POR CH.14

What amount invested at the end of each year at 10 percent annually will grow to $10,000 at the end of five years?

1,637.97

What is the present value of $500 received at the end of each of the next three years and $1,000 received at the end of the fourth year, assuming a required rate of return of 15 percent?

1,713.37

What is the present value of the following series of cash flows discounted at 12 percent: $40,000 now; $50,000 at the end of the first year; $0 at the end of year the second year; $60,000 at the end of the third year; and $70,000 at the end of the fourth year?

171,836 (without rounding, answer is 171,835.94

How much would you pay today for the right to receive $80 at the end of 10 years if you can earn 15 percent interest on alternative investments of similar risk?

19.77

How much will a $50 deposit made today be worth in 20 years if interest is compounded annually at a rate of 10 percent?

336.37

How much would you pay today for the right to receive nothing for the next 10 years and $300 a year for the following 10 years if you can earn 15 percent interest on alternative investments of similar risk?

372.17

If a landowner purchased a vacant lot six years ago for $25,000, assuming no income or holding costs during the interim period, what price would the landowner need to receive today to yield a 10 percent annual return on the land investment?

44,289.03

How much would you pay today to receive $50 in one year and $60 in the second year if you can earn 15 percent interest on alternative investments of similar risk?

88.85

A property owner has set up a contract in which he agrees to sell a warehouse 5 years from now to the tenant who currently leases the space. The tenant has agreed to continue to pay $20,000 in rent at the end of each year, including year five, at which time he will purchase the building for an additional $1,500,000. Assuming the required rate of return on a similar investment is 10% (annual), how much is this deal presently worth to the original owner of the property?

A. $1,007,197.20

The purchase price of an income producing property today is $570,000. After analysis of the expected future cash flows, expected sales price, and expected yield, the investor determines that the future cash flows have a present value (PV) of $580,000. Taking into consideration the price of the property today, what is the net present value (NPV) of this investment opportunity, and should the investor take the deal?

A. $10,000; Yes

Suppose an investor deposits $2500 in an interest-bearing account at her local bank. The account pays 2.5% interest compounded annually. If the investor plans on withdrawing the original principal plus accumulated interest at the end of 7 years, what is the total amount that

A. $2,971.71

Upon starting his first job after graduation, Jon has completed the necessary paperwork to set up direct deposit of his paycheck into his savings account. After taxes, medical benefits, and retirement account contributions have been taken out of John's gross salary, he is left with a direct deposit of $4000 at the end of each month. If John started with no other savings in his account, how much will John have in his savings account at the end of 12 months if he is able to earn an annual interest rate of 3%, with interest being compounded monthly?

A. $48, 665.53

Suppose your personal financial goal is to retire with a million dollars in your savings account. How much must you deposit monthly in an account paying 5% a year (with interest being compounded monthly and your deposits occurring at the end of the month), to accumulate $1,000,000 by your 65th birthday if you begin your deposits on your 22nd birthday? (Note: Assume that you started with no savings in the account prior to your first deposit at age 22 and you do not make a deposit on your 65th birthday)

A. $552.13

Suppose an investor is interested in purchasing the following income producing property at a current market price of $490,000. The prospective buyer has estimated the expected cash flows over the next four years to be as follows: Year 1 = $48,000, Year 2 = $49,440, Year 3 = $50,923, Year 4 = $52,451. Assuming that the required rate of return is 14% and the estimated proceeds from selling the property at the end of year four is $560,000, what is the NPV of the project?

A. -$12,860.53

With compound interest, the investor earns interest on the principal amount invested plus interest on accumulated interest. Which of the following compounding frequencies would yield the investor the greatest ending balance assuming all else is equal?

A. Daily

The internal rate of return (IRR) and the net present value (NPV) are tools that are widely used in real estate investment and finance decision making. An investor would most likely pursue an investment if which of the following circumstances was true?

A. The going-in IRR exceeds the investor's required rate of return

Assuming all else the same, the ___________ of an annuity due will be _____________ that of an ordinary annuity.

A. future value; greater than

The Real Estate Research Corporation (RERC) regularly surveys a sample of institutional investors and managers in order to gain insight into the required returns and risk adjustments used by industry professionals when making real estate acquisitions. Most of the properties that RERC examines are large, relatively new, located in major metropolitan areas and fully or substantially leased. These classifications of properties are commonly referred to as:

A. investment grade properties

Suppose that a landlord is interested in renting out a two-bedroom apartment for $1000 a month for the next year. The landlord requires rent to be paid at the beginning of the month, at which point he will deposit the rental check into a local savings account. If the annual interest that the tenant can earn on this account is 5% and interest is compounded monthly, how much will the tenant have in his savings account at the end of the year?

B. $12,330.01

Assuming that an investor requires a 10% annual yield over the next 12 years, how much would she be willing to pay for the right to receive $20,000 at the end of year 12?

B. $6,372.62

Suppose an investor is interested in purchasing the following income producing property at a current market price of $450,000. The prospective buyer has estimated the expected cash flows over the next four years to be as follows: Year 1 = $40,000, Year 2 = $45,000, Year 3 = $50,000, Year 4 = $55,000. Assuming that the required rate of return is 12% and the estimated proceeds from selling the property at the end of year four is $500,000, what is the NPV of the project?

B. $9,889.56

Assume that an industrial building can be purchased for $1,500,000 today, is expected to yield cash flows of $80,000 for each of the next five years (with the cash flows occurring at the end of each year), and can be sold at the end of the fifth year for $1,625,000. Calculate the internal rate of return (IRR) for this transaction.

B. 6.78%

You have just had a tenant sign a lease contract that guarantees you payments of $100,000 at the end of each year for the next five years. If you wish to determine the present value of these future cash flows (i.e. the value of this cash flow stream to you today), you would use which of the following time value of money processes?

B. Discounting

The rate that is used to discount expected future cash flows can be thought of as the return the investor is forgoing on an alternative investment of equal risk. In this framework, the discount rate is being thought of as which of the following?

B. Opportunity cost

Since investors prefer to have money now rather than later, money received next week, instead of today, is not worth as much to those receiving it, assuming the magnitude of the cash flow in each period is the same. Therefore an adjustment to the prospective cash flows is required. This process is referred to as:

B. discounting

Risk is the possibility that actual outcomes will vary from what was expected when the asset was purchased. If investors require a higher rate of return for undertaking more risk, the underlying assumption is that investors are:

B. risk averse

(PRACTICE PROBLEM) An investor agreed to sell a warehouse 5 years from now to the tenant who currently rents the space. The tenant will continue to pay $20,000 rent at the end of each year including year five in which he will purchase the building for an additional $150,000. Assuming the investor's required rate of return is 10%, how much is this deal presently worth to the investor who was willing to sell?

C x ((1-(1+r)^-time)/(rate)) = PV C = 20,000 Time = 5 Rate = 10 20,000 x ((1-(1+0.10)^-5)/(0.10)) = 75,815.73539 (Nominal)/((1+rate)^time) = PV Nominal = 150,000 Rate = 0.1 Time = 5 (150,000)/((1+0.10)^5) = 93,138.198459 Add both together = 75,815.73539 + 93,138.198459 = 168,953.93 ANSWER: 168,953.93

Suppose a bank decides to make a mortgage loan to an individual so that they may purchase a home. The homeowner will pay the bank $1,500 per month in mortgage payments for the next 30 years. The bank will collect the mortgage payments at the end of the month. If the borrower does not default on their loan, how much money will the bank have accumulated if they could reinvest the monthly income at an annualized rate of 5% for the entire investment horizon? Suppose a bank decides to make a mortgage loan to an individual so that she may purchase a home. The homeowner will pay the bank $1,500 per month in mortgage payments for the next 30 years. The bank will collect the mortgage payments at the end of the month. What is this promised stream of cash flows worth to the bank today if they could reinvest the monthly income at an annualized rate of 5% for the entire investment horizon?

C) $279,422.43

Assume that an individual puts $10,000 into a savings account that pays 3% interest, with interest being compounded monthly. The individual plans to withdraw the balance in 5 years to buy a car. If he does not make any further deposits over this period, how much will the individual be able to put towards his purchase?

C. $11,616.17

An investor just purchased an office building for $100,000. He knows for certain that he can sell the building for $110,000 in 5 years. Approximately how much does he need to charge in annual rent in order to achieve a 15% annual return on the deal (rounded to the nearest hundred dollars)?

C. $13,500

Suppose a bank decides to make a mortgage loan to an individual so that they may purchase a home. The homeowner will pay the bank $1500 per month in mortgage payments for the next 30 years. The bank will collect the mortgage payments at the end of the month. What is this promised stream of cash flows worth to the bank today if they could reinvest the monthly income at an annualized rate of 5% for the entire investment horizon?

C. $279,422.43

Suppose you own a house that you are renting out to a group of college students for the 10 month academic year. You are charging $1000 per month in rent. You will collect the first rent payment today and then on the 1st of the month each month thereafter. What is the value of this investment opportunity to you today if you could reinvest your income at a rate of 6%?

C. $9,779.06

An investor originally paid $22,000 for a vacant lot 12 years ago. If the investor is able to sell the lot today for $62,000, what would his annual rate of return be on this investment (rounded to the nearest percent)?

C. 9%

Suppose that an industrial building can be purchased today for $2,500,000. If it is expected to produce cash flows of $180,000 for each of the next five years (assume CFs are received at the end of each year) and can be sold at the end of the fifth year for $2,800,000, what is the internal rate of return (IRR) on this investment?

C. 9.20%

When discussing time-value-of-money it is necessary to understand some key terminology. Which of the following terms refers to a fixed amount of money paid or received at the end of every period (i.e. a series of equal lump sums)?

C. Ordinary annuity

Assume that a piece of land is currently valued at $50,000. If this piece of land is expected to appreciate at an annual rate of 5% per year for the next 20 years, how much will the land be worth 20 years from now?

D. $132,664.89

28. Suppose you are starting a Ph.D. program with only $1,000 in your savings account. The university has agreed to waive your tuition, cover all of your living expenses, and pay you an additional stipend of $2,000 at the beginning of each month, as long as you teach one course per semester over the course of five years. If your savings account is able to earn 5.5% per year for the five years that you will be in this program, how much will you have accumulated in your savings account by the end of the program if interest is compounded on a monthly basis?

D. $139,708.76

Suppose you have found a tenant who wishes to rent out your vacation home for the next twelve months. You are charging $800 per month in rent. You will collect the first rent payment today and then on the 1st of the month each month thereafter. What is the value of this investment opportunity to you today if you could reinvest your income at an annual rate of 3% with interest compounded on a monthly basis?

D. $9,469.42

Suppose that a property can generate cash flows of $10,000 per year for eight years and can sell for $80,000 at the end of the investment period. Assuming a discount rate of 10%, what is the present value of this property (Assume end of period cash flows in your calculation)?

D. $90,670

Uncertainty of cash flows can vary significantly across property types. Which of the following property types is often considered to have the most uncertain expected cash flows?

D. Hospitality

(PRACTICE PROBLEM) You are at retirement age and one of your benefit options is to accept an annual annuity of $75,000 for 15 years. The first payment would be received two years from today. What lump sum settlement, if paid today, would have the same present value as the $75,000 annual annuity? Assume a 10 percent annual discount rate.

N = 15 I = 10% PMT = 75,000 FV = 0 PV = ? ANSWER: (570,455.96)

Assume an investment is priced at $5,000 and has the following income stream (year 1, $1,000; year 2, -$2,000; year 3, $3,000; and year 4, $3,000). Would an investor with a required rate of return of 15 percent be wise to invest at a price of $5,000

No, because the investment has a net present value of -$1,954.91

As the level of perceived risk increases,

Values decrease and expected returns increase.

(PRACTICE PROBLEM) You are thinking about purchasing some vacant land. You expect to be able to sell the land 10 years from now for $500,000. a. What is the most you can pay for the land today if your required rate of return is 15 percent?b. What is the expected (annualized) return on this investment over the 10-year holding period if you purchase the land for $170,000?

a.) N = 10 I = 15% PMT = 0 FV = 500,000 PV = ? ANSWER: = 123,592.35 b.) N = 10 I = ? PMT = 0 FV = 500,000 PV = -170,00 ANSWER: 11.39%