HW605-2-I-Chapter3 (2)

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Texas A&M University *

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Feb 20, 2024

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Assignment Chapter 3 Real Estate Finance and Investments AGEC 605 Instructor: David J. Leatham Answer the following questions: 1. What is the essential concept in understanding compound interest? 2. What general rule can be developed concerning maximum values and compounding intervals within a year? What is an equivalent annual yield? 3. What does the time value of money (TVM) mean? 4. How does discounting, as used in determining present value, relate to compounding, as used in determining future value? How would present value ever be used? 5. What is an annuity? How is it defined? What is the difference between an ordinary annuity and an annuity due? 6. Why can’t interest factors for annuities be used when evaluating the present value of an uneven series of receipts? What factors must be used to discount a series of uneven receipts? 7. What is the sinking-fund factor? How and why is it used? 8. What is an internal rate of return? How is it used? How does it relate to the concept of compound interest? Answer the following problems: 1. Jim makes a deposit of $12,000 in a bank account. The deposit is to earn interest annually at the rate of 9 percent for seven years. a. How much will Jim have on deposit at the end of seven years? b. Assuming the deposit earned a 9 percent rate of interest compounded quarterly, how much would he have at the end of seven years? c. In comparing (a) and (b), what are the respective effective annual yields? (Hint: Consider the value of each deposit after one year only.) Which alternative is better? 2. Would you prefer making a $25,000 investment that will earn interest at the rate of 7 percent compounded monthly or making the same $25,000 investment at 8 percent compounded annually. ( Hint : Consider one year only.) 3. Suppose you deposit $1,250 at the end of each quarter in an account that will earn interest at an annual rate of 15 percent compounded quarterly. How much will you have at the end of four years? 4. Suppose you deposit $2,500 at the end of year 1, nothing at the end of year 2, $750 at the end of year 3, and $1,300 at the end of year 4. Assuming that these amounts will be compounded at an annual rate of 9 percent, how much will you have on deposit at the end of five years?

5. Suppose you have the opportunity to make an investment in a real estate venture that expects to pay investors $750 at the end of each month for the next eight years. You believe that a reasonable return on your investment should be 17 percent compounded monthly. a. How much should you pay for the investment? b. What will be the total sum of cash you will receive over the next eight years? c. Why is there such a large difference between (a) and (b)? 6. An investor is considering an investment that will pay $2,150 at the end of each year for the next 10 years. He expects to earn an annual return of 18 percent on his investment. How much should he pay today for the investment? How much should he pay if the investment returns are paid at the beginning of each year? 7. An investor can make an investment in a real estate development and receive an expected cash return of $45,000 after six years. Based on a careful study of other investment alternatives, she believes that an 18 percent annual return compounded quarterly is a reasonable return to earn on this investment. How much should she pay for it today? 8. John is considering the purchase of a lot. He can buy the lot today and expects the price to rise to $15,000 at the end of 10 years. He believes that he should earn an investment yield of 10 percent annually on his investment. The asking price for the lot is $7,000. Should he buy it? What is the internal rate of return on the investment if John purchases the property for $7,000 and is able to sell it 10 years later for $15,000? 9. The Dallas Development Corporation is considering the purchase of an apartment project for $100,000. They estimate that they will receive $15,000 at the end of each year for the next 10 years. At the end of the 10 th year, the apartment project will be worth nothing. If Dallas purchases the project, what will be its internal rate of return? If the company insists on a 9 percent return compounded annually on its investment, is this a good investment? 10. A corporation is considering the purchase of an interest in real estate syndication at a price of $75,000. In return, the syndication promises to pay $1,020 at the end of each month for the next 25 years (300 months). If purchased, what is the expected internal rate of return, compounded monthly? How much total cash would be received on the investment? How much is profit and how much is return of capital? 11. An investment in a real estate venture will provide returns at the end of the next four years as follows: year 1, $5,500; year 2, $7,500; year 3, $9,500; year 4, $12,500. An investor wants to earn a 13 percent annual return on her investment. How much should she pay for the investment? Assuming that the investor wanted to earn an annual rate of 13 percent compounded monthly , how much would she pay for this investment? Why are these two amounts different? 12. A pension fund is making an investment of $100,000 today and expects to receive $1,500 at the end of each month for the next five years. At the end of the fifth year, the

capital investment of $100,000 will be returned. What is the internal rate of return on investment?

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