(Straight Line Depreciation) A new machine cost $100,000, and will increase inventory by $10,000, A/R by...

(Straight Line Depreciation) A new machine cost $100,000, and will increase inventory by $10,000, A/R by $15,000, and A/P by $5,000. This machine will reduce our expenses by $18,000 per year. The machine will be depreciated to a zero book value in 10 years, but could be sold for $12,000 at the end of 10 years. The marginal tax rate is 35%, and the cost of capital is 12%. Calculate the payback, NPV, IRR, and PI.

Expert Solution

Step 1: Calculate depreciation schedule:

Depreciation Schedule
Year	Opening Balance	Investment	Depreciation	Closing balance
-		100000-12000= 88,000.00		88,000.00
1.00	88,000.00		88000/10= 8,800.00	79,200.00
2.00	79,200.00		8,800.00	70,400.00
3.00	70,400.00		8,800.00	61,600.00
4.00	61,600.00		8,800.00	52,800.00
5.00	52,800.00		8,800.00	44,000.00
6.00	44,000.00		8,800.00	35,200.00
7.00	35,200.00		8,800.00	26,400.00
8.00	26,400.00		8,800.00	17,600.00
9.00	17,600.00		8,800.00	8,800.00
10.00	8,800.00		8,800.00	-

Step 2: Calculate annual CF:

CF calculation
Year	Remarks	1 to 9	10.00
Annual Benefit	Given	18000	18000
Depreciation	as per schedule	8,800.00	8800
EBIT	Annual Benefit-Depreciation	9,200.00	9,200.00
Tax	0.35 x EBIT	3,220.00	3,220.00
NI	EBIT-Tax	5980	5980
Depreciation	Added back being a non cash expense	8800	8800
CF		14780	14780
Wcinv Recovery	increase in inventory+ increase in AR -increase in AP		20000
Salvage value	sale value of investment		12000
Tax on profit of sale	0.35x12000 (as equipment is completely depreciated, entire salvage value is profit)		4200
Total CF	Wcinv Recovery+Salvage value-Tax on profit of sale	14780	52580

Step 3: Calculate NPV & PI

Year	CF	Discount factor			Discounted CF
0	-1,20,000.00	1/(1+0.12)^0	=	1	1*-120000	=	-120000
1	14780	1/(1+0.12)^1	=	0.892857143	0.892857142857143*14780	=	13196.42857
2	14780	1/(1+0.12)^2	=	0.797193878	0.79719387755102*14780	=	11782.52551
3	14780	1/(1+0.12)^3	=	0.711780248	0.711780247813411*14780	=	10520.11206
4	14780	1/(1+0.12)^4	=	0.635518078	0.635518078404831*14780	=	9392.957199
5	14780	1/(1+0.12)^5	=	0.567426856	0.567426855718599*14780	=	8386.568928
6	14780	1/(1+0.12)^6	=	0.506631121	0.506631121177321*14780	=	7488.007971
7	14780	1/(1+0.12)^7	=	0.452349215	0.452349215336893*14780	=	6685.721403
8	14780	1/(1+0.12)^8	=	0.403883228	0.403883227979369*14780	=	5969.39411
9	14780	1/(1+0.12)^9	=	0.360610025	0.36061002498158*14780	=	5329.816169
10	42580	1/(1+0.12)^10	=	0.321973237	0.321973236590696*42580	=	13709.62041
					NPV = sum of discounted CF	=	-27538.8477
					PI = NPV/initial investment	=	-0.23

Step 4: Calculate IRR, the rate at which NPV = 0 (Using either hit and trial or excel goal seek function)

Year	CF	Discount factor			Discounted CF
0	-1,20,000.00	1/(1+0.0666779932462238)^0	=	1	1*-120000	=	-120000
1	14780	1/(1+0.0666779932462238)^1	=	0.937490045	0.937490045104144*14780	=	13856.10287
2	14780	1/(1+0.0666779932462238)^2	=	0.878887585	0.87888758466937*14780	=	12989.9585
3	14780	1/(1+0.0666779932462238)^3	=	0.823948361	0.823948361393159*14780	=	12177.95678
4	14780	1/(1+0.0666779932462238)^4	=	0.772443386	0.772443386485958*14780	=	11416.71325
5	14780	1/(1+0.0666779932462238)^5	=	0.724157985	0.724157985237119*14780	=	10703.05502
6	14780	1/(1+0.0666779932462238)^6	=	0.678890902	0.678890902242472*14780	=	10034.00754
7	14780	1/(1+0.0666779932462238)^7	=	0.636453463	0.636453462564088*14780	=	9406.782177
8	14780	1/(1+0.0666779932462238)^8	=	0.596668785	0.596668785325896*14780	=	8818.764647
9	14780	1/(1+0.0666779932462238)^9	=	0.559371046	0.559371046467409*14780	=	8267.504067
10	42580	1/(1+0.0666779932462238)^10	=	0.524404788	0.524404787582683*42580	=	22329.15586
					NPV	=	0.000704527

IRR comes to 6.6677993%

jeff jeffy answered 2 years ago

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