Question

8. Abandonment options Aa Aa Shan 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. What would be the expected net present value (NPV) of this project if the project's cost of capital is 12%? O $21,182 O $18,535 O $15,887 O $17,652

Answer 1

Calculating Expected NPV

Initial investment in project = 15000, Cost of capital = 12%

Cash flow in base case for year 1 to 4 = 12000

NPV in base case cash flows = - Initial investment + Sum of present values of base cash cash flows discounted at cost of capital of 12%

= -15000 + 12000 / ( 1 + 12%) + 12000 / ( 1 + 12%)² + 12000 / (1 + 12%)³ + 12000 / (1 + 12%)⁴

= -15000 + 10714.2857 + 9566.3265 + 8541.3629 + 7626.2169 = 21448.1920

Cash flow in best case for year 1 to 4 = 20000

NPV in best case cash flows = - Initial investment + Sum of present values of best cash cash flows discounted at cost of capital of 12%

= -15000 + 20000 / ( 1 + 12%) + 20000/ ( 1 + 12%)² + 20000 / (1 + 12%)³ + 20000 / (1 + 12%)⁴

= -15000 + 17857.1428 + 15943.8775 + 14235.6049 + 12710.3615 = 45746.9867

Cash flow in worst case for year 1 to 4 = -1000

NPV in worst case cash flows = - Initial investment + Sum of present values of worst cash cash flows discounted at cost of capital of 12%

= -15000 - 1000 / ( 1 + 12%) - 1000 / ( 1 + 12%)² - 1000 / (1 + 12%)³ - 1000 / (1 + 12%)⁴

= -15000 - 892.8571 - 797.1933 - 711.7802 - 635.5180 = -18037.3491

Expected NPV = Probability of base cash flows x NPV in base case cash flows + Probability of best case cash flows x NPV in best case cash flows + Probability of worst case cash flow x NPV in worst case cash flows

= 50% x 21448.1920 + 25% x 45746.9867 + 25% x -18037.3491

= 10724.0960 + 11436.7466 - 4509.3372 = 17651.5054 = 17652 (rounded to nearest dollar)

Answer : $17652

Calculating expected NPV when taking abandonment option into account

Since the project is abandoned in year 2 when it generates worst case cash flows,

Cash flow in year 1 of worst case cash flows = -1000

Cash flow in year 2 of worst case cash flows = 4750

Cash flow in year 3 of worst case cash flows = Cash flow in year 4 of worst case cash flows = 0

NPV in case worst cash flows when abandonment option is taken in account = -Intial investment + Sum of present values of cash flows for year 1 to 4 discounted at cost of capital of 12%

= -15000 - 1000 / ( 1 + 12%) + 4750 / ( 1 + 12%)² - 0 / (1 + 12%)³ - 0 / (1 + 12%)⁴

= -15000 - 892.8571 + 3786.6709 + 0 + 0 = -12106.1862

In case of base case and best case cash flows there will not be any abandonment of project, hence

NPV in base case cash flows = 21448.1920 ( as calculated above)

NPV in best case cash flows = 45746.9867 ( as calculated above)

Expected NPV when taking abandonment option into account = Probability of base cash flows x NPV in base case cash flows + Probability of best case cash flows x NPV in best case cash flows + Probability of worst case cash flow x NPV in case worst cash flows when abandonment option is taken in account

= 50% x 21448.1920 + 25% x 45746.9867 x 25% x -12106.1862

= 10724.0960 + 11436.7466 - 3026.5465 = 19134.29 = 19134 (rounded to nearest dollar)

Answer:$19134

Calculating value of option to abandon the project

Value of option to abandon the project = Expected NPV when taking abandonment option in account - Expected NPV without abandonment option = 19134 - 17652 = 1482

Hence value of option to abandon the project = $1482