Question

1 (Chapter 7). You are considering a new project. In the first year, you expect to sell 9000 units at $50 net cash apiece, giving you operating cash flow of $450,000. At the end of the first year, you will know whether the project is doing “well” or doing “poorly.” If it is doing well, you will expect sales of 15,000 units per year for the next 10 years. If it is doing poorly, you will expect sales of 4,000 units per year for the next 10 years. You also have the option to (a) expand after the first year, or (b) dismantle the project after the first year and sell components for $1.3 million. The initial (time 0) investment cost for the project is $1.9 million. The cost of expansion is an additional $2 million, and doubles your sales projections in the event that the project is successful in the first year. (Expansion doesn’t alter sales projections if the project is not successful in the first year.) Assume the price of the product remains constant at $50 regardless of success or failure. All cash flows are real, and the real discount rate is 15%. For simplicity, assume no taxes, so investment costs and operating cash flows (the net revenues of $50 per unit) are all your cash flows. The probability of success is 40%.

a. What is your best strategy when you experience success after one year: Do you expand, continue operations without expansion, or abandon the project?

b. What is your best strategy when the project does poorly in the first year: Do you expand, continue operations without expansion, or abandon the project?

c. In view of your answers to a) and b), construct a decision tree for this project and evaluate its NPV. Should you invest at time 0?

Answer 1

(a) When we experience success after first year,

If we expand , Present value of cost of expansion (outflow) = 2000000/1.15 = 1739130

Present value of sales (inflow) = 15000*2*50/(1.15^2) + 15000*2*50/(1.15^3) + - - - - -- - + 15000*2*50/(1.15^11) = 6546220

NPV during expansion = 6546220 - 1739130 = 4807090

When we abandon the project then NPV = 1300000/1.15 = 1130434

As the NPV of expansion is much greater than NPV of abandon, we consider expanding the project.

(b)

(a) When the project does poorly in first year,

If we expand , Present value of cost of expansion (outflow) = 2000000/1.15 = 1739130

Present value of sales (inflow) = 4000*2*50/(1.15^2) + 4000*2*50/(1.15^3) + - - - - -- - + 4000*2*50/(1.15^11) = 1745659

NPV during expansion = 1745659 - 1739130 = 6528

When we abandon the project then NPV = 1300000/1.15 = 1130434 = 4807090

As the NPV of expansion is much lesser than NPV of abandon, we consider abandoning the project.

(c)

Years	0	1			2	3-11
				Expand	(15000*2*50-2000000)/(1.15^2)*(0.4) = -151229	=((15000*2*50)(1/(1.15^3)+1/(1.15^4)+ - - - - + 1/(1.15^11))*0.4 = 2164802
			Success (0.4)
				Abandon	1300000/(1.15)*0.4 = 452174
Alternative	-1900000	9000*50/1.15=391304
				Expand	(4000*2*50-2000000)/(1.15^2)*(0.6) = -725897	=((15000*2*50)(1/(1.15^3)+1/(1.15^4)+ - - - - + 1/(1.15^11))*0.6=865921
			Poor (0.6)
				Abandon	1300000/(1.15)*0.6 = 678261