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**Risk, Return, and the Time Value of Money**

Chapter 14 Risk, Return, and the Time Value of Money

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**Relationship Between Risk and Return**

return – profit as a percentage of total investment risk – uncertainty about the actual rate of return over an investment period risk and return are directly related (investors require greater returns for greater risk)

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Figure 14.1

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Types of Risk Business risk – uncertainty arising from changing economic conditions that affect an investment’s ability to generate returns Financial risk – uncertainty associated with the possibility of defaulting on borrowed funds used to finance an investment Purchasing power risk – uncertainty arising from the possibility that the amount of goods and services that can be acquired with a given amount of money will decline over time (inflation) Liquidity risk – possibility of loss resulting from not being able to convert an asset into cash quickly should the need arise

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**Time Value of Money Principle**

Money in hand today is worth more than money to be received in the future

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**Calculator Setup 1.) All keystrokes shown are for the HP 10B or 10BII**

2.) All cash outflows are negative numbers 3.) All cash inflows are designated as positive numbers 4.) Calculator should be set to END Mode. If it is in BEGIN mode, press SHIFT KEY, then BEG/END. Note: If the calculator gets put into BEGIN Mode you will see it designated in the display. 5.) Calculator should be set to the correct number of payments per year. - Enter the number of payments then the SHIFT KEY and P/YR.

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**Future Value of a Lump Sum**

Compound interest – during any given period, interest is earned not only on the original principal amount, but also on any interest previously earned by the principal amount Compounding – the process of determining future value Example: What is the future value of $70,000 compounded at 10% annual interest over 3 years? Calculator keystrokes shown on page 315. FV = PV (1 + i)n

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Table 14-1 (page 313)

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**Future Value of a Lump Sum**

What is the future value of $100,000 compounded at 5% interest over 10 years?

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**Future Value of a Lump Sum**

What is the future value of $10,000 compounded at 8% interest over 30 years?

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**Present Value of a Lump Sum**

Discounting – the process of determining present value Example: What is the present value of $93,170 discounted at 10% annual interest for 3 years? Calculator keystrokes shown on page 316. PV = FV [1 / (1+i)n]

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**Present Value of a Lump Sum**

What is the present value of $25,000 discounted at 12% annual interest for 10 years?

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**Present Value of a Lump Sum**

What is the present value of $100,000 discounted at 25% annual interest for 5 years?

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**Present Value of a Cash Flow Stream**

What if there is periodic cash flow instead of a lump sum future payment? - How do you calculate the Present Value of the total investment? Example: What is the Present Value of an investment that pays you $100 at the end of the first year, $500 at the end of the second year and $1000 at the end of the third year if the required rate of return is 10% ? PV = FV [1/(1+i)n]

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**Present Value of an Annuity**

Definition: A series of equal cash flows. PVA = A[(1-(1/(1+i)n ))/ i] Example: What is the present value of a series of three payments of $1,000 received at the end of each year if the discount rate is 10%?

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**Future Value of an Annuity**

FVA = A[((1+i)n -1))/ i] Example: What is the future value of a series of five payments of $100 received at the end of each year if the compound interest rate is 10%?

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**Sinking Fund Payments SFP = FVA [ i / ((1+i)n -1))]**

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

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**Mortgage Payments PMT =**

PVA [ i / ((1 - (1/(1+i)n )))] Example: What annual payment would be necessary to amortize a loan for $100,000 over ten years at 10% interest?

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**Financial Decision Rules**

Net Present Value (NPV) - difference between how much an investment costs and how much it is worth to an investor in present value dollars NPV = present value of cash inflows minus present value of cash outflows NPV Decision Rule: If the NPV is equal to or greater than zero, we choose to invest Internal Rate of Return (IRR) - the discount rate that makes the NPV equal to zero IRR = the rate of return on the investment IRR Decision Rule: If the IRR is greater than or equal to our required rate of return, we choose to invest

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**NPV / IRR Example Would you invest in the following opportunity:**

Investment of $10,000 Cash Flows: $100 – Year 1 $1,600 – Year 2 $1,800 – Year 3 $450 – Year 4 $12,500 – Year 5 12% Required Rate of Rtn What is the NPV? What is the IRR?

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Review #1 How much should Joe be willing to pay today for an investment that is expected to pay $1,000 ten years in the future if he requires a 10% rate of return? (Future Value of a Lump Sum)

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Review #2 Joe is offered the opportunity to receive $1,000 each year for 10 years. How much would he be willing to pay for this future income stream if he desires a 12% return? (Present Value of an Annuity)

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Review #3 Joe expects to receive $1,000 each year for the next 10 years beginning one year from today. If he deposits each payment into an account earning 8% interest annually, what will be the balance of the account when the last payment is deposited? (Future Value of an Annuity)

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Review #4 Joe Saver deposits $1,000 in a savings account. To what value will his money accumulate in 5 years if the account pays 5% interest compounded annually? (Future Value of a Lump Sum)

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Review #5 Harold and Helen purchase a $150,000 house using a down payment of $15,000 and a fixed rate mortgage for $135,000. The annual interest rate on the loan is 10% and the term is 30 years. What monthly payment is necessary to amortize this loan?

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Review #6 An investor with a required rate of return of 14% is considering the purchase of a retail center for $82,000 with the following cash flows: YEAR 1 = $10,000 YEAR 2 = $12,000 YEAR 3 = $11,000 YEAR 4 = $14,000 YEAR 5 = $95,000 Based on this forecast, what is the NPV? IRR? Should the investor invest in the retail center?

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Review #7 An investor with a required rate of return of 10% is considering the purchase of a 4-Plex for $299,000 with the following cash flows: YEAR 1 = $30,000 YEAR 2 = $30,000 YEAR 3 = $30,000 YEAR 4 = $40,000 YEAR 5 = $310,000 Based on this forecast, what is the NPV? IRR? Should the investor invest in the 4-Plex?

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Review #8 An investor with a required rate of return of 12% is considering the purchase of an Office building for $100,000 with the following cash flows: YEAR 1 = $30,000 YEAR 2 = $40,000 YEAR 3 = $35,000 YEAR 4 = $70,000 Based on this forecast, what is the NPV? IRR? Should the investor invest in the Office building?

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Review #9 Old Bank offers to pay 6 percent interest, compounded annually. New Bank, to be competitive, offers 6 percent interest, compounded monthly. If you buy from each bank a five year, $1,000 certificate of deposit, with all interest compounded, what is the difference in values at the end of five years?

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Review #10 An apartment house has a projected net income of $15,000 per year, and its projected net sales price after five years is $150,000. Considering its risk, you require a 14 annual percent return on this investment. How much would you be willing to pay for it?

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Review #11 Jane Ire is offered a real estate investment that promises to pay $80,000 after 5 years. She feels, based on the investment’s riskiness, that the annual rate of return should be 15 percent, compounded quarterly. What price should she pay for the property?

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Review #12 Peter Piper is offered an investment that will pay $5,000 at the end of each year for the next 10 years. He wants to earn an annual rate of return of 16 percent. How much is he willing to pay for the investment today?

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Review #13 Jim Douglas pays $10,000 for a mortgage contract that will pay $3,000 at the end of each of the next 5 years. What rate of return will he earn?

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Review #14 The value of a house today is $98,000. If it has increased in value at 6% per year, what was the value eight years ago?

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Review #15 Doctor John purchased 50 acres of land ten years ago for $800 per acre. a. If he could have alternatively invested the money at 8 percent per year, what price must he receive today to breakeven with his opportunity rate? b. If Doctor John sold the land for $1,400 per acre today, what was his actual rate of return?

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Review #16 Suppose you are interested in buying 25 acres of land to start a blueberry farm. The owner is willing to finance 70 percent of the $100,000 purchase price at 10% interest over 8 years. a. What will be the payment assuming annual amortization? b. What would the payment be if monthly payments are required?

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Review #17 The Smiths desire to purchase a house and they open a savings account that pays 5.75 percent interest, with monthly compounding. If they put $120 per month beginning one month from now and they must have 20 percent of the price of a house as a down payment, what price can they pay for a house after saving for 5 years?

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Review #18 Mr. Winter purchases 10 duplexes (20 rentable units) and he expects to have to replace the air conditioning equipment in each rentable unit 10 years from now at a cost of $5,000 per unit. The bank that loaned Mr. Winter the money to purchase the duplexes requires that he deposit a part of the monthly rents into an account earning 6 percent interest to insure that the money will be available to replace the air conditioning units. How much money must Mr. Winter deposit at the end of each month?

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Review #19 You are considering the purchase of 75 acres of land that you believe will be developed as a shopping center. You estimate that you can sell the land three years from now at $25,000 per acre. How much should you pay now for the land if the required rate of return is 25 percent?

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Review #20 What is the present worth of an income-producing property which receives an after-tax cash flow of $20,000 in year one, $22,000 in year two, $25,000 in year three, $30,000 in year four, and $32,000 in year five? Assume the discount rate is 15 percent.

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End Chapter 14 Questions?

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NPV and the Time Value of Money

NPV and the Time Value of Money

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