Question

Yoder Technologies is considering expanding its production capacity by purchasing a new machine, the TB-2000. The cost of the TB-2000 is $3 million. Unfortunately, installing this machine will take several months and will partially disrupt production. The firm has just completed a $50,000 feasibility study to analyze the decision to buy the TB-2000, resulting in the following estimates: • Marketing: Once the TB-2000 is operating next year, the extra capacity is expected to allow for $12 million per year in additional sales, which will continue for the 10-year life of the machine. Operations: The disruption caused by the installation will decrease sales by $4 million this year. The cost of goods for the products produced by the TB-2000 is expected to be 75% of their sale price, the same as with existing equipment. The increased production will require additional inventory on hand of $2 million to be added in year 0 and depleted in year 10. Human Resources: The expansion will require additional sales and administrative personnel at a cost of $1.5 million per year. Accounting: The TB-2000 will be depreciated via the straight-line method over the 10-year life of the machine. The firm expects receivables from the sales to be 10 percent of revenues and payables to be 15 percent of the cost of goods sold. Billingham's marginal corporate tax rate is 40 percent. For simplicity, assume that any changes in payables and receivables begin in year 1 and are closed out at the end of year 10. If the appropriate cost of capital for the expansion is 15 percent, calculate the incremental free cash flows associated with installing the TB-2000 and compute the NPV and IRR of the project. Should Yoder Technologies purchase this new machine?

Answer 1

Solution:

A) Computation of Net Present Value ( NPV)

Step 1: Computation of Cash Outflow at Year 0, i.e now

Particulars	Amount ( In $ ' million)
a) Initial Cash outlay	3
b) Add: Increased Inventory	2
c) Less: reversion/ depletion of Inventory at the end ( 2* PVF10 years, 15%) ( 2* 0.2471)	0.4942
d) Net Cash Outflow ( a+b-c)	4.5058

Note: Feasibility Study Expenses of $ 50,000 shall be ignored in Capital budgeting Decision , as these are sunk cost.

Calculation of Changes in Working Capital and Cash flows

	Years
Particulars	0	1	2	3	4	5	6	7	8	9	10
(Decrease)/ Increase in Sales	(4)	12	12	12	12	12	12	12	12	12	12
a)Collection in period of Sales ( 90% of Sales)	-	10.8	10.8	10.8	10.8	10.8	10.8	10.8	10.8	10.8	12 (Note)
b)Collection in period after Sales ( 10% of Sales)		-	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2
c) Total Collection	(4)	10.8	12	12	12	12	12	12	12	12	13.2
d) Cost of Goods Sold ( 75% of Sale )	(3)*	9	9	9	9	9	9	9	9	9	9
e) Cost of Goods Sold made in the current period (85% of COGS)		7.65	7.65	7.65	7.65	7.65	7.65	7.65	7.65	7.65	9 ( Note)
f) Cost of Goods Sold to be made in the next period (15% of COGS)	-	-	1.35	1.35	1.35	1.35	1.35	1.35	1.35	1.35	1.35
g) Total Payments	(3)	7.65	9	9	9	9	9	9	9	9	10.35
h) Changes in Working ( b-f) Capital ( Increase in Working Capital )			0.15	0.15	0.15	0.15	0.15	0.15	0.15	0.15	0.15
Net Cash Flows (c-g)	(1)	3.15	3	3	3	3	3	3	3	3	2.85

Discounted Free Cash Flows

	Years and Amount in $ Million
Particulars	0	1	2	3	4	5	6	7	8	9	10
Net Cash Flows	(1)	3.15	3	3	3	3	3	3	3	3	2.85
Less: Administrative Expenses	-	1.5	1.5	1.5	1.5	1.5	1.5	1.5	1.5	1.5	1.5
Less: Increased Working Capital			0.15	0.15	0.15	0.15	0.15	0.15	0.15	0.15	0.15
Less: Depreciation ( Note 2)		0.3	0.3	0.3	0.3	0.3	0.3	0.3	0.3	0.3	0.3
Earning Before Income Taxes	(1)	1.2	1.05	1.05	1.05	1.05	1.05	1.05	1.05	1.05	0.90
Less: Income Taxes @ 40%		0.48	0.42	0.42	0.42	0.42	0.42	0.42	0.42	0.42	0.36
Earning After Taxes	(1)	0.72	0.63	0.63	0.63	0.63	0.63	0.63	0.63	0.63	0.54
Add: Depreciation		0.3	0.3	0.3	0.3	0.3	0.3	0.3	0.3	0.3	0.3
Free Cash Flows	(1)	1.02	0.93	0.93	0.93	0.93	0.93	0.93	0.93	0.93	0.84
Discounting Factor @ 15%	1	0.8695	0.7561	0.6575	0.5717	0.4971	0.4323	0.3759	0.3269	0.2842	0.2471
Discounted Free Cash Flows	(1)	0.8869	0.7031	0.6115	0.5317	0.4623	0.4020	0.3496	0.3040	0.2643	0.2075

Aggregate Discounted Cash In Flows = $ 3.7229 million

Net Present Value = Aggregate Discounted Cash In Flows - Cash Outflows = $ 3.73 million - $ 4.51 million = $- 0.78 million .

The Project should not be accepted.

* Cash Savings

Notes

1. There would not be any receivable/payable for the Year 10, as it closes out.
2. Depreciation= $3 million / 10 = $0.3 million

B) IRR of the project.

Here, Net Cash Inflow = Net Cash outflows .

Net cash Outflow = $ 4.51 million

Net Cash Inflow = $ 3.73 million

$ 4.51= 3.73 / (1+r)¹⁰

$\equiv$ 4.51 /3.73 = 1/ (1+r ) ¹⁰

$\equiv$ 1.2091 = 1 / (1+r) ¹⁰

Using the Excel Sheet , with the formula of =+IRR(values, [guess]) , we get IRR of 10 years is 110.73 %, where it will be indifferent point.

IRR = 110.73 % or 111%,

Please refer the excel sheet for details.

New Microso Office Excel WorseetM Home Insert Pge Layout Formulas Data Review View Calibri १। Wrap Text Percentage Cops te Fomat Painter Merge & Center % 4 Conditional Format Ce Formatting as Table Styles Styles nsert Delete Cleboard Font Alignment Number Cells B16 &IRR(B4:B14,0.1) 10 D E F G K N L M Cash Years -5.51 4 0 1 1.02 6 2 0.93 7 3 0.93 8 0.93 0.93 10 6 0.93 11 7 0.93 12 8 0.93 13 9 0.93 14 10 0.84 15 111% 16 17 18 19 20 21 22 23 24 Sheet7 Sheet8 Sheet9 Sheet5 Sheet6 Sheet1 Sheet2 Sheet4 Sheet3 Ready

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