Question

You have an opportunity to invest in a new car manufacturing plant for $5M. Expectations as of today: ✓ Annual cash flow in year 1: $600,000 ✓ Perpetual growth rate: 2% per year ✓ Cost of capital: 12% ✓ Risk-Free rate: 5% A publicly traded car manufacturer exists. This firm is a perfect comparable for the investment and has a return volatility = 40% You have the possibility to invest today, or delay by exactly one year.

(a) What is the NPV of the project if you invest today?

(b) What is the NPV of the project if you wait for one year? Please use the Black Scholes Model. (You may use Excel).

(c) Real investment decisions always come with the option to wait. Please elaborate (at least a one-page write-up) on some pros and cons of delaying investment decision.

Answer 1

(a) NPV of the project if u invest today:

C0 = -5 million $ annual cash flow : $600,000 growth rate : 2% cost of capital : 12%

cash flow at t=0 : $ -5,000,000

cash flow at t=1 : 600,000*1.02/ (0.12-.02) applying gordon growth model

= $ 6,120,000

PV of this amount at t=0 : 5,464,285.71

NPV = $ 464,285.71

(b) NPV if the investment is done after one year :

cash flow at t=0 : -5,000,000 $

value of the project : $6,120,000

NPV : $1,120,000/1.12 = $1,000,000

(c) Advantages of delaying investment decisions :

A real option is the right, but not the obligation, to make a decision regarding an investment in real assets, such as to expand production capacity or abandon a project. While the underlying assets on which real options derive their value are generally not traded in competitive markets, like financial options, the principles of option valuation can often be used to determine their values.

The presence of real options can significantly increase the value of an investment opportunity, especially when there is a lot of uncertainty. Thus, to correctly evaluate an investment, the value of these options should be included in the analysis.

When there is not an option to wait, it is optimal to invest in any positive-NPV project immediately. When there exists the option of delaying the acceptance of a project, it is usually optimal to invest only when the NPV is substantially greater than zero.

By delaying an investment, you can base your decision on additional information. The option to wait is most valuable when there is a great deal of uncertainty regarding what the value of the investment will be in the future.

However, similar to the idea that it may be optimal to exercise a call option early on a dividend-paying stock, there may be value from the investment that is forgone by waiting.