Impact of a Longer Depreciation Schedule on After-Tax PW and IRR

Suppose the machinery in Example 7-15 had been classified in the 10-year MACRS (GDS) property class. Calculate the new after-tax PW and after-tax IRR. Why are these results different than the results of Example 7-15?

Question

Impact of a Longer Depreciation Schedule on After-Tax PW and IRR

Suppose the machinery in Example 7-15 had been classified in the 10-year MACRS (GDS) property class. Calculate the new after-tax PW and after-tax IRR. Why are these results different than the results of Example 7-15?

Accepted Answer

If the machinery in Example 7-15 had been classified in the 10-year MACRS (GDS) property class instead of the five-year property class, depreciation deductions would be slowed down in the early years of the study period and shifted into later years, as shown in Table 7-7. Compared with entries in Table 7-6, entries in columns [latex]C, D[/latex], and [latex]E[/latex] of Table 7-7 are less favorable, in the sense that a fair amount of ATCF is deferred until later years, producing a lower after-tax PW and IRR. For instance, the [latex]\mathrm{PW}[/latex] is reduced from [latex]\$ 17,208[/latex] in Table [latex]7-6[/latex] to [latex]\$ 9,136[/latex] in Table 7-7. The basic difference between Table 7-6 and Table 7-7 is the timing of the ATCF, which is a function of the timing and magnitude of the depreciation deductions. In fact, the curious reader can confirm that the sums of entries in columns [latex]A[/latex] through [latex]E[/latex] of Tables 7-6 and 7-7 are nearly the same (except for the half-year of depreciation only in year 10 of Table 7-7). The timing of cash flows does, of course, make a difference!

Depreciation does not affect BTCF. Fast (accelerated) depreciation produces a larger PW of tax savings than does the same amount of depreciation claimed later in an asset’s life.

TABLE 7-6 ATCF Analysis of Example 7-15
	(A)	(B)		Depreciation Deduction			(C) = (A)−(B)	(D) = −0.38(C)	(E) = (A) + (D)
End of Year, k	BTCF	Cost Basis	X	GDS Recovery Rate	=	Deduction	Taxable Income	Cash Flow for Income Taxes	ATCF
0	-$180,000	—		—		—			-$180,000
1	36,000	$180,000	X	0.2000	=	$36,000	0	0	36,000
2	36,000	180,000	X	0.3200	=	57,600	-21,600	+8,208	44,208
3	36,000	180,000	X	0.1920	=	34,560	1,440	-547	35,453
4	36,000	180,000	X	0.1152	=	20,736	15,264	-5,800	30,200
5	36,000	180,000	X	0.1152	=	20,736	15,264	-5,800	30,200
6	36,000	180,000	X	0.0576	=	10,368	25,632	-9,740	26,260
7-10	36,000	0				0	36,000	-13,680	22,320
10	30,000						[latex]30,000^{a} [/latex]	[latex]-11,400^{b} [/latex]	18,600
Total	$210,000							Total	$130,201
								PW (10%) =	$17,208
[latex]{ }^{a}[/latex] Depreciation recapture [latex]=\mathrm{MV}_{10}-\mathrm{BV}_{10}=\$ 30,000-0=\$ 30,000[/latex] (gain on disposal). [latex]{ }^{b}[/latex] Tax on depreciation recapture [latex]=\$ 30,000(0.38)=\$ 11,400[/latex]. After-tax IRR: Set PW of column [latex]\mathrm{E}=0[/latex] and solve for [latex]i^{\prime}[/latex] in the following equation: [latex]\begin{aligned}0=&-\$ 180,000+\$ 36,000\left(P / F, i^{\prime}, 1 ight)+\$ 44,208\left(P / F, i^{\prime}, 2 ight)+\$ 35,453\left(P / F, i^{\prime}, 3 ight)+\$ 30,200\left(P / F, i^{\prime}, 4 ight)+\$ 30,200\left(P / F, i^{\prime}, 5 ight)+\$ 26,260\left(P / F, i^{\prime}, 6 ight) \ &+\$ 22,320\left(P / A, i^{\prime}, 4 ight)\left(P / F, i^{\prime}, 6 ight)+\$ 18,600\left(P / F, i^{\prime}, 10 ight) ; \operatorname{IRR}=12.4 \%\end{aligned}[/latex].

TABLE 7-7 ATCF Analysis of Example 7-16 [Reworked Example 7-15 with Machinery in the 10-Year MACRS (GDS) Property Class]
	(A)	(B)		Depreciation Deduction			(C) = (A)−(B)	(D) = −0.38(C)	(E) = (A) + (D)
End of Year, k	BTCF	Cost Basis	X	GDS Recovery Rate	=	Deduction	Taxable Income	Cash Flow for Income Taxes	ATCF
0	-$180,000	—		—		—			-$180,000
1	36,000	$180,000	x	0.1000	=	$18,000	$18,000	-$6,840	29,160
2	36,000	180,000	x	0.1800	=	32,400	3,600	-1,368	34,632
3	36,000	180,000	x	0.1440	=	25,920	10,080	-3,830	32,170
4	36,000	180,000	x	0.1152	=	20,736	15,264	-5,800	30,200
5	36,000	180,000	x	0.0922	=	16,596	19,404	-7,374	28,626
6	36,000	180,000	x	0.0737	=	13,266	22,734	-8,639	27,361
7	36,000	180,000	x	0.0655	=	11,790	24,210	-9,200	26,800
8	36,000	180,000	x	0.0655	=	11,790	24,210	-9,200	26,800
9	36,000	180,000	x	0.0656	=	11,808	24,192	-9,193	26,807
10	36,000	180,000	x	0.0655/ 2	=	5,895	30,105	-11,440	24,560
10	30,000						[latex]18,201^{a} [/latex]	-6,916	23,084
								Total	$130,196
								PW (10%) [latex]\simeq[/latex]	$9,136
								IRR =	11.2%
[latex]{ }^{a} ext { Gain on disposal }=\mathrm{MV}_{10}-\mathrm{BV}_{10}=\$ 30,000-\left(\frac{0.0655}{2}+0.0328 ight)(\$ 180,000)=\$ 18,201[/latex].

Question 7.16: Impact of a Longer Depreciation Schedule on After-Tax PW and...

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