Question

Sugar Land Company is considering adding a new line to its product mix, and the capital budgeting analysis is being conducted by a MBA student. The production line would be set up in unused space in Sugar Land’ main plant. Total cost of the machine is $260,000. The machinery has an economic life of 4 years, and MACRS will be used for depreciation. The machine will have a salvage value of 40,000 after 4 years.


The new line will generate Sales of 1,350 units per year for 4 years and the variable cost per unit is $100 in the first year. Each unit can be sold for $200 in the first year. The sales price and variable cost are expected to increase by 3% per year due to inflation. Further, to handle the new line, the firm’s net working capital would have to increase by $30,000 at time zero (The NWC will be recouped in year 4). The firm’s tax rate is 40% and its weighted average cost of capital is 10%.

1. What are the annual depreciation expenses for years 1 through 4? (10 Points)

	Year 1	Year 2	Year 3	Year 4
Depreciation

2. Calculate the annual sales revenues and costs (other than depreciation), years 1 through 4. (10 points)

	Year 1	Year 2	Year 3	Year 4
$ Sales
$ Variable costs

3. Estimate annual (Year 1 through 4) operating cash flows (40 points)

	Year 1	Year 2	Year 3	Year 4
Sales
OCF

4. Estimate the after tax salvage cash flow (10 points)
5. Estimate the cash flow of this project (10 Points)

	Year 0	Year 1	Year 2	Year 3	Year 4
CF of the project

6. Estimate the NPV, IRR, MIRR, and profitability Index of the project. (20 points)

NPV =
IRR =
MIRR =
PI

Answer 1

Time line		0	1	2	3	4
Cost of new machine		-260000
Initial working capital		-30000
=Initial Investment outlay		-290000
3 years MACR rate			33.33%	44.45%	14.81%	7.41%
Sales			275000	278100	286443	295036.2
-variable cost			135000	139050	143221.5	147518.1
Profits			135000	139050	143221.5	147518.1
			0	0	0	0
-Depreciation	=Cost of machine*MACR%		-86658	-115570	-38506	-19266
=Pretax cash flows			48342	23480	104715.5	128252.1
-taxes	=(Pretax cash flows)*(1-tax)		29005.2	14088	62829.3	76951.29
+Depreciation			86658	115570	38506	19266
=after tax operating cash flow			115663.2	129658	101335.3	96217.29
reversal of working capital						30000
+Proceeds from sale of equipment after tax	=selling price* ( 1 -tax rate)					24000
+Tax shield on salvage book value	=Salvage value * tax rate					0
=Terminal year after tax cash flows						54000
Total Cash flow for the period		-290000	115663.2	129658	101335.3	150217.3
Discount factor=	(1+discount rate)^corresponding period	1	1.1	1.21	1.331	1.4641
Discounted CF=	Cashflow/discount factor	-290000	105148.4	107155.4	76134.71	102600.4
NPV=	Sum of discounted CF=	101038.9

PI= (NPV+initial inv.)/initial inv.

=(101038.88+290000)/290000

1.35

IRR is the rate at which NPV =0	0
IRR	24.80%
Year	0	1	2	3	4
Cash flow stream	-290000.000	115663.200	129658.000	101335.300	150217.300
Discounting factor	1.000	1.248	1.557	1.944	2.426
Discounted cash flows project	-290000.000	92681.078	83251.307	52137.280	61930.336
NPV = Sum of discounted cash flows
NPV Project =	0.000
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Discounting Approach		Discount rate	10.000%
All negative cash flows are discounted back to the present at the required return and added to the initial cost		Year	0	1	2	3	4
Thus year 0 modified cash flow=-290000		Cash flow stream	-290000.000	115663.200	129658.000	101335.300	150217.300
=-290000		Discounting factor (Using discount rate)	1.000	1.100	1.210	1.331	1.464
		Discounted cash flows	-290000.000	105148.364	107155.372	76134.711	102600.437
		Modified cash flow	-290000.000	115663.200	129658.000	101335.300	150217.300
		Discounting factor (using MIRR)	1.000	1.248	1.557	1.944	2.426
		Discounted cash flows	-290000.000	92681.078	83251.307	52137.280	61930.336
		NPV = Sum of discounted cash flows
		NPV =	0.00
		MIRR is the rate at which NPV = 0
		MIRR=	24.80%
		Where
		Discounting factor =	(1 + discount rate)^(Corresponding period in years)
		Discounted Cashflow=	Cash flow stream/discounting factor
Reinvestment Approach		Discount rate	10.000%
All cash flows except the first are compounded to the last time period and IRR is calculated		Year	0	1	2	3	4
Thus year 4 modified cash flow=(153947.72)+(156886.18)+(111468.83)+(150217.3)		Cash flow stream	-290000.000	115663.200	129658.000	101335.300	150217.300
=572520.03		Compound factor (Using discount rate)	1.000	1.331	1.210	1.100	1.000
		Compounded cash flows	-290000.000	153947.72	156886.18	111468.83	150217.3
		Modified cash flow	-290000.000	0	0	0	572520.030
		Discounting factor (using MIRR)	1.000	1.185	1.405	1.665	1.974
		Discounted cash flows	-290000.000	0.000	0.000	0.000	290000.000
		NPV = Sum of discounted cash flows
		NPV =	0.00
		MIRR is the rate at which NPV = 0
		MIRR=	18.54%
		Where
		Compounding factor =	(1 + discount rate)^(time of last CF-Corresponding period in years)
		Discounted Cashflow=	Cash flow stream*discounting factor
Combination approach		Discount rate	10.000%
All negative cash flows are discounted back to the present and all positive cash flows are compounded out		Year	0	1	2	3	4
to the end of the project’s life		Cash flow stream	-290000.000	115663.200	129658.000	101335.300	150217.300
		Compound factor (Using discount rate)	1.000	1.100	1.210	1.331	1.464
		Compound factor (Using discount rate)	1.000	1.331	1.210	1.100	1.000
Thus year 4 modified cash flow=(153947.72)+(156886.18)+(111468.83)+(150217.3)		Discounted cash flows	-290000.000	0	0	0	0
=572520.03		Compounded cash flows	0.000	153947.72	156886.18	111468.83	150217.3
Thus year 0 modified cash flow=-290000		Modified cash flow	-290000.000	0	0	0	572520.030
=-290000		Discounting factor (using MIRR)	1.000	1.185	1.405	1.665	1.974
		Discounted cash flows	-290000.000	0.000	0.000	0.000	290000.000
		NPV = Sum of discounted cash flows
		NPV Discount rate =	0.00
		MIRR is the rate at which NPV = 0	0.00
		MIRR=	18.54%
		Where
		Discounting factor =	(1 + discount rate)^(Corresponding period in years)
		Discounted Cashflow=	Cash flow stream/discounting factor
		Compounding factor =	(1 + discount rate)^(time of last CF-Corresponding period in years)
		Discounted Cashflow=	Cash flow stream*discounting factor