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Internal Rate of Return

Internal Rate of Return. Different Investment Choices. Investment Decision If PVB>PVC, Invest Compare different investment possibilities Should I invest in graduate school? Should I buy stocks instead? The investment with the highest rate of return is the most financially profitable.

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Internal Rate of Return

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  1. Internal Rate of Return

  2. Different Investment Choices • Investment Decision • If PVB>PVC, Invest • Compare different investment possibilities • Should I invest in graduate school? • Should I buy stocks instead? • The investment with the highest rate of return is the most financially profitable

  3. Internal Rate of Return • How large could the discount rate be and still render the investment profitable? • Remember • As the discount rate increases • The PVB decreases • Are the benefits so large that even a high discount leaves the project still worthwhile

  4. Internal Rate of Return • Solve for the discount rate that sets the PVB=PVC for each investment • This discount rate is the internal rate of return • The investment with the highest internal rate of return is the best investment

  5. Internal Rate of Return • Goal is to find r such that PVC=PVB • Assume initial investment costs are paid up front • Need not discount costs • Costs = B0/(1+r)^0 + B1/(1 + r)^1 + B2/(1 + r)^2 + ..+ Bn/(1 + r)^t • Because B0 = B1 = B2 = B3 = …. = B • the constant benefits per period, this equation reduces to • Costs = ∑ B/(1+r)^t • Right hand side of the expression = B ∑ [ 1/(1+r)^t] • where we sum from t=0 to the final period

  6. Internal Rate of Return • As t becomes large, the expression ∑ [ 1/(1+r)^t] can be shown to reduce to 1/r • Costs = B/r • r = B/Costs • Note • Costs are one-time, paid in the beginning • Many periods of receiving benefits • Benefits are the same each period • Invest $100,000, receive benefits of $6000 per year, for 40 years • R=B/C=6000/100000=.06

  7. IRR Function • =IRR (values,guess) • Values is an array or a reference to cells that contain numbers for which you want to calculate the internal rate of return • Not limited to constant benefits each period • Values must contain • at least one positive value (Benefits) • one negative value (Costs) • IRR uses the order of values to interpret the order of cash flows • If an array or reference argument contains text, logical values, or empty cells, those values are ignored

  8. IRR Function • Guess is a number that you guess is close to the result of IRR • Usually omit guess • If guess is omitted, it is assumed to be 0.1 (10 percent) • Excel uses an iterative technique for calculating IRR • Starting with guess, IRR cycles through the calculation until the result is accurate within 0.00001 percent. • If IRR can't find a result that works after 20 tries, the #NUM! error value is returned • If IRR gives the #NUM! error value, or if the result is not close to what you expected, try again with a different value for guess

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