufacturing equipment has a 7-year recovery period for MACRS. The VDB function (see Section 12.9) is used to compute the MACRS deduction in column B of Exhibit 15.11. Column C uses the differential inflation rate to state this tax deduction in year-0

EXHIBIT 12.7 Recovery periods for MACRS

EXHIBIT 15.11 Depreciation and inflation at Copper River Valves

dollars. (Since the first cost is at time 0 and the tax deduction is at the end of the first year, Equation 15.1 is used.)

F_{T+t} = F_{T} (1 + f )^{t}                (15.1)

Column D shows the taxable income in year-0 dollars. This is computed by subtracting the column C values from the operations cost of −$45,000 ($A$4). Column E computes the tax savings, or negative tax, from the costs of this equipment by  multiplying each year’s value in column D times the tax rate shown in cell $A$6. From Chapter 13, that tax rate is 35% with $40M in pretax profits.
Column F computes the ATCF by subtracting the negative tax in column E from the operations cost of −$45,000 in $A$4. The function NPV(A7,F11:F20) + F10 is used to find in year-0 dollars the PW of −$385,166. The EAC is found by multiplying this value by (A/P,9%,10), or .1558, to get $60,017.
To calculate the value ignoring inflation’s impact on depreciation, the easiest approach is to change the differential inflation rate for the MACRS deduction to 0%, as shown in Exhibit 15.12. At −$372,685, the PW is better (less negative) when ignoring inflation, since the MACRS deduction is larger in year-0 dollars. The EAC is $58,072, which is $1945 or 3.2% lower. While this difference is small, in some industries profits are less than 10% of costs, so this difference could amount to half of the potential profits linked to this machinery.

EXHIBIT 15.12 Ignoring inflation’s impact on depreciation at Copper River Valves