Question

8. Abandonment options Acme Co. is considering a four-year project that will require an initial investment of $15,000. The base-case cash flows for this project are projected to be $12,000 per year. The best-case cash flows are projected to be $19,000 per year, and the worst-case cash flows are projected to be -$3,000 per year. The company's analysts have estimated that there is a 50% probability that the project will generate the base-case cash flows. The analysts also think that there is a 25% probability of the project generating the best-case cask flows and a 25% probability of the project generating the worst-case cash flows. What would be the expected net present value (NPV) of this project if the project's cost of capital is 13%? $14,745 O $14,008 $16,220 $16,957

Answer 1

1. NPV of the project will be sum of the product of the NPV and probability of the occurence of each scenario.

NPV for base case scenario = $20,694

NPV for best case scenario = $41,515

NPV for worst case scenario = $-23,923

FINAL NPV = $14,745

Cost of capital	13%
Probability	50%
BASE CASE SCENARIO	0	1	2	3	4
Initial Investment	-15000	12000	12000	12000	12000
NPV	20693.65591	10619.47	9397.76	8316.602	7359.825
Probability	25%
BEST CASE SCENARIO	0	1	2	3	4
Initial Investment	-15000	19000	19000	19000	19000
NPV	41514.95519	16814.16	14879.79	13167.95	11653.06
Probability	25%
WORST CASE SCENARIO	0	1	2	3	4
Initial Investment	-15000	-3000	-3000	-3000	-3000
NPV	-23923.41398	-2654.87	-2349.44	-2079.15	-1839.96
FINAL NPV	14744.71326

WITH FORMULAS:

Cost of capital	0.13
Probability	0.5
BASE CASE SCENARIO	0	1	2	3	4
Initial Investment	-15000	12000	12000	12000	12000
NPV	=SUM(C4,D5:G5)	=D4/(1+$C$1)^D3	=E4/(1+$C$1)^E3	=F4/(1+$C$1)^F3	=G4/(1+$C$1)^G3
Probability	0.25
BEST CASE SCENARIO	0	1	2	3	4
Initial Investment	-15000	19000	19000	19000	19000
NPV	=SUM(C9,D10:G10)	=D9/(1+$C$1)^D8	=E9/(1+$C$1)^E8	=F9/(1+$C$1)^F8	=G9/(1+$C$1)^G8
Probability	0.25
WORST CASE SCENARIO	0	1	2	3	4
Initial Investment	-15000	-3000	-3000	-3000	-3000
NPV	=SUM(C14,D15:G15)	=D14/(1+$C$1)^D13	=E14/(1+$C$1)^E13	=F14/(1+$C$1)^F13	=G14/(1+$C$1)^G13
FINAL NPV	=C2*C5+C7*C10+C12*C15

2. Taking abandonment into consideration: FINAL NPV = $17,242

EXCEL WORKINGS:

Cost of capital	13%
Probability	50%
BASE CASE SCENARIO	0	1	2	3	4
Initial Investment	-15000	12000	12000	12000	12000
NPV	20693.65591	10619.47	9397.76	8316.602	7359.825
Probability	25%
BEST CASE SCENARIO	0	1	2	3	4
Initial Investment	-15000	19000	19000	19000	19000
NPV	41514.95519	16814.16	14879.79	13167.95	11653.06
Probability	25%
WORST CASE SCENARIO	0	1	2	3	4
Initial Investment	-15000	-3000	4750	0	0
NPV	-13934.92051	-2654.87	3719.947	0	0
FINAL NPV	17241.83662

SHOWING FORMULAS:

Cost of capital	0.13
Probability	0.5
BASE CASE SCENARIO	0	1	2	3	4
Initial Investment	-15000	12000	12000	12000	12000
NPV	=SUM(C4,D5:G5)	=D4/(1+$C$1)^D3	=E4/(1+$C$1)^E3	=F4/(1+$C$1)^F3	=G4/(1+$C$1)^G3
Probability	0.25
BEST CASE SCENARIO	0	1	2	3	4
Initial Investment	-15000	19000	19000	19000	19000
NPV	=SUM(C9,D10:G10)	=D9/(1+$C$1)^D8	=E9/(1+$C$1)^E8	=F9/(1+$C$1)^F8	=G9/(1+$C$1)^G8
Probability	0.25
WORST CASE SCENARIO	0	1	2	3	4
Initial Investment	-15000	-3000	4750	0	0
NPV	=SUM(C14,D15:G15)	=D14/(1+$C$1)^D13	=E14/(1+$C$1)^E13	=F14/(1+$C$1)^F13	=G14/(1+$C$1)^G13
FINAL NPV	=C2*C5+C7*C10+C12*C15

VALUE OF THE OPTION TO ABANDON THE PROJECT = 17242-14745 = $2,497