Exam 14: The Effects of Time and Risk on Value

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 she should expect to receive assuming interest rates do not change?

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?

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)?

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)

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?

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:

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 recurring period (i.e. a series of equal lump sums)?

Suppose an investor has the opportunity to make an investment that promises to pay her $100,000 5 years from now. How much should this investor be willing to pay today for this investment opportunity if he could otherwise invest his money in an interest bearing account that yields 5% (annual) and compounds interest on a monthly basis?

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?

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?

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?

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?

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?

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?

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?

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?

Which of the following terms refers to a fixed amount of money paid or received at the beginning of every recurring period (i.e. a series of equal lump sums)?

Suppose an investor deposits $5,000 in an interest-bearing account at her local bank. The account pays 2.5% (annual) with interest compounded monthly. If the investor plans on withdrawing the original principal plus accumulated interest at the end of 10 years, what is the total amount that she should expect to receive assuming interest rates do not change?

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?

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?