Principles of Corporate Finance Brealey and Myers  Sixth Edition Making Investment Decisions with the Net Present Value Rule Slides by Matthew Will Irwin/McGraw Hill Chapter ©The McGraw-Hill Companies, Inc., 200 6- Topics Covered  What To Discount  IM&C Project  Project Interaction Timing  Equivalent Annual Cost  Replacement  Cost of Excess Capacity  Fluctuating Load Factors  Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- What To Discount Only Cash Flow is Relevant Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- What To Discount Only Cash Flow is Relevant Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- What To Discount Points to “Watch Out For” Do not confuse average with incremental payoff Include all incidental effects Do not forget working capital requirements Forget sunk costs Include opportunity costs Beware of allocated overhead costs Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- Inflation INFLATION RULE  Be consistent in how you handle inflation!!  Use nominal interest rates to discount nominal cash flows  Use real interest rates to discount real cash flows  You will get the same results, whether you use nominal or real figures Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- Inflation Example You own a lease that will cost you $8,000 next year, increasing at 3% a year (the forecasted inflation rate) for additional years (4 years total) If discount rates are 10% what is the present value cost of the lease? Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- Inflation Example You own a lease that will cost you $8,000 next year, increasing at 3% a year (the forecasted inflation rate) for additional years (4 years total) If discount rates are 10% what is the present value cost of the lease? 1+nominal interest rate + real interest rate = 1+inflation rate Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- Inflation Example - nominal figures Year Cash Flow PV @ 10% 8000 8000 1.10 8000x1.03 = 8240 8000x1.032 = 8240 8240 1.102 8487 20 1.103 8741.82 1.104 8000x1.03 = 8487.20 = 7272.73 = 6809.92 = 6376.56 = 5970.78 $26,429.99 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- 10 Inflation Example - real figures Year Cash Flow 8000 1.03 8240 1.032 8487.20 1.033 8741.82 1.034 = 7766.99 = 7766.99 = 7766.99 = 7766.99 PV@6.7961% 7766.99 1.068 7766.99 1.0682 7766.99 1.0683 7766.99 1.0684 = 7272.73 = 6809.92 = 6376.56 = 5970.78 = $26,429.99 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- 17 IM&C’s Guano Project Revised cash flow analysis ($1000s) Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- 18 Timing  Even projects with positive NPV may be more valuable if deferred  The actual NPV is then the current value of some future value of the deferred project Net future value as of date t Current NPV = t (1 + r ) Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- 19 Timing Example You may harvest a set of trees at anytime over the next years Given the FV of delaying the harvest, which harvest date maximizes current NPV? Harvest Year Net FV ($1000s) 50 64.4 77.5 89.4 % change in value 28.8 20.3 15.4 11.9 Irwin/McGraw Hill 100 109.4 9.4 ©The McGraw-Hill Companies, Inc., 200 6- 20 Timing Example - continued You may harvest a set of trees at anytime over the next years Given the FV of delaying the harvest, which harvest date maximizes current NPV? 64.4 NPV if harvested in year = = 58.5 1.10 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- 21 Timing Example - continued You may harvest a set of trees at anytime over the next years Given the FV of delaying the harvest, which harvest date maximizes current NPV? 64.4 NPV if harvested in year = = 58.5 1.10 NPV ($1000s) 50 58.5 Irwin/McGraw Hill Harvest Year 64.0 67.2 68.3 67.9 ©The McGraw-Hill Companies, Inc., 200 6- 22 Equivalent Annual Cost Equivalent Annual Cost - The cost per period with the same present value as the cost of buying and operating a machine Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- 23 Equivalent Annual Cost Equivalent Annual Cost - The cost per period with the same present value as the cost of buying and operating a machine present value of costs Equivalent annual cost = annuity factor Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- 24 Equivalent Annual Cost Example Given the following costs of operating two machines and a 6% cost of capital, select the lower cost machine using equivalent annual cost method Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- 25 Equivalent Annual Cost Example Given the following costs of operating two machines and a 6% cost of capital, select the lower cost machine using equivalent annual cost method Machine A B Irwin/McGraw Hill Year 15 10 6 PV@6% 28.37 21.00 EAC ©The McGraw-Hill Companies, Inc., 200 6- 26 Equivalent Annual Cost Example Given the following costs of operating two machines and a 6% cost of capital, select the lower cost machine using equivalent annual cost method Machine A B Irwin/McGraw Hill Year 15 10 6 PV@6% 28.37 21.00 EAC 10.61 11.45 ©The McGraw-Hill Companies, Inc., 200 6- 27 Machinery Replacement Annual operating cost of old machine = Cost of new machine Year: 15 5 NPV @ 10% 27.4 Equivalent annual cost of new machine = 27.4/(3-year annuity factor) = 27.4/2.5 = 11 MORAL: Do not replace until operating cost of old machine exceeds 11 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- 28 Cost of Excess Capacity A project uses existing warehouse and requires a new one to be built in Year rather than Year 10 A warehouse costs 100 & lasts 20 years Equivalent annual cost @ 10% = 100/8.5 = 11.7 10 11 With project 0 11.7 11.7 11.7 Without project 0 0 11.7 Difference 0 11.7 11.7 PV extra cost = 11.7 + 11.77 + + 11.7 10 = 27.6 (1.1) (1.1) (1.1) Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- 29 Fluctuating Load Factors Annual output per machine Two Old Machines 750 units Operating cost per machine × 750 = $1,500 PV operating cost per pachine 1,500/.10 = $15,000 PV operating cost of two machines ì 15,000 = $30,000 Irwin/McGraw Hill âThe McGraw-Hill Companies, Inc., 200 6- 30 Fluctuating Load Factors Two New Machines Annual output per machine 750 units Capital cost pe machine $6,000 Operating cost per machine × 750 = $750 PV operating cost per pachine 6,000 + 750/.10 = $13,500 PV operating cost of two machines × 13,500 = $27,000 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- 31 Fluctuating Load Factors One Old Machine Annual output per machine 500 units Capital cost pe machine Operating cost per machine × 500 = $1,000 PV operating cost per pachine 1,000/.10 = $10,000 PV operating cost of two machines $26,000 Irwin/McGraw Hill One New Machine 1,000 units $6,000 × 1,000 = $1,000 6,000 + 1,000 / 10 = $16,000 ©The McGraw-Hill Companies, Inc., 200 ... 8741.82 1.034 = 7766.99 = 7766.99 = 7766.99 = 7766.99 PV@6.7961% 7766.99 1 .068 7766.99 1 .068 2 7766.99 1 .068 3 7766.99 1 .068 4 = 7272.73 = 6809.92 = 6376.56 = 5970.78 = $26,429.99 Irwin/McGraw Hill... valuable if deferred  The actual NPV is then the current value of some future value of the deferred project Net future value as of date t Current NPV = t (1 + r ) Irwin/McGraw Hill ©The McGraw-Hill... 200 6- 27 Machinery Replacement Annual operating cost of old machine = Cost of new machine Year: 15 5 NPV @ 10% 27.4 Equivalent annual cost of new machine = 27.4/(3-year annuity factor) = 27.4/2.5