1 / 21

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

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

mattox
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 17Risk, 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(FVIFn, i) = 10000(45.259) =$452,592.56

  7. Present value of a lump sum PV = FV/(1+i)n = FV (PVIFn, 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(PVIFn, i) = 1,000,000(.022095) = $22,095

  9. Present Value of an Annuity: • PVA = A 1 - _ 1__ = A(PVAIFn, i) __(1+i)n i • Example: PVA = ? A = Known 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(PVAIFn, i) = 10,000(9.779051) = $97,790.51

  11. Future Value of an annuity: • FVA= A _(1+i)n- 1__ = A(FVAIFn, i) i • Example: A = Known 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(FVAIFn, i) =1000(442.592) = $442, 592

  13. Sinking Funds: • SFP= FVA (1+i)n = FVA(SFIFn, i) i • 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(SFIFn, 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(PMTIFn, i) = 100,000(.102259) = $10,225.90 Loan Amt. x 40 yrs. 409,036 -100,000 prin. 309,036 int. exp.

  16. Mortgage Payments: • Pmt= PVA __ i___ = PVA(PMTIFn, i) 1 - _ 1__ (1+i)n • Example • Monthly Compounding PVA = Known = Orig. Loan PMT = ? PMT = ? PMT = ? PMT = ? PMT = ? • 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(PMTIFn=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(PMTIFn360, i=10%) = 100,000(.008776) = $877.60 2. OLB=PVA=A(PVAIFn=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(PAVIFn=5, i=10%) + 600000(PVIFn=5, i=10%) = 48000(3.790787) + 600000(.620921) = 181,958+372,553 = 554,511 = PV - Cost = NPV 554,511 - 500000 = +54,511 Accept Project

More Related