Question

You own a wholesale plumbing supply store. The store currently generates revenues of $1 million per year. Next year, revenues will either decrease by 8% or increase by 10%, with equal probability, and then stay at that level as long as you operate the store. You own the store outright. Other costs run $900,000 per year. There are no costs for shutting down; in that case, you can always sell the store for $330,000. Cost of capital is fixed at 10%

a. What would the business be worth today if there were no option to abandon (to sell the store and go out of business)?
b. What is the business worth today with the option to abandon?
c. What is the value of the real option to abandon?

Answer 1

The value of the business today without the option to abandon can be calculated using the present value of future cash flows. The value of the business today with the option to abandon is the maximum of the present value and the selling price. The value of the real option to abandon is the difference between the value with and without the option to abandon.

Step-by-step explanation:

To calculate the value of the business today without the option to abandon, we need to calculate the present value of the future cash flows. The cash flows can be either an 8% decrease or a 10% increase in revenues next year, each with a 50% probability. The present value can be calculated using the formula PV = CF / (1 + r), where PV is the present value, CF is the cash flow, and r is the discount rate. The discount rate is given as 10%. Therefore, the value of the business today without the option to abandon would be:

PV = (0.5 * (1 million * (1 - 0.08))) / (1 + 0.1) + (0.5 * (1 million * (1 + 0.10))) / (1 + 0.1)

To calculate the value of the business today with the option to abandon, we need to consider the possibility of shutting down and selling the store for $330,000. The value of the business today with the option to abandon would be the maximum of the present value calculated above and the selling price of $330,000.

The value of the real option to abandon is the difference between the value of the business today with the option to abandon and the value of the business today without the option to abandon. This represents the additional value gained from having the option to abandon the business.