Question

We are examining a new project. We expect to sell 6,600 units per year at $60 net cash flow apiece for the next 10 years. In other words, the annual operating cash flow is projected to be $60 × 6,600 = $396,000. The relevant discount rate is 14 percent, and the initial investment required is $1,770,000. After the first year, the project can be dismantled and sold for $1,640,000. Suppose you think it is likely that expected sales will be revised upward to 9,600 units if the first year is a success and revised downward to 5,200 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 19,200. 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? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) NPV $ What is the value of the option to expand?

Answer 1

Formula sheet

A	B	C	D	E	F	G	H	I	J	K	L	M	N	O
2
3
4		Initial investment	1770000
5		Cash Flow per unit	60
6		Normal units per Year	6600
7		Number of units in case of success	9600
8		Number of units in case of failure	5200
9		Units per year after expansion	=D7*2
10
11		Condition	Prob.	t=0	t=1	t=2-10
12		Success	0.5	=-D4	=D6*D5	=D7*D5
13		Failure	0.5	=-D4	=D6*D5	=D8*D5
14		WACC	0.14
15		Salvage Value (year1)	1640000
16		Calculation of NPV
17		Without any abondonment option
18
19		Year0				1	2	3	…	10	NPV	Probability	Probability*NPV
20						=F12	=$G$12	=$G$12	=$G$12	=$G$12	=$C$21+G20*(1/((1+$D$14)^$G$19))+H20*PV($D$14,9,-1,0)*(1/((1+$D$14)^$G$19))	0.5	=L20*M20	=L20*M20
21		=-D4	Tax will not pass	0.5
22			Tax will pass	0.5
23						=F12	=$G$13	=$G$13	=$G$13	=$G$13	=$C$21+G23*(1/((1+$D$14)^$G$19))+H23*PV($D$14,9,-1,0)*(1/((1+$D$14)^$G$19))	0.5	=M23*L23	=M23*L23
24
25												Expected NPV	=N23+N20	=N23+N20
26
27
28		With abondonment option
29
30		Year0				1	2	3	…	10	NPV	Probability	Probability*NPV
31						=G20	=H20	=I20	=J20	=K20	=$C$21+G31*(1/((1+$D$14)^$G$19))+H31*PV($D$14,9,-1,0)*(1/((1+$D$14)^$G$19))	0.5	=L31*M31	=L31*M31
32		=-D4	Tax will not pass	0.5
33			Tax will pass	0.5
34						=G23+D15					=$C$21+G34*(1/((1+$D$14)^G30))	0.5	=M34*L34	=M34*L34
35
36												Expected NPV	=N34+N31	=N34+N31
37
38
39		With Expansion and abondonment option
40
41		Year0				1	2	3	…	10	NPV	Probability	Probability*NPV
42						=G20	=$D$9*$D$5	=$D$9*$D$5	=$D$9*$D$5	=$D$9*$D$5	=$C$21+G42*(1/((1+$D$14)^$G$19))+H42*PV($D$14,9,-1,0)*(1/((1+$D$14)^$G$19))	0.5	=L42*M42	=L42*M42
43		=-D15	Tax will not pass	0.5
44			Tax will pass	0.5
45						=F13+D15					=$C$21+G45*(1/((1+$D$14)^G41))	0.5	=M45*L45	=M45*L45
46
47												Expected NPV	=N45+N42	=N45+N42
48
49
50
51		Hence
52		Expected NPV of the project is	=N25
53
54		Expected NPV of the project with abandonment	=N36
55		Expected NPV of the project with expansion and abandonment	=N47
56
57		Value of option to exapand	=D55-D54	=D55-D54
58