Question

We are examining a new project. We expect to sell 6,700 units per year at $61 net cash flow apiece for the next 10 years. In other words, the annual operating cash flow is projected to be $61 × 6,700 = $408,700. The relevant discount rate is 15 percent, and the initial investment required is $1,780,000. After the first year, the project can be dismantled and sold for $1,650,000. Suppose you think it is likely that expected sales will be revised upward to 9,700 units if the first year is a success and revised downward to 5,300 units if the first year is not a success. Suppose the scale of the project can be doubled in one year in the sense that twice as many units can be produced and sold. Naturally, expansion would be desirable only if the project were a success. This implies that if the project is a success, projected sales after expansion will be 19,400. Note that abandonment is an option if the project is a failure.

  

a.	If success and failure are equally likely, what is the NPV of the project? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.	What is the value of the option to expand? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:-

As Per Given Data
Selling Data	61
Sales Units	6700
Initial Investment	1780000
Annual Cash Flow	408700
Discount Rate	15%
After One year selling Price	1650000
Revised units for success	9700
Revised units for failure	5300
Life of project in years	9
(1) Calculate the NPV for the project if the success and failure are equally
Calculate the Present Value of cash flows for revised units for success i.e., 9700 units as follows
Present Value = Units * Price per unit * PVIFA1(15% * 10years)
= 9700*61*4.7716 = 2823355.72
The abandonment Value is $1,650,000 which is higher than the present value of cash flows of failures. So calculating the present value for success and failures with equal opportunity as follows;
Present Value = 28233355.72+1650000/2 = 2236677.86
Calculate the NPV for the project if success and failure are equally as follows:
NPV = Present Value of future cash flows - Initial cost
= (408700+2236677.86/1.15) - 1780000 = 520328.57
The NPV of the project is 520328.57
(2) Calculate the Value of the option to abandon:
Calculate the present value of cash flows for revised units for failure i.e., 5300 units as follows:
Present Value = Units * Price per unit * PVIFA1(15% * 10years)
= 5300 * 61*4.7716 = 1542658.28
Calculate the gain from the option to abadon as follows:
Gain = 1650000-1542658.28 = 107341.72
Calculate the Value of the option to abadon as follows:
Value of option to abadon = Probability of failure * Gain /1+Discount rate
= 0.50*107341.72/1+0.15 = 46670.31
The Value of the option to abandon is 46670.31