Question

You are considering a project that has been assigned a discount rate of 14.3 percent. If you start the project today, you will incur an initial cost of $11,400 and will receive cash inflows of $6,800 a year for two years. If you wait one year to start the project, the initial cost will rise to $12,100 and the cash flows will increase to $7.200 a year for two years. What is the value of the option to wait?

Answer 1

Answer-

The discount rate = r = 14.3 % = 0.143
The first option

Initial cost = $ 11400
Cash inflows / year = $6800 / year for two years
Therefore

NPV = - $ 11400 + $ 6800 / ( 1 + r) + $ 6800 / ( 1 + r )2
NPV = - $ 11400 + $ 6800 / ( 1 + 0.143) + $ 6800 / ( 1 + 0.143 )2
NPV = - $ 11400 + $ 6800 / ( 1.143) + $ 6800 / ( 1.143 )2
NPV = - $ 11400 + $ 6800 / 1.143 + $ 6800 / 1.306
NPV = - $ 11400 + $ 5949.26 + $ 5206.74
NPV = - $ 11400 + $ 11156
NPV = - $ 244

The second option

Initial cost = $ 12100
Cash inflows / year = $ 7200 / year for two years
Therefore

NPV = - $ 12100 + $ 7200 / ( 1 + r) + $ 7200 / ( 1 + r )2
NPV = - $ 12100 + $ 7200 / ( 1 + 0.143) + $ 7200 / ( 1 + 0.143 )2
NPV = - $ 12100 + $ 7200 / ( 1.143) + $ 7200 / ( 1.143 )2
NPV = - $ 12100 + $ 7200 / 1.143 + $ 7200 / 1.306
NPV = - $ 12100 + $ 6299.21 + $ 5513
NPV = - $ 12100 + $ 11812.21
NPV = - $ 287.79

The value of the option to wait is negative NPV of - $ 287.79 and the first option value is negative NPV of - $ 244.