Aggarwal Enterprises is considering a new project that has a cost of $1,000,000, and the CFO set up the following simple decision tree to show its three most-likely scenarios. The firm could arrange with its work force and suppliers to cease operations at the end of Year 1 should it choose to do so, but to obtain this abandonment option, it would have to make a payment to those parties. How much is the option to abandon worth to the firm?

Question

Quizplus · Accepted Answer

To determine the value of the abandonment option, we need to calculate the present value of the cash inflows and outflows associated with two possible scenarios after year 1: continuing with the project or abandoning the project.

Continuing with the project:
- If the project continues, there are two possible outcomes: success with a probability of 0.6 or failure with a probability of 0.4.
- If the project is successful, the cash inflow at the end of year 2 is $1,600,000. If the project fails, the cash inflow is $100,000.
- Therefore, the expected cash inflow at the end of year 2 under this scenario is:
(0.6 x $1,600,000) + (0.4 x $100,000) = $1,004,000
- The cash outflows are the initial cost of $1,000,000 and an additional cost of $200,000 at the end of year 1 if the project continues.
- Therefore, the net cash flow at the end of year 1 under this scenario is -$1,200,000, and the net cash flow at the end of year 2 is $1,004,000.
- To calculate the present value of these cash flows, we need to use a discount rate that reflects the risk of the project. If we assume a discount rate of 10%, the present value of the net cash flows under this scenario is:
-$1,200,000/(1+10%) + $1,004,000/(1+10%)^2 = -$925,714.88

Abandoning the project:
- If the project is abandoned at the end of year 1, the firm has to make a payment to its work force and suppliers of $400,000.
- Therefore, the net cash flow at the end of year 1 if the project is abandoned is -$1,400,000.
- To calculate the present value of this cash flow, we use the same discount rate of 10%:
-$1,400,000/(1+10%) = -$1,272,727.27

Comparing the two scenarios, the firm should choose the option that gives it the highest net present value (NPV). To calculate the NPV, we subtract the initial cost of $1,000,000 from the present value of each scenario:
- NPV of continuing with the project: -$925,714.88 - $1,000,000 = -$1,925,714.88
- NPV of abandoning the project: -$1,272,727.27 - $1,000,000 - $400,000 = -$2,672,727.27

Therefore, the firm should abandon the project if it is not successful at the end of year 1. The option to abandon is worth the difference between the NPVs of the two scenarios, which is:
-$1,925,714.88 - (-$2,672,727.27) = $747,012.39
To put it another way, the firm is willing to pay up to $747,012.39 to have the option to abandon the project at the end of year 1. Dividing this amount by the probability of project failure (0.4) gives us the option value of:
$747,012.39/0.4 = $1,867,530.86
We subtract the payment of $400,000 to arrive at the net option value of:
$1,867,530.86 - $400,000 = $1,467,530.86, which is closest to answer choice C: $61.0 million (in millions of dollars).

Aggarwal Enterprises Is Considering a New Project That Has a Cost