Question

We are examining a new project. We expect to sell 5,600 units per year at $70 net cash flow apiece for the next 10 years. In other words, the annual operating cash flow is projected to be $70 × 5,600 = $392,000. The relevant discount rate is 18 percent, and the initial investment required is $1,550,000. After the first year, the project can be dismantled and sold for $1,270,000. Suppose you think it is likely that expected sales will be revised upward to 8,600 units if the first year is a success and revised downward to 4,200 units if the first year is not a success. Suppose the scale of the project can be doubled in one year in the sense that twice as many units can be produced and sold. Naturally, expansion would be desirable only if the project were a success. This implies that if the project is a success, projected sales after expansion will be 17,200. Note that abandonment is an option if the project is a failure. If success and failure are equally likely, what is the NPV of the project? What is the value of the option to expand?

Answer 1

		Present Value (PV) of Cash Flow:
		(Cash Flow)/((1+i)^N)
		i=Discount Rate=18%=0.18
		N=Year of Cash Flow
		SCENARIO 1: SUCCESS
		Probability	0.5
		Expected Cash Flow without expansion
		Cash flow per annum=8600*70	$602,000
	N	Year	0	1	2	3	4	5	6	7	8	9	10
	B	Cash Flow	-$1,550,000	$602,000	$602,000	$602,000	$602,000	$602,000	$602,000	$602,000	$602,000	$602,000	$602,000	SUM
	C=B/(1.18^N)	Present Value of cash flow	-$1,550,000	$510,169	$432,347	$366,396	$310,505	$263,140	$223,000	$188,983	$160,155	$135,725	$115,021	$1,155,440
		NPV with 50% Probability	$1,155,440
		Expected Cash Flow with expansion
		Cash flow per annum=2*8600*70	$1,204,000
	N	Year	0	1	2	3	4	5	6	7	8	9	10
	B	Cash Flow	-$1,550,000	$1,204,000	$1,204,000	$1,204,000	$1,204,000	$1,204,000	$1,204,000	$1,204,000	$1,204,000	$1,204,000	$1,204,000
	X	Additional investment in year1		-$1,550,000
	C=B+X	Net Cash flow	-$1,550,000	-$346,000	$1,204,000	$1,204,000	$1,204,000	$1,204,000	$1,204,000	$1,204,000	$1,204,000	$1,204,000	$1,204,000	SUM
	D=C/(1.18^N)	Present Value of cash flow	-$1,550,000	-$293,220	$864,694	$732,792	$621,010	$526,279	$446,000	$377,966	$320,310	$271,449	$230,042	$2,547,321
		NPV with 50% Probability	$2,547,321