CH 17 Risk, Return & Time Value of Money

2 Outline  I. Relationship Between Risk and Return  II. Types of Risk  III. Time Value of Money  IV. Effective Rates vs. Stated Rates  V. Financial Decision Rules (NPV & IRR)  VI. A Real Estate TVM Practice Problem

3 I. Relationship Between Risk and Return  % return = profit as a percentage of total initial investment  risk and return are related (investors require returns for greater risk).  The formula that shows the relationship between risk and return is known as

4 II. Types of Risk  Business risk: The risk created by factors.  Financial risk: The risk created by the inability to.  Purchasing power risk The risk created by. The result is that money is worth over time.  Liquidity risk The risk created by the inability to without the.

5 III. Time Value of Money  Def: Money in hand today is worth than money to be received in the future.  The process of determining future value:  The process of determining present value:

6 Time Value of Money Calculations An Overview Cash Flow (CF) Simple CF (Lump Sum)Multiple CF 4 TVM Keys N, I/Y, PV, FV (do not use PMT) Equal CFsUnequal CFs - Annuity: 4 TVM Keys N, I/Y, PMT, PV Or N, I/Y, PMT, FV - Perpetuity: PV=C/r CF, NPV, IRR

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8 The Financial Calculator What to watch out for  For “TVM” calculations, remember to either clear the 5 th key or CLR TVM. For unequal multiple CF calculations, remember to clear the CF register (CLR WORK).  PV and FV have opposite signs  PV and PMT or FV and PMT have opposite signs  I/Y = period interest rate - P/Y & C/Y must equal 1 so that the I/Y is an effective period rate - Interest is entered as a percent, not a decimal  Set decimal places to 9  Calculator should be in END mode (exception: annuity due = BGN)

9 Future Value of a Simple CF (Lump Sum)  Example: What is the future value of $70,000 compounded at 10% annual interest over 3 years?

10 Present Value of Simple CF  Example: What is the present value of $90,000 discounted at 10% annual interest for 3 years?

11 Another Simple CF Calculation  Example: If you have $15,000 to invest, can earn 8% return, and need to have $30,000 at the end of your investment period, how long do you have to wait?

12 Present Value of an Annuity  Example: What is the present value of a series of three payments of $1,000 to be received at the end of each year if the discount rate is 10%?

13 Future Value of an Annuity  Example: What is the future value of a series of five payments of $100 received at the end of each year if the interest rate is 10%?

14 Annuity Due  Example: Your interest rate is 1% per month, you borrow $10,000 and you pay $ per month. Assuming that you pay at the beginning of each month, how long does it take to repay your loan?

15 Annuity  Example: What is the amount of money that must be deposited into an account each year that earns 10% per year for five years in order to accumulate $20,000?

16 Annuity  Example: What annual payment would be necessary to amortize a loan for $100,000 over ten years at 10% interest?

17 IV. Effective Rates vs. Stated Rates  Effective Rates: rate compounded once per period  Effective Annual Rate (EAR): annual rate compounded once per year  Quoted Rate: rate compounded more than once per period  Annual Percentage Rate (APR): annual rate compounded more than once per year  Always use rates for TVM calculations.  Always match the interest rate (I/Y) to the time periods (N).  In an annuity: “the frequency” of the payment determines the interest rate and time period.

18 Effective Rates vs. Stated Rates  Example: You invest $5,000 at 6% APR, compounded monthly. How much will you have in 4 years?

19 Effective Rates vs. Stated Rates  Example: You borrow $10,000. The loan calls for monthly payments for 3 years. The APR is 9%, compounded monthly, what are the monthly payments?

20 V. Financial Decision Rules  Net Present Value (NPV) - difference between how much an investment and how much it.  NPV Decision Rule: invest if the NPV.  Internal Rate of Return (IRR) - the discount rate that makes the NPV equal to.  IRR Decision Rule: invest if the IRR the required rate of return.

21 Multiple Uneven CFs  Example: You are offered an investment that costs you $1,800 and will pay you $400 in one year, $600 in two years, $1000 in three years, and $500 in four years. If you can earn 11% on an investment with similar risk would you invest? What is the IRR on this investment?

22 VI. A Real Estate TVM Practice Problem  You are ready to buy a house and have $20,000 for a down payment and closing costs. Closing costs are estimated to be 4% of the loan value. You have an annual salary of $36,000 and the bank is willing to allow your monthly mortgage payment to be equal to 28% of your monthly income. The interest rate on the loan is 6% per year with monthly compounding for a 30-year fixed-rate loan. 1. How much money will the bank loan you?. 2. How much money can you offer for the house?.