Question

1. A machine is needed to produce parts at the rate of 60 per hour. The operator to run the machine will be paid $11.47 per hour. The parts cost $.47 each and will be sold for $.93 each after this operation. This operation is expected to be needed for 7 years. SOYD depr will be used and 10% salvage is assumed. Assume that revenues, labor, and material costs flow uniformly and continuously throughout the year, and that the machine will run for 8 hours per day, 250 days per year. a. If the tax rate is 47% and MARR is 20%, how much can be spent on this machine? Solve this using the AEC equation and then construct a spreadsheet and use solver to solve this problem. b. Assume SL depreciation is used. Repeat part a. c. Assume 5 yr MACRS is used. Repeat part a. d. Assume the first cost is expensed and the salvage is income in year 7. Repeat part a. e. Find how much can be spent with SL depr by varying the debt ratio from ( to 1.0.

Answer 1

a. SOYD depreciation
Sale value/part	93
Less:Cost / part	47
Less: Opg. labor cost /part(11.47/60)	0.19
Net revenue/part	45.81
Total for 60 parts(1 hr.)	2748.53
Total annual net revenues
2748.53*8 hrs./day*250 days	5497060
Less: Tax at 47%	2583618.2
After-tax annual revenues	2913441.8
PV of After-tax annual revenues
P/A,20%,7,2913442
2913442*3.60459		10501764
Add: Salvage	10%*x*(1-47%)
P/F,20%,7th yr.		(10%*x*(1-47%))*0.27908
Add: PV of 7 yr. Depn. Tax shields
((7/28*0.9x*47%)*0.83333)+((6/28*0.9x*47%)*0.69444)+((5/28*0.9x*47%)*0.57870)+((4/28*0.9x*47%)*0.48225)+((3/28*0.9x*47%)*0.40188)+((2/28*0.9x*47%)*0.33490)+((1/28*0.9x*47%)*0.27908)
0.47*0.9x*((7/28*0.83333)+(6/28*0.69444)+(5/28*0.57870)+(4/28*0.48225)+(3/28*0.40188)+(2/28*0.33490)+(1/28*0.27908))
Simplifying the above part, we get
0.47*0.9x*0.60632
Forming an equation of the above,
Cost of the M/c
x=10501764+((10%*x*(1-47%))*0.27908)+0.47*0.9x*0.60632
Solving for x
we get the PV of the m/c ,ie the amt. that can be spent on the m/c as
14410900

	SOYD depreciation table
Year	Depreciable base	Rem.life	Depn. Fraction	PV F at 20%	PV F *Dep fraction
0					x
1	0.9x	7	7/28	0.83333	0.20833
2	0.9x	6	6/28	0.69444	0.14881
3	0.9x	5	5/28	0.57870	0.10334
4	0.9x	4	4/28	0.48225	0.06889
5	0.9x	3	3/28	0.40188	0.04306
6	0.9x	2	2/28	0.33490	0.02392
7	0.9x	1	1/28	0.27908	0.00997
		28			0.60632

b. Straight-line depreciation
PV of Depreciation tax shield part alone will differ
Annual depn. Will be 0.9x/7
Annual depn. Tax shield will be 0.9x/7*47%
So, this part of the equation for PV will be
0.9x/7*47%*3.60459
(P/A,20%,7)
Now,
Forming an equation combining with first 2 equation-parts from a. above,
Cost of the M/c
x=10501764+((10%*x*(1-47%))*0.27908)+(0.9x/7*47%*3.60459)
Solving for x
we get the PV of the m/c ,ie the amt. that can be spent on the m/c as
13685100

c. 5 year MACRS depn.
Here, the after-tax cash flow & PV of depn. Tax shield wil change.
PV of Depreciation tax shield part :
(x*20%*47%*0.83333)+(x*32%*47%*0.69444)+(x*19.2%*47%*0.5787)+(x*11.52%*47%*0.48225)+(x*11.52%*47%*0.40188)+(x*5.76%*47%*0.33490)
Simplifying the above,
x*47%*0.62114
PV of after-tax salvage
(Salvage-Carrying value)*(1-Tax rate)*0.27908
(x*10%-5.76%*x)*0.27908
x*4.24%*0.53*0.27908
Now,
Forming an equation combining the above 2 equation-parts & the first 1 from a. above,
Cost of the M/c
x=10501764+x*47%*0.62114+x*4.24%*0.53*0.27908		P/F,20%,Yr.7
Solving for x
we get the PV of the m/c ,ie the amt. that can be spent on the m/c as
14964200

Dep.base	MACRS%	PV F at 20%	(2*3)
x	20	0.83333	0.16667
x	32	0.69444	0.22222
x	19.2	0.57870	0.11111
x	11.52	0.48225	0.05556
x	11.52	0.40188	0.04630
x	5.76	0.33490	0.01929
			0.62114

d. First cost is expensed & salvage is income in Yr. 7
In which case, there will be no depreciation or any tax savings on that account.
For Year 1
Total annual net revenues
2748.53*8 hrs./day*250 days	5497060
Less expense on M/c	x
PV Equation for this part
(5497060-x)*(1-47%)*0.83333
For the balance 2 to 7 yrs.
After-tax annual revenues	2913442
PV of the above
2913442*(3.60459-0.83333)=
8073905
Equation for the salvage income part:
x*10%*0.27908
Forming an equation
x=((5497060-x)*(1-47%)*0.83333)+8073905+(x*10%*0.27908)
Solving for x,
we get the PV of the m/c ,ie the amt. that can be spent on the m/c as
7428270
Annual equivalent cost of m/c	NPV	Div.By ((1-1.2^-7)/0.2)
SOYD	14410900	3997928
St.line	13685100	3796574
5 Year MACRS	14964200	4151427