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A project requires an investment of $330 million and has expected annual cash flows of $27...

A project requires an investment of $330 million and has expected annual cash flows of $27 million in perpetuity, starting in one year. In fact, future cash flows will be either $78 million or $16 million, in perpetuity. The company can end the project in 1 year after collecting the first cash flow and thus finding out the amount of future cash flows, and then sell all project assets for $330 million (after taxes). The appropriate discount rate for the project is 14% and the risk-free rate is 5%.

a. What is the NPV of the project ignoring the option to abandon (in $ million)?

b. What is the value of the project after one year in the down state without abandonment (in $ million)?

c. What is the down factor (d) in the binomial option valuation model? Hint: It should be a number between 0 and 1. What is the risk-neutral probability of the up movement?

d. What is the option exercise value in year 1 in the down state if the company abandons the project after 1 year (in $ million)?

e. What is the value of the option to abandon (in $ million)?

f. What should the company do? A. Start the project, then abandon it after one year B. Never start the project C. Start the project and never abandon it D. Start the project, then decide about abandonment in one year E. Cannot say, need more information

Solutions

Expert Solution

a) NPV without option to abandon (million $) = -330+27/0.14= -137.14

So,NPV without option to abandon is -$137.14 million

b) Value of the project after one year in down state (without abandonment)

= 16+16/0.14

= $130.29 million

c) Down factor d = 130.29/330 = 0.3948

Up factor u = (Value of project in upside after one year)/ Value or cost today

= (78+78/0.14) / 330

=1.9247

Risk - neutral probability of up-movement (p)= (1.05-0.3948)/(1.9247-0.3948) = 0.4283

d)

Value of project after one year in down state in case of abandonment = $346 million  

option exercise value in year 1 in the down state if the company abandons the project after 1 year (in $ million)

=$346 million - $130.29 million

= $215.71 million

e) Value of option to abandon

= (p* value of abandonment in upstate + (1-p)*value of abandonment in downstate) / 1.05

= (0.4283*0+0.5717*215.71)/1.05

=$117.46 million

jeff jeffy answered 1 year ago
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