Final answer:
GM should proceed with the factory project if the discount rate is 5%, as the present value of future returns ($123.4 million) is higher than the investment cost ($100 million). However, if the discount rate is 8%, the present value of the returns ($92.3 million) is less than the investment cost, making the project unattractive.
Step-by-step explanation:
Financial Decision-Making in Business
When GM is considering building a new factory with a cost of $100 million and an expected return of $200 million after 10 years, the decision to proceed depends on the discount rates applied to the future returns. Discount rates represent the time value of money and serve to compare future returns to today's dollars. When evaluating a long-term investment such as this, GM must look at the present value of the expected returns to determine if the investment is profitable.
Using a 5% discount rate, the present value (PV) of the future $200 million is calculated using the formula PV = FV / (1 + r)^n, where FV is the future value, r is the discount rate, and n is the number of years. In this case, PV = $200 million / (1 + 0.05)^10, which results in a present value of approximately $123.4 million. This present value is greater than the $100 million cost, suggesting that the investment is attractive at a 5% discount rate.
If we apply an 8% discount rate, the present value calculation becomes PV = $200 million / (1 + 0.08)^10, yielding approximately $92.3 million. This present value is less than the initial cost of $100 million, which would suggest that the investment is not profitable when the discount rate is 8%.
In benefit-cost analysis, a project with a present value higher than its cost is typically considered to be a good investment. Therefore, GM would likely decide to proceed with the project if the relevant discount rate is 5%, but not if it is 8%.