Question

Blooper’s analysts have come up with the following revised estimates for its magnoosium mine:

	Range
	Pessimistic				Optimistic
Initial investment	+	50	%		–	25	%
Revenues	–	15	%		+	25	%
Variable costs	+	25	%		–	15	%
Fixed cost	+	25	%		–	30	%
Working capital	+	40	%		–	30	%
Solve for below info Project NPV Pessimistic Expected Optimistic Initial investment Revenues Variable costs Fixed costs Working capital

	A. Inputs
	Initial investment ($ thousands)	10,000
	Salvage value ($ thousands)	2,000
	Initial revenues ($ thousands)	15,000
	Variable costs (% of revenues)	40.0%
	Initial fixed costs ($ thousands)	4,000
	Initial total expenses ($ thousands)	10,000
	Inflation rate (%)	5.0%
	Discount rate (%)	12.0%
	Receivables (% of sales)	16.7%
	Inventory (% of next year's costs)	15.0%
	Tax rate (%)	35.0%
	Year:	0	1	2	3	4	5	6
	B. Fixed assets
	Investments in fixed assets	10,000
	Sales of fixed assets							1,300
	Cash flow from fixed assets	-10,000						1,300
	C. Operating cash flow
	Revenues		15,000	15,750	16,538	17,364	18,233
	Variable expenses		6,000	6,300	6,615	6,946	7,293
	Fixed expenses		4,000	4,200	4,410	4,631	4,862
	Depreciation		2,000	2,000	2,000	2,000	2,000
	Pretax profit		3,000	3,250	3,513	3,788	4,078
	Tax		1,050	1,138	1,229	1,326	1,427
	Profit after tax		1,950	2,113	2,283	2,462	2,650
	Operating cash flow		3,950	4,113	4,283	4,462	4,650
	D. Working capital
	Working capital	1,500	4,075	4,279	4,493	4,717	3,039	0
	Change in working capital	1,500	2,575	204	214	225	-1,679	-3,039
	Cash flow from investment in working capital	-1,500	-2,575	-204	-214	-225	1,679	3,039
			0.408	0.408	0.408	0.408	0.250
	E. Project valuation
	Total project cash flow	-11,500	1,375	3,909	4,069	4,238	6,329	4,339

Answer 1

Soln : For pessimistic view:

Year		0	1	2	3	4	5	6
	B. Fixed assets
	Investments in fixed assets	15,000
	Sales of fixed assets							2,000
	Cash flow from fixed assets	-15,000						2,000
	C. Operating cash flow
	Revenues		12,750	13,388	14,057	14,760	15,498
	Variable expenses		7,500	7,875	8,269	8,682	9,116
	Fixed expenses		5,000	5,250	5,513	5,788	6,078
	Depreciation		3,000	3,000	3,000	3,000	3,000
	Pretax profit		-2,750	-2,738	-2,724	-2,711	-2,696
	Tax		0	0	0	0	0
	Profit after tax		-2,750	-2,738	-2,724	-2,711	-2,696
	Operating cash flow		250	263	276	289	304
	D. Working capital
	Working capital	2,100	5,705	5,990	6,290	6,604	4,255	0
	Change in working capital	2,100	3,605	285	300	314	-2,350	-4,255
	Cash flow from investment in working capital	-2,100	-3,605	-285	-300	-314	2,350	4,255
	E. Project valuation
	Total project cash flow	-17,100	-3,355	-23	-24	-25	2,654	6,255
	Discount factor	1	0.8929	0.7972	0.7118	0.6355	0.5674	0.5066
	PV	-17100	-2995.53	-18.13	-17.00	-15.93	1505.68	3168.775
	NPV	-15472.15

For estimated the table is given , we need to calculate the NPV with discounting @12%

Total project cash flow	-11,500	1,375	3,909	4,069	4,238	6,329	4,339
Discount factor	1	0.89	0.80	0.71	0.64	0.57	0.51
PV	-11500	1227.68	3116.23	2896.23	2693.33	3591.24	2198.27
NPV	4222.99

For Optimistic view:

Year		0	1	2	3	4	5	6
	B. Fixed assets
	Investments in fixed assets	7,500
	Sales of fixed assets							1,300
	Cash flow from fixed assets	-7,500						1,300
	C. Operating cash flow
	Revenues		18,750	19,688	20,672	21,705	22,791
	Variable expenses		5,100	5,355	5,623	5,904	6,199
	Fixed expenses		2,800	2,940	3,087	3,241	3,403
	Depreciation		1,500	1,500	1,500	1,500	1,500
	Pretax profit		9,350	9,893	10,462	11,060	11,688
	Tax		3,273	3,462	3,662	3,871	4,091
	Profit after tax		6,078	6,430	6,800	7,189	7,597
	Operating cash flow		7,578	7,930	8,300	8,689	9,097
	D. Working capital
	Working capital	1,050	2,853	2,995	3,145	3,302	2,127	0
	Change in working capital	1,050	1,803	143	150	157	-1,175	-2,127
	Cash flow from investment in working capital	-1,050	-1,803	-143	-150	-157	1,175	2,127
	E. Project valuation
	Total project cash flow	-8,550	5,775	7,788	8,151	8,532	10,272	4,127
	Discount factor	1	0.8929	0.7972	0.7118	0.6355	0.5674	0.5066
	PV	-8550	5156.25	6208.14	5801.45	5422.18	5828.71	2091.02
	NPV	21957.76