Final answer:
Calculating the IRR involves finding a discount rate that brings the net present value of cash flows to zero, which generally requires complex calculations. The decision to undertake an investment when borrowing at an 11 percent interest rate depends on whether the present value of benefits exceeds the present value of costs. The choice of a discount rate considers the opportunity cost of capital and a risk premium, as illustrated in the 15% example rate.
Step-by-step explanation:
To calculate the internal rate of return (IRR) of an investment, one would consider the project's cash flows, which are -$100 in year one, -$50 in year two, $150 in year three, and $25 in year four. To find the IRR, we need to find the discount rate that would make the net present value of these cash flows equal to zero. This calculation usually requires the use of financial software or an IRR financial calculator, as it involves solving a complex polynomial equation.
Regarding the present value of benefits, when borrowing at an interest rate of 11 percent, if the present value of returns (benefits) is greater than the present value of costs, the investment should be undertaken because it implies a net gain. Conversely, if the present value of returns is less than the present value of costs, the investment should not be undertaken as it would result in a net loss. This situation represents a scenario where the cost of financial capital is considered, along with the additional returns that go beyond just covering the initial investment.
A financial investor would consider various interest rates to value future payments, reflecting the rate of return on other financial opportunities and a risk premium. For example, if an investor uses a 15% discount rate to assess the present value of future payments, this rate would include both the opportunity cost of capital and a premium for associated risks.