Your company asked you to evaluate two potential projects. These projects are active for 10 years and have no salvage life. Both have the same upfront costs, but the revenue stream from each of the projects is subject to variation, so risk is involved.
You are given the following information:
Firm’s cost of capital: 10%
Each project will require three years of investment before revenues are generated.
The following cost distribution is given:
Probability of Outcome Year 1 Investment Costs Year 2 Investment Costs Year 3 Investment Costs Expected Annual Revenues in Year 4 Expected Rate of Increase in Annual Revenues
Outcome A 20% $1,000 $2,000 $1,000 500 2%
Outcome B 40% $1,000 $2,000 $1,000 650 3%
Outcome C 40% $1,000 $2,000 $1,000 850 4%
Outcome A 10% $1,000 $2,000 $1,000 675 2%
Outcome B 50% $1,000 $2,000 $1,000 700 2.40%
Outcome C 40% $1,000 $2,000 $1,000 725 2.80%
In a new worksheet in Excel, answer the following:
1. What is the expected value of the NPV for each of the projects?
2. What is the standard deviation of the NPV for each of the projects?
3. What is the coefficient of variation of the NPV for each of the projects?
4. Which project has a higher expected return? Which has more risk?
5. Which one would you recommend to your company? How does its attitude toward risk affect your answer?
Consider the two options in the following table, both of which have random outcomes:
a. Determine the expected value of each option.
b. Determine the variance and standard deviation of each option.
c. Which option is most risky?
Problem 12-05 (Algo)
A risk-neutral consumer is deciding whether to purchase a homogeneous product from one of two firms. One firm produces an unreliable product and the other a reliable product. At the time of the sale, the consumer is unable to distinguish between the two firms’ products. From the consumer’s perspective, there is an equal chance that a given firm’s product is reliable or unreliable. The maximum amount this consumer will pay for an unreliable product is $0, while she will pay $110 for a reliable product.
a. Given this uncertainty, what is the most this consumer will pay to purchase one unit of this product?
b. How much will this consumer be willing to pay for the product if the firm offering the reliable product includes a warranty that will protect the consumer?
Problem 12-18 (Algo)
Pelican Point Financial Group’s clientele consists of two types of investors. The first type of investor makes many transactions in a given year and has a net worth of over $2 million. These investors seek unlimited access to investment consultants and are willing to pay up to $10,000 annually for no-fee-based transactions, or alternatively, $50 per trade. The other type of investor also has a net worth of over $2 million but makes few transactions each year and therefore is willing to pay $85 per trade.
You are the manager of a firm that sells a “commodity” in a market that resembles perfect competition, and your cost function is C(Q) = 2Q + 3Q2. Unfortunately, due to production lags, you must make your output decision prior to knowing for certain the price that will prevail in the market. You believe that there is a 70 percent chance the market price will be $200 and a 30 percent chance it will be $600.
a. Calculate the expected market price.
b. What output should you produce in order to maximize expected profits?
c. What are your expected profits?
As the manager of Smith Construction, you need to make a decision on the number of homes to build in a new residential area where you are the only builder. Unfortunately, you must build the homes before you learn how strong demand is for homes in this large neighborhood. There is a 60 percent chance of low demand and a 40 percent chance of high demand. The corresponding (inverse) demand functions for these two scenarios are P = 300,000 – 400Q and P = 500,000 – 275Q, respectively. Your cost function is C(Q) = 140,000 + 240,000Q.
How many new homes should you build, and what profits can you expect?