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Unformatted text preview: Tradeoffs RiskYield Tradeoffs
• Investments vary in their degree of risk. • Generally, higher risk investments also tend to entail higher expected benefits (i.e., high yields). higher risk investments. • If they did not, no one would invest money in the • For this reason, lenders often charge higher interest rates on loans to highrisk borrowers, while large, low risk, firms can borrow at the prime rate. • Net Present Value (NPV) is the sum of the present Criteria for Evaluating Alternative Criteria for Evaluating Alternative Allocations of Resources Over Time values of the net benefits accruing from an investment or project. • Net benefit in time period t is Bt Ct, where Bt is the Total Benefit in time period t and Ct is the Total Cost in time period t. – The discrete time formula for N time periods with Ν constant r: (Βτ − Χτ ) NPV = ∑ τ. τ= 0 (1 + ρ) NFV and IRR NFV and IRR
• Net Future Value (NFV) is the sum of compounded differences between project benefits and project costs.
– The discrete time formula for N time periods with constant r:
Ν τ= 0 • Internal Rate of Return (IRR) is the interest rate that is NFV = ∑ (Βτ − Χτ ) ⋅ (1 + ρ) Ν −τ associated with zero net present value of a project. IRR is the x that solves the equation: 0= τ= 0 (1 + ξ) ∑ Ν (Βτ − Χτ )
τ The Relationship Between IRR and The Relationship Between IRR and NPV
• If r < IRR then the project has a positive NPV • If r > IRR then the project has a negative NPV • It is not worthwhile to invest in a project if you can get a better rate of return on an alternate investment. Familiarizing Ourselves with the Familiarizing Ourselves with the Previous Concept
• Two period model: If we invest $I today, and receive $B next year in returns on this investment, the NPV of the investment is: $I + $B/(1 + r). Notice that the NPV declines as the interest rate r increases, and vice versa. considering an investment which costs you $100 now but which will pay you $150 next year.
– – – If r = 10%, then the NPV is: 100 + 150/1.1 = $36.36 If r = 20%, then the NPV is: 100 + 150/1.2 = $25 If r = 50%, then the NPV is: 100 + 150/1.5 = $0 • Three period model: Suppose you are Familiarizing Ourselves with the Familiarizing Ourselves with the Previous Con...
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