Chapter 3 answers.docx

1、Chapter 3 answersCHAPTER 3MEASURING YIELDANSWERS TO QUESTIONS FOR CHAPTER 3(Questions are in bold print followed by answers.)1. A debt obligation offers the following payments:Years from NowCash Flow to Investor1$2,0002$2,0003$2,5004$4,000Suppose that the price of this debt obligation is $7,704. Wha

2、t is the yield or internal rate of return offered by this debt obligation?The yield on any investment is the interest rate that will make the present value of the cash flows from the investment equal to the price (or cost) of the investment.Mathematically, the yield on any investment, y, is the inte

3、rest rate that satisfies the equation:P = where CFt = cash flow in year t, P = price of the investment, and N = number of years. The yield calculated from this relationship is also called the internal rate of return. To solve for the yield (y), we can use a trial-and-error (iterative) procedure. The

4、 objective is to find the interest rate that will make the present value of the cash flows equal to the price. To compute the yield for our problem, different interest rates must be tried until the present value of the cash flows is equal to $7,704 (the price of the financial instrument). Trying an

5、annual interest rate of 10% gives the following present value:Years from NowPromised Annual Payments(Cash Flow to Investor)Present Value of Cash Flow at 10%1$2,000$1,818.182$2,000$1,652.893$2,500$1,878.294$4,000$2,732.05 Present value = $8,081.41Because the present value of $8,081.41 computed using

6、a 10% interest rate exceeds the price of $7,704, a higher interest rate must be used, to reduce the present value. Trying an annual interest rate of 13% gives the following present value:Years from NowPromised Annual Payments(Cash Flow to Investor)Present Value of Cash Flow at 13%1$2,000$1,769.912$2

7、,000$1,566.293$2,500$1,732.634$4,000$2,453.27 Present value = $7,522.10Because the present value of $7,522.10 computed using a 13% interest rate is below the price of $7,704, a lower interest rate must be used, to reduce the present value. Thus, to increase the present value, a lower interest rate m

8、ust be tried. Trying an annual interest rate of 12% gives the following present value:Years from NowPromised Annual Payments(Cash Flow to Investor)Present Value of Cash Flow at 12%1$2,000$1,785.712$2,000$1,594.393$2,500$1,779.454$4,000$2,542.07 Present value = $7,701.62Using 12%, the present value o

9、f the cash flow is $7,701.62, which is almost equal to the price of the financial instrument of $7,704. Therefore, the yield is close to 12%. The precise yield using Excel or a financial calculator is 11.987%.Although the formula for the yield is based on annual cash flows, it can be generalized to

10、any number of periodic payments in a year. The generalized formula for determining the yield iswhere CFt = cash flow in period t, and n = number of periods.Keep in mind that the yield computed is the yield for the period. That is, if the cash flows are semiannual, the yield is a semiannual yield. If

11、 the cash flows are monthly, the yield is a monthly yield. To compute the simple annual interest rate, the yield for the period is multiplied by the number of periods in the year.2. What is the effective annual yield if the semiannual periodic interest rate is 4.3%?To obtain an effective annual yiel

12、d associated with a periodic interest rate, the following formula is used:effective annual yield = (1 + periodic interest rate)m 1where m is the frequency of payments per year. In our problem, the periodic interest rate is a semiannual rate of 4.3% and the frequency of payments is twice per year. In

13、serting these numbers, we have:effective annual yield = (1.043)2 1 = 1.087849 1 = 0.087849 or about 8.785%.3. What is the yield to maturity of a bond?The yield to maturity is the interest rate that will make the present value of the cash flows equal to the price (or initial investment). For a semian

14、nual pay bond, the yield to maturity is found by first computing the periodic interest rate, y, which satisfies the relationship:P = where P = price of the bond, C = semiannual coupon interest (in dollars), M = maturity value (in dollars), and n = number of periods (number of years times 2).It is mu

15、ch easier to compute the yield to maturity for a zero-coupon bond because we can use:.The yield-to-maturity calculation takes into account not only the current coupon income but also any capital gain or loss that the investor will realize by holding the bond to maturity. In addition, the yield to maturity considers the timing of the cash flows.4. What is the yield to maturity calculated on a bond-equivalent basis?For a semiannual pay bond, doubling the periodic interest rate or discount rate (y) gives the yield to maturity, which understates the effective annual yield. The