Question

A potential new project would cost $1000 today. The 1st stage of the project would last 2 years. There are 2 possible scenarios for Stage 1 net cash flows in years 1 and 2: 1) $1,060 per year, with 50% probability; or 2) $0 per year, with 50% probability. If the 1st stage outcome is good (with non-zero outcomes), the firm will reinvest an equal amount in year 2 (the same amount invested at year 0) and extend the project into Stage 2 (years 3 and 4). The possible Stage 2 outcomes are either: 1) net cash flows in years 3 and 4 doubling relative to the good Stage 1 outcome (with probability of 50%), or 2) net cash flows of 0 in years 3 and 4 (with probability of 50%). If the Stage 1 outcome is bad, the firm will abandon the project at the conclusion of Stage 1.

The cost of capital is 9%. The overall expected NPV of the project (at year 0), considering Stage 1 and the option to expand the project into Stage 2, is $_______.

Answer 1

		IF STAGE ONE OUTCOME IS GOOD
		Stage 2 Cash flow if outcome is good =2*1060	$2,120
		Expected Cash Flow in Year 3 and 4	$1,060	(50%*2120)
		Investment in Year 2	$1,000
		Present Value (PV) of cash flow:
		(Cash Flow)/((1+i)^N)
		i=discount rate =cost of capital =9%=	0.09
		N=Year of cash flow
		Net Present Value of Investment in Year2:
		(1060/(1.09^2)+(1060/1.09)-1000=	$864.66
		Year 2 Cash flow with Probability 50%	$1,924.66	(1060+864.66)
			YEAR 1			YEAR2
			Cash flow	Probability	Cash flow* Probability	Cash flow	Probability	Cash flow* Probability
			$1,060	0.5	$530.00	$1,924.66	0.5	$962.33
			$0	0.5	$0.00	$0	0.5	$0.00
				SUM	$530.00		SUM	$962.33
		Expected Cash Flow in Year 1	$530.00
		Expected Cash Flow in Year2 (Including NPV of Year3 and4)	$962.33
		Investment in Year 0	$1,000
		Net Present Value with expansion Option:
		(962.33/(1.09^2)+(530/1.09)-1000=	$296.21
		OVERALL EXPECTED NPV OF THE PROJECT	$296.21