1. Chapter 17 Risk, Return, and the Time Value of Money

2. Relationship between risk and return (Fig. 14.1): Risk Required Rate of Return Risk-free Rate Types of Risk Business Risk Financial Risk Purchasing Power of Risk Liquidity Risk Risk

3. Time Value of Money: A dollar in hand is worth more than a dollar to be received in the future because it can either be consumed immediately or or put to work to earn a return. Discounting Compounding

4. Time Value of Money Tables Col. 1:FV=PV (FVIF n=, i=)Future value of $ Col. 2:FVA=A (FVAIF n=, i=)Future Value of an Annuity Col. 3:SFP=FV (SFIF n=, i=)Sinking Fund Payment Col. 4:PV=FV (PVIF n=, i=)Present Value of $ Col. 5:PVA=A (PVAIF n=, i=)Present Value of an Annuity Col. 6:PMT=PVA (PMTIF n=, i=) Amortization Payment OLB = Outstanding Loan Balance = PV of remaining payments discounted at the contract interest rate OLB = PVA = Pmt (PVAIF n=, i=) NPV = Net Present Value = PV of CF’s discounted at investor’s required rate - cost; if NPV > 0 project equals or exceeds investor’s required rate of return.

5. Time Value of Money Formulas: Future value of a lump sum Compound interest (Table 14.1) FV = PV (1+i) n = PV (FVIF n,i ) PV FV = ? n = Known i = known

6. Future value of $ : Col. 1 If you invest $10,000 today which will earn 10% interest for 40 yrs., what sum will you accumulate? FV=PV(FVIF n, i )= 10000(45.259) =$452,592.56

7. Present value of a lump sum PV = FV/(1+i) n = FV (PVIF n, i ) PV = ? FV n = Known i = known

8. Present Value of $: Col. 4 You will inherit $1,000,000 forty years from now. If you “discount” money at 10%, what is the million dollars worth today? PV=FV(PVIF n, i ) = 1,000,000(.022095) = $22,095

9. Present Value of an Annuity: 1 PVA = A 1 - _ 1__ = A(PVAIF n, i ) __(1+i) n i 2 Example: PVA = ? A = Known n = Known i = known

10. Present Value of an Annuity: Col. 5 Your wealthy grandparents have setup a trust fund for you that pays out $10,000 at the end of each year for the next forty years. You want to borrow against this fund. If money is discounted at 10%, what is the present value of your trust fund? PVA=A(PVAIF n, i ) = 10,000(9.779051) = $97,790.51

11. Future Value of an annuity: 1 FVA= A _(1+i) n - 1__ = A(FVAIF n, i ) i 2 Example: A = Known FVA = ? n = Known i = known

12. Future value of an Annuity: Col. 2 If you invest $1,000 at the end of each year that earns 10% interest, how much will you accumulate after 40 deposits? FVA=A(FVAIF n, i ) =1000(442.592) = $442, 592

13. Sinking Funds: 1 SFP= FVA (1+i) n = FVA(SFIF n, i ) i 2 Example: SFP = ? SFP FVA = Known n = Known i = known

14. Sinking Fund Payment: Col. 3 Forty years from now you wish to have accumulated $1,000,000. If you can earn 10% annually, how much will you have to deposit annually? SFP=FV(SFIF n, i ) = 1,000,000(.002259) = $2,259

15. Amortization Payment: Col. 6 You just borrowed $100,000 to buy a house. The loan will be repaid annually for forty years at 10% interest. What will your annual payment be? PMT=PVA(PMTIF n, i ) = 100,000(.102259) = $10,225.90 Loan Amt. x 40 yrs. 409,036 -100,000 prin. 309,036 int. exp.

16. Mortgage Payments: 1 Pmt= PVA __ i___ = PVA(PMTIF n, i ) 1 - _ 1__ (1+i) n 2 Example 3 Monthly Compounding PMT = ? PVA = Known = Orig. Loan n = Known i = known

17. Monthly Compounding Algebraic formulas that adjust the six basic calculations (FV, PV, PVA, FVA, SFP, PMT) are found on p. 302 in your text. A handout of the compound interest table (10%) with monthly interest factors will be provided. Previous Example: $100,000 mortgage, 40 yrs @ 10%. What would monthly payments be? Use same formula, but interest factors for monthly compounding. PMT=PVA(PMTIF n=480, i=10% ) = 100,000(.008491) =$849.10/mo.

18. Calculating the outstanding loan balance (OLB) on an amortized loan: OLB = PV of remaining payments discounted at contract rate. Ex.: you borrow $100,000 to buy a home at 10% interest, 30 years, monthly payments. What would the OLB be after the 60th payment? 1. PMT=PVA(PMTIF n360, i=10% ) = 100,000(.008776) = $877.60 2. OLB=PVA=A(PVAIF n=300, i=10% ) = 877.60 (110.047230) = $96,577.45

19. Financial Decision Rules: NPV and IRR Net Present Value decision rule (NPV) Internal Rate of Return decision rule (IRR) Examples of NPV and IRR rules (Table 14.2)

20. NPV Example: You have a chance to invest in an apartment complex which will generate annual cash flows of $48,000. The property can be purchased for $500,000 today and you expect to sell it after 5 yrs for $600,000. Will this property be a wise investment?

21. TimeCash FlowPVIF @ 10% PV 0 -500000 1.000000-500000 1 48000 0.909091 43636 2 48000 0.826446 39669 3 48000 0.751315 36063 4 48000 0.683013 32785 5 648000 0.620921 402357 NPV +54510 OR PV = 48000(PAVIF n=5, i=10% ) + 600000(PVIF n=5, i=10% ) = 48000(3.790787) + 600000(.620921) = 181,958+372,553 = 554,511 = PV - Cost = NPV 554,511 - 500000 = +54,511 Accept Project