CH 17Risk, Return & Time Value of Money

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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

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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

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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 .

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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:

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Time Value of Money CalculationsAn Overview

Cash Flow (CF)

Simple CF (Lump Sum) Multiple CF4 TVM KeysN, I/Y, PV, FV(do not use PMT) Equal CFs Unequal CFs

- Annuity:4 TVM KeysN, I/Y, PMT, PVOrN, I/Y, PMT, FV

- Perpetuity:PV=C/r

CF , NPV, IRR

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The Financial CalculatorWhat to watch out for

For “TVM” calculations, remember toeither clear the 5th 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)

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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?

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Present Value of Simple CF

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

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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?

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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%?

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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%?

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Annuity Due

Example: Your interest rate is 1% per month, you borrow $10,000 and you pay $603.78 per month. Assuming that you pay at the beginning of each month, how long does it take to repay your loan?

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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?

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Annuity

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

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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.

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Effective Rates vs. Stated Rates

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

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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?

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V. Financial Decision Rules

Net Present Value (NPV) - difference betweenhow 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.

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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?

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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?

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