Question

Please use excel: (Comprehensive problem) The Shome Corporation, a firm in the 34 percent marginal tax bracket with a 15 percent required rate of return or cost of capital, is considering a new project. The project involves the introduction of a new product. This project is expected to last 5 years and then, because this is somewhat of a fad ­product, be terminated. Given the following information, determine the free cash flows associated with the project, the project’s net present value, the profitability index, and the internal rate of return. Apply the appropriate decision criteria.

Cost of new plant and equipment	$6,900,000
Shipping and installation costs	$  100,000
Unit sales	YEAR	UNITS SOLD
	1	80,000
	2	100,000
	3	120,000
	4	70,000
	5	70,000
Sales price per unit	$250/unit in years 1 through 4, $200/unit in year 5
Variable cost per unit	$130/unit
Annual fixed costs	$300,000 per year in years 1–5
Working-capital requirements	There will be an initial working-capital requirement of $100,000 just to get production started. For each year, the total investment in net working capital will be equal to 10 percent of the dollar value of sales for that year. Thus, the investment in working capital will increase during years 1 through 3, then decrease in year 4. Finally, all working capital is liquidated at the termination of the project at the end of year 5.
Depreciation method	Use the simplified straight-line method over 5 years. Assume that the plant and equipment will have no salvage value after 5 years

Answer 1

Solution:

Computation of the free cash flow can be made as follows using the MS-Excel.

Calculation of the free cash flow
Years	1	2	3	4	5
Sales (units)	80000	100000	120000	70000	70000
Sales value	=B3*250	=C3*250	=D3*250	=E3*250	=F3*200
Less: Variable cost	=B3*130	=C3*130	=D3*130	=E3*130	=F3*130
Contribution	=B4-B5	=C4-C5	=D4-D5	=E4-E5	=F4-F5
Less: Fixed cost	300000	300000	300000	300000	300000
EBIDTA	=B6-B7	=C6-C7	=D6-D7	=E6-E7	=F6-F7
Less: Depreciation	1400000	1400000	1400000	1400000	1400000
EBT	=B8-B9	=C8-C9	=D8-D9	=E8-E9	=F8-F9
Less: Taxes @ 34%	=B10*34%	=C10*34%	=D10*34%	=E10*34%	=F10*34%
EAT	=B10-B11	=C10-C11	=D10-D11	=E10-E11	=F10-F11
Add: Depreciation	1400000	1400000	1400000	1400000	1400000
Less: Increase in working capital	1900000	500000	500000	0	0
Add: Decrease in working capital	0	0	0	1250000	0
Free cash flows	=B12+B13-B14+B15	=C12+C13-C14+C15	=D12+D13-D14+D15	=E12+E13-E14+E15	=F12+F13-F14+F15

The result of the above table is as follows:

Calculation of the free cash flow
Years	1	2	3	4	5
Sales (units)	80000	100000	120000	70000	70000
Sales value	20000000	25000000	30000000	17500000	14000000
Less: Variable cost	10400000	13000000	15600000	9100000	9100000
Contribution	9600000	12000000	14400000	8400000	4900000
Less: Fixed cost	300000	300000	300000	300000	300000
EBIDTA	9300000	11700000	14100000	8100000	4600000
Less: Depreciation	1400000	1400000	1400000	1400000	1400000
EBT	7900000	10300000	12700000	6700000	3200000
Less: Taxes @ 34%	2686000	3502000	4318000	2278000	1088000
EAT	5214000	6798000	8382000	4422000	2112000
Add: Depreciation	1400000	1400000	1400000	1400000	1400000
Less: Increase in working capital	1900000	500000	500000	0	0
Add: Decrease in working capital	0	0	0	1250000	0
Free cash flows	4714000	7698000	9282000	7072000	3512000

The calculation of the increase or decrease in the working capital is as follows using MS-Excel.

Calculation of the working capital requirement
Years	0	1	2	3	4
Working capital	100000	2000000	2500000	3000000	1750000
Increase / (Decrease)	0	1900000	500000	500000	-1250000

The computation of the NPV and IRR is as follows using the MS-Excel.

Calculation of the net present value and IRR
Years	Cash flow	PVF @ 15%	PV
0	=-6900000-100000-100000	1	=J9*K9
1	4714000	0.87	=J10*K10
2	7698000	0.756	=J11*K11
3	9282000	0.658	=J12*K12
4	7072000	0.572	=J13*K13
5	=3512000+9350000	0.497	=J14*K14
NPV	=SUM(L9:L14)
IRR	=IRR(J9:J14,1)

The result of the above table is as follows:

Calculation of the net present value and IRR
Years	Cash flow	PVF @ 15%	PV
0	-7100000	1	-7100000
1	4714000	0.87	4101180
2	7698000	0.756	5819688
3	9282000	0.658	6107556
4	7072000	0.572	4045184
5	12862000	0.497	6392414
NPV	19366022
IRR	89%

The formula to calculate the amount of depreciation is as follows:

Depreciation = (Total amount involved – salvage value) / Number of years

                      = (($6,900,000 + $100,000) – 0) / 5

                      = $1,400,000

Hence, the amount of depreciation is $1,400,000 per annum.

The formula to calculate the profitability index (PI) is as follows:

PI = Present value of the cash inflow / Initial investments

    = $26,466,022 / $7,100,000

     = 3.73

Hence, the PI is 3.73.

Calculation of the total amount of the cash outflow at the year 0 is as follows:

Cash outflow in year 0 = Cost of plant and equipment + installation cost + working capital

                                    = $6,900,000 + $100,000 + $100,000

                                    = $7,100,000

Hence, the cash outflow in the year 0 is $7,100,000.

The most preferred method of taking the decision in this case is on the basis of the NPV. This is because as the NPV provides the answer in absolute amount and it also considers the factor of time value of money.

As the NPV in the above project is positive, therefore, it is advisable to opt for the project.