Question

A] A company is considering whether to outlay $500,000 for a machine that will generate $150,000 p.a. over the next 5 years. What is the NPV of this project, given an opportunity cost of capital of 10%?

B] Apply the IRR rule to a project that costs $100 million and yields $106 million in one year when the opportunity cost of capital is 7%.

Answer 1

Solution a
			10.00%
	Year	Cash Flow	PV factor = 1/ (1+r)^t	PV
	0	$(500,000)	1.000	$(500,000.00)
	1	$ 150,000	0.909	$ 136,363.64
	2	$ 150,000	0.826	$ 123,966.94
	3	$ 150,000	0.751	$ 112,697.22
	4	$ 150,000	0.683	$ 102,452.02
	5	$ 150,000	0.621	$    93,138.20
			NPV	$    68,618.02

Solution B		5.00%						6.00%
Year	Cash Flow	PV factor = 1/ (1+r)^t	PV					PV factor = 1/ (1+r)^t	PV
0	$                       (100)	1.000	$         (100)					1.000	$ (100.00)
1	$                         106	0.952	$          101					0.943	$ 100.00
		Total PV	$              1					Total	$          -
NPV @ 0.05	0.95
NPV @ 0.06	-
Difference in both	0.95
IRR	=Lower rate + Difference in rates*(NPV at lower rate)/(Lower rate NPV-Higher rate NPV)
	'=5%+ (6%-5%)*(0.9523/(0.9523+0)
IRR	6.000%