【正文】 7%at $400 C of PV1???? Risk and Present Value 357.121400PV12%at $400 C of PV1???? Rate of Return Rule Accept investments that offer rates of return in excess of their opportunity cost of capital Rate of Return Rule Accept investments that offer rates of return in excess of their opportunity cost of capital Example In the project listed below, the foregone investment opportunity is 12%. Should we do the project? 14%or .14350,000 350,000400,000investm entprofi tRetu rn ???? Net Present Value Rule Accept investments that have positive present value Net Present Value Rule Accept investments that have positive present value Example Suppose we can invest $50 today and receive $60 in one year. Should we accept the project given a 10% expected return? $60+50=NPV ? Short Cuts Perpetuity PV = C r Short Cuts Perpetuity PV = C r Constant Growth Perpetuity PV = C r g Short Cuts Perpetuity PV = C r Constant Growth Perpetuity PV = C r g Annuity PV = C [ ] 1 1 r r(1+r)t _ Application of PV, NPV, DCF ? Value bonds ? Value stocks ? Value projects ? Value panies (MA) ? Value Capital Structure (debt vs. equity) Opportunity Cost of Capital How much “return” do you EXPECT to earn on your money? Opportunity Cost of Capital Example The pany may invest $100,000 today. Depending on the state of the economy, they may get one of three possible cash payoffs: 140,000110,000$80,000PayoffBoomNorm alSlum pEconom y000,110$3 000,140000,110000,80C payoff Expected 1 ????? Opportunity Cost of Capital Example continued The stock is trading for $. Depending on the state of the economy, the value of the stock at the end of the year is one of three possibilities: 140110$80eStoc k PricBoomNorm alSlum pEconom y Opportunity Cost of Capital Example continued The stock’s expected payoff leads to an expected return. 15%or 15. expectedreturn Expected110$314011080C payoff Expected1?????????investment Opportunity Cost of Capital Example continued Discounting the expected payoff at the expected return leads to the PV of the project 650,95$110 ,000PV ?? Internal Rate of Return IRR is related to Opportunity Cost of Capital Pay Attention to Math Internal Rate of Return Example You can purchase a turbo powered machine tool gadget for $4,000. The investment will generate $2,000 and $4,000 in cash flows for two years, respectively. What is the IRR on this investment? Internal Rate of Return Example You can purchase a turbo powered machine tool gadget for $4,000. The investment will generate $2,000 and $4,000 in cash flows for two years, respectively. What is the IRR on this investment? 0)1(000,4)1(000,2023,421 ??????? IR RIR RNPV Internal Rate of Return Example You can purchase a turbo powered machine tool gadget for $4,000. The investment will generate $2,000 and $4,000 in cash flows for two years, respectively. What is the IRR on this investment? 0)1(000,4)1(000,2023,421 ??????? IR RIR RNPV%?IRR Internal Rate of Return 2 0 0 01 5 0 01 0 0 05 0 00500100015002023250010 20 30 40 50 60 70 80 90100D i s c o u n t r a te (% )NPV (,000s)IRR=28% Internal Rate of Return Pitfall 1 Lending or Borrowing? With some cash flows (as noted below) the NPV of the project increases s the discount rate increases. This is contrary to the normal relationship between NPV and discount rates. 75.%20728,1320,4600,3000,1%103210??????NPVIRRCCCC Internal Rate of Return Pitfall 1 Lending or Borrowing? With some cash flows (as noted below) the NPV of the project increases s the discount rate increases. This is contrary to the normal relationship between NPV and discount rates. Discount Rate NPV Internal Rate of Return Pitfall 2 Multiple Rates of Return Certain cash flows can generate NPV=0 at two di