Question

You are considering a new product launch. The project will cost R1,700,000, have a four-year life, and have no salvage value; depreciation is 20 per cent reducing-balance. Sales are projected at 190 units per year; price per unit will be R18,000, variable cost per unit will be R11,200, and fixed costs will be R410,000 per year. The required return on the project is 12 per cent, and the relevant tax rate is 28 per cent. (a) Based on your experience, you think the unit sales, variable cost and fixed cost projections given here are probably accurate to within ±10 per cent. What are the upper and lower bounds for these projections? What is the base-case NPV? What are the best-case and worst-case scenarios? (b) Evaluate the sensitivity of your base-case NPV to changes in fixed costs. (c) What is the cash break-even level of output for this project (ignoring taxes)? (d) What is the accounting break-even level of output for this project?

Answer 1

Q1. What are the upper and lower bounds for these projections?

Soln :

	Base Case	Upper Bound	Lower Bound
Unit Sales	190	209	171
Price per unit	18000	19800	16200
Variable cost per unit	11200	12320	10080
Fixed Cost per year	410000	451000	369000

Depreciation table

Year	1	2	3	4
Opening Balance	1700000	1360000	1088000	870400
Depreciation @ 20%	340000	272000	217600	174080
Closing Balance	1360000	1088000	870400	696320

Q2.What is the base-case NPV? What are the best-case and worst-case scenarios?

Soln: Remember that we assign high costs and low prices and volume for the worst-case and just the opposite for the best-case scenario

Base Case
Year		1	2	3	4	Total
Unit Sales		190
Unit Price		18000
Unit Variable Cost	11200
Unit Contribution	6800
Total Contribution	1292000	1292000	1292000	1292000
Fixed cost		410000	410000	410000	410000
Depreciation	340000	272000	217600	174080
PBT		542000	610000	664400	707920
Tax @ 28%		151760	170800	186032	198217.6
PAT		390240	439200	478368	509702.4
Depreciation	340000	272000	217600	174080
CashPAT		730240	711200	695968	683782.4
PV Factor @ 12%	0.8929	0.7972	0.7118	0.6355
Present Value	652031.3	566968.64	495390.02	434543.72	2148934
				-	Outflow	1700000
					NPV	448933.7
Best Case
Year		1	2	3	4	Total
Unit Sales		209
Unit Price		19800
Unit Variable Cost	10080
Unit Contribution	9720
Total Contribution	2031480	2031480	2031480	2031480
Fixed cost		369000	369000	369000	369000
Depreciation	340000	272000	217600	174080
PBT		1322480	1390480	1444880	1488400
Tax @ 28%		370294.4	389334.4	404566.4	416752
PAT		952185.6	1001145.6	1040313.6	1071648
Depreciation	340000	272000	217600	174080
CashPAT		1292186	1273145.6	1257913.6	1245728
PV Factor @ 12%	0.8929	0.7972	0.7118	0.6355
Present Value	1153793	1014951.67	895382.9	791660.14	3855787
				-	Outflow	1700000
					NPV	2155787
Worst Case
Year		1	2	3	4	Total
Unit Sales		171
Unit Price		16200
Unit Variable Cost	12320
Unit Contribution	3880
Total Contribution	663480	663480	663480	663480
Fixed cost		451000	451000	451000	451000
Depreciation	340000	272000	217600	174080
PBT		-127520	-59520	-5120	38400
Tax @ 28%		-35705.6	-16665.6	-1433.6	10752
PAT		-91814.4	-42854.4	-3686.4	27648
Depreciation	340000	272000	217600	174080
CashPAT		248185.6	229145.6	213913.6	201728
PV Factor @ 12%	0.8929	0.7972	0.7118	0.6355
Present Value	221604.9	182674.872	152263.7	128198.14	684741.6
				-	Outflow	1700000
					NPV	-1015258

b) Evaluate the sensitivity of your base-case NPV to changes in fixed costs?

(c) What is the cash break-even level of output for this project (ignoring taxes)?

(d) What is the accounting break-even level of output for this project?

Accounting Break Even
Year	1	2	3	4
Fixed Cost	410000	410000	410000	410000
Depreciation	340000	272000	217600	174080
Total	750000	682000	627600	584080
Unit Contribution	6800	6800	6800	6800
Break even	110.29	100.29	92.29	85.89