Question

Herman 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 $20,000 per year, and the worst-case cash flows are projected to be –$1,000 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 cash flows and a 25% probability of the project generating the worst-case cash flows.

1. What would be the expected net present value (NPV) of this project if the project’s cost of capital is 14%?

1. $16,323

2. $19,588

3. $18,771

4. $17,955

Herman now wants to take into account its ability to abandon the project at the end of year 2 if the project ends up generating the worst-case scenario cash flows. If it decides to abandon the project at the end of year 2, the company will receive a one-time net cash inflow of $3,000 (at the end of year 2). The $3,000 the company receives at the end of year 2 is the difference between the cash the company receives from selling off the project’s assets and the company’s –$1,000 cash outflow from operations. Additionally, if it abandons the project, the company will have no cash flows in years 3 and 4 of the project.

2. Using the information in the preceding problem, find the expected NPV of this project when taking the abandonment option into account.

1. $17,409

2. $22,632

3. $21,761

4. $20,891

3. What is the value of the option to abandon the project?

1. $1,086

2. $923

3. $977

4. $760

5. $1,140

Answer 1

a) Calculation of NPV

Year	Base case	Best case	Worst case	Probability	Probability × Cashflow	Discount rate 14%	Present Value
0	($15,000)	($15,000)	($15,000)	Base Case	Best Case	worst Case	Base case	Best case	worst case
1	$12,000	$20,000	($1,000)	0.50	0.25	0.25	$6,000	$5,000	($250)	$10,750	$10,750/(1+14%)^1	=$9,430
2	$12,000	$20,000	($1,000)	0.50	0.25	0.25	$6,000	$5,000	($250)	$10,750	$10,750/(1+14%)^2	=$8,272
3	$12,000	$20,000	($1,000)	0.50	0.25	0.25	$6,000	$5,000	($250)	$10,750	$10,750/(1+14)^3	=$7256
4	$12,000	$20,000	($1,000)	0.50	0.25	0.25	$6,000	$5,000	($250)	$10,750	$10,750/(1+14%)^4	=$6,365
											Present Value Cashflow	$31,323
											Investment	($15,000)
											NPV	$16,323

1) NPV of Project is $16,323.

b) Calculation of NPV after Abandon

Year	Base case	Best Case	Worst Case	Probability	× Case Cashflow	Base Case	Best Case	Worst Case	Total Cashflow	Discount rate 14	Present value Cashflow
0	($15,000)	($15,000)	($15,000)	base Case	Best Case	Worst case		($15,000)
1	$12,000	$20,000	($1,000)	0.50	0.25	0.25	$6,000	$5,000	(250)	$10,750	$10,750/(1+14%)^1	=$9,430
2	$12,000	$20,000	$3,000	0.50	0.25	0.25	$6,000	$5,000	$750	$11,750	$11,750/(1+14%)^2	=$9,041
3	$12,000	$20,000	0	0.50	0.25	0.25	$6,000	$5,000	0	11,000	$11,000/(1+14%)^3	=$7,425
4	$12,000	$20,000	0	0.50	0.25	0.25	$6,000	$5,000	0	11,000	$11,000/(1+14%)^4	=$6513
											Present Value Cashflow	=$ 32,409
											Investment	(15,000)
											NPV	$17,409

2.NPV after Abandon is $17,409

3. Value of option Abandon the Project = NPV with abandon - NPV without abandon projects

= $17,409 - $16,323 =$ 1,086.