Question

Check My Work eBook Problem 11-12 New-Project Analysis Madison Manufacturing is considering a new machine that costs $350,000 and would reduce pre-tax manufacturing costs by $110,000 annually. Madison would use the 3-year MACRS method to depreciate the machine, and management thinks the machine would have a value of $33,000 at the end of its 5-year operating life. The applicable depreciation rates are 33.33 %, 44.45 % , 14.81%, and 7.41 % Working capital would increase by $35,000 initially, but it would be recovered at the end of the project's 5-year life. Madison's marginal tax rate is 40% , and a 11 % cost of capital is appropriate for the project. a. Calculate the project's NDV

Answer 1

Solution :

In order to find Project's expected NPV, at first we need to find out the Expected Present Cash inflows and Expected Cash Outflows.

Step 1: Calculation of Cash Outflows.

Sl No	Particulars	Amount ( In $)
a)	Initial Cash Outlay	350,000
b)	Additional working Capital at the beginning ( 40,000*0.35 + 35,000* 0.35 + 30,000* 0.30)	35,250
c)	Recovery of Expected Working Capital at the end, PVF (5year, 11%)* 35,250= 35,250*0.5934	20,917.35
d)	Net Initial Cash Outflow (a+b-c)	364,332.65

Step 2 : Calculation of Expected Cash Inflows

Year	Probability =0.35	Probability= 0.35	Probability= 0.30	Total	Discount factor @ 11%	Discounted Value
	(In $)	(In $)	(In $)	(In $)		(In $)
1	88,000*0.35 = 30,800	110,000*0.35= 38,500	132,000*0.30= 39,600	108,900	0.9009	98,108.01
2	88,000*0.35 = 30,800	110,000*0.35= 38,500	132,000*0.30= 39,600	108,900	0.8116	88,383.24
3	88,000*0.35 = 30,800	110,000*0.35= 38,500	132,000*0.30= 39,600	108,900	0.7311	79,616.79
4	88,000*0.35 = 30,800	110,000*0.35= 38,500	132,000*0.30= 39,600	108,900	0.6587	71,732.43
5	88,000*0.35 = 30,800	110,000*0.35= 38,500	132,000*0.30= 39,600	108,900	0.5934	64,621.26
5( Salvage Value)	28,000*0.35= 9,800	33,000*0.35= 11,550	38,000*0.35= 13,300	34,650	0.5934	20,561.31

Calculation of Tax Saving on Depreciation

Year	Original Cost of Machine (In $) (a)	Depreciation Rate As per MACR (b)	Depreciation (In $) (c)   a*b	Tax Rates	Tax Saving on Depreciation,e = c * Tax Rate (In $)	Discounting factor @ 11%	Discounted Value = e * Discounting factor (In $)
1	110,000	33.33%	36,663	40%	14,665.2	0.9009	13,211.88
2	110,000	44.45%	48,895	40%	19,958	0.8116	16,197.91
3	110,000	14.81%	16,291	40%	6,561.4	0.7311	4,797.04
4	110,000	7.41%	8,151	40%	3,260.40	0.6587	2,147.63

The probability of depreciation in each year is 1, as it is mandatory that depreciation will arise each year.

Value of Assets at the end of 4th year = nil , since Original Cost - Depreciation for 4 years.

Expected Profit on Sale of Assets = Expected Salvage Value - Value of Assets at the end of 4th year.

= $ 34,650- 0 = $34,650

Expected Tax expenses at profit on sale of assets = 34,650* 40% = $13,860

Present Value of Tax expenses at the terminal period = $13,860 * 0.5934 = $8,224.52

Calculation of Expected Cash Inflows = Discounted Cash Inflows + Discounted tax Savings on Depreciation

Years	Discounted Cash Inflows ( In $)	Discounted Tax Savings on depreciation (In $)	Total Expected Cash Inflows (In $)
1	98,108.01	13,211.88	111,319.89
2	88,383.24	16,197.91	104,581.15
3	79,616.79	4,797.04	84,413.83
4	71,732.43	2,147.63	73,880.06
5	64,621.26	0	64,621.26
5 (Salvage)	20,561.31	0	20,561.31
5 (Tax Expenses)	(8224.52)	0	(8224.52)
Total Cash inflows ( In $)			451,152.98

Expected NPV = Total Cash inflows ( In $) - Net Initial Cash Outflow

= 451,152.98 - 364,332.65 = $86,820.33

Expected NPV = $86,820.33 or $86,820 (rounded off)

b) Project Standard Deviation.

NPV of worst case

Cash Inflow = 88,000* PVAF ( 11%, 5years) + 28,000 * 0.5934 - (28,000*40%*0.5934) = $88,000* 3.6958 + 16,615.2 - $6,646.08 = $325,230.40 + $16,615.2 - $6,646.08 = $ 335,199.52

Cash Outflow = $ 350,000+ 40,000- 40,000*0.5934 = $350,000+$40,000-$23,736 = $ 366,264

NPV = $335,199.52 - $ 366,264 = $ -31,064.48

NPV of base case

Cash Inflow = $110,000* 3.6958 + 33,000* 0.5934 - (33,000*40%*0.5934) = $ 406,538+19,528.20 - 7832.88 =$418,233.32

Cash Outflow = $(350,000+ 35,000 - 35,000* 0.5934) = $ 364,231

NPV of base case = $418,233.32 - $ 364,231 = $ 54,002.32

NPV of best Case

Cash Inflows = $132,000* 3.6958 + 38,000*5934 - (38,000*40%* 0.5934) = $487,845.60 + 22,549.20 - 9,019.68 = $ 501,375.12

Cash outflows = 350,000 +30,000 - 30,000* 0.5934 = $362,198

NPV of best case = $ 501,375.12 - $362,198 = $139,177.12

Standards Deviation = $\sqrt{}$ worst prob ( NPV - Expected NPV )²+ base case( NPV - Expected NPV )² + best case ( NPV - Expected NPV )²

In other words, square root of worst prob ( NPV - Expected NPV )²+ base case( NPV - Expected NPV )² + best case ( NPV - Expected NPV )²

Therefore, $\sqrt{}$ 0.35 ( -31,064.48 - $86,820.33)² + 0.35($ 54,002.32 - $86,820.33)² + 0.30( $139,177.12 -  $86,820.33)²

$\equiv$$\sqrt{}$0.35 (13,849,667,430.8) + 0.30( 1,077,021,780.36) + 0.30 (2,741,233,459.10)

$\equiv \sqrt{}$4,847,383,600.78 + 323,106,534.10 + 822,370,037.73

$\equiv \sqrt{}$5,992,860,172.61

$\equiv$ 77, 413.56

Standard Deviation of project = $ 77,414

C) Expected Coefficient of Variation of Project

Coefficient of Variation of Project = (Standard Deviation of Project / Expected NPV from the Project)

=  ($ 77,414/ 86,820) = 0.89

Coefficient of Variation of Project = 0.89

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