Select the correct answer:

1. When the interest rate used to calculate the NPV is equal to the IRR it holds that:

1. The initial investment is greater than the present discounted value of the cash flows.

2. The initial investment is equal to the present discounted value of the cash flows.

3. The initial investment is lower than the present discounted value of the cash flows.

4. None of the above.

2. Consider a ten-year annuity and a perpetual bond. Assume that both securities pay an annual coupon of US$ 50, and that the annual yield is 8%. Which of the two securities has the highest price?

1. The annuity.

2. The perpetual bond.

3. They have the same price.

4. None of the above

3. The price of a coupon bond increases when, all else equal:

1. The coupon rate increases.

2. The yield-to-maturity (YTM) increases.

3. The time to maturity increases.

4. None of the above

4. Consider the following bonds:

Bond X: 2-year zero coupon bond, pays $201 at maturity;

Bond Y: 1- year zero coupon bond, pays $10 at maturity;

Bond Z: 2-year, 5% coupon (paid semiannually) bond, face value = $200.

Suppose you construct a portfolio X+Y consisting of (long positions of) Bond X and Bond Y.

If the YTM is the same for all bonds and the portfolio considered, which of the following is true?

1. Price(Z) > Price(X+Y)

2. Price(Z) = Price(X+Y)

3. Price(Z) < Price(X+Y)

4. Cannot determine which price is greater without further information

5. You are offered a perpetual bond paying an annual cash flow of $50. If the annual interest rate is 8%, what is the price you will be willing to pay?

1. $400

2. $550

3. $625

4. $650

6. What is the price of the above perpetual bond if the annual interest rate declines from 8% to 6%?

1. $300.33

2. $670.45

3. $833.33

4. $850.50

7. Consider a bond maturing in 20 years, paying 8% semiannual coupons, with face value of $1,000. Assume the YTM is 6%. Find the bond price.

1. 1231

2. 1231.15

3. 1230.15

4. 1235

8. Consider a bond maturing in 20 years, paying 8% semiannual coupons, with face value of $1,000. Assume the YTM is 10%. Find the bond price.

1. 828.11

2. 830.25

3. 828.41

4. 850

9. Consider a 9% semiannual coupon bond with 20 years to maturity and a face value of $1,000. Assume the YTM is 12%. Calculate the bond price using both Method 1 (Bond Pricing Formula) or Method 2 (Sum of discounted cash flows).

1. 774.31

2. 775

3. 774.1

4. 774

10. Consider a 7% semiannual coupon bond with 30 years to maturity and a face value of US$1,000. Assume that the YTM is 12%;

Calculate the bond price.

1. 596.12

2. 595.96

3. 595.12

4. 595

11. Consider a 7% semiannual coupon bond with 20 years to maturity and a face value of US$1,000. Assume that the YTM is 12%;

Calculate the bond price.

1. 625

2. 623.84

3. 623.16

4. 623.48

12. Consider a zero-coupon bond with face value of US$1,000 and with a YTM of 6%? Using Method 1 (Bond Pricing Formula) calculate the bond price if the bond matures in 10 years and the price if it matures in 20 years.

Hint: In this case the bond pricing formula will reduce to a simple expression. Also, you should apply the formula as if the coupon payment period were semi-annual and therefore frequency of payment = 2, and a semi-annual YTM will be used to discount the cash flow. This is because yields are quoted on a bond-equivalent, rather than effective basis.

1. 10 yr price is 553.68 and 20 yr price is 306.56

2. 10 yr price is 553.68 and 20 yr price is 306.22

3. 10 yr price is 553.11 and 20 yr price is 306.56

4. 10 yr price is 553.11 and 20 yr price is 306.22

13. Suppose that the price of a bond is equal to $900. You know that using a YTM equal to 8% to discount the bond cash flows, you obtain a present value equal to $850. Hence, we can assume that the YTM will definitely be:

1. Higher than 8%

2. Lower than 8%

3. Equal to 8%

4. Cannot determine how large the YTM can be without further information

14. If the semi annual YTM equals to 6.0%, what are the Bond-Equivalent YTM and the Effective annual Yield, respectively?

1. 12.00% and 12.36%

2. 12.00% and 12.26%

3. 12.00% and 12.56%

4. 12.36% and 12.00%

15. What is the YTM of a $100 face value 15-year bond paying 7.5% annual coupons and priced at US$102.45?

1. 7.80%

2. 7.23%

3. 7.32%

4. None of the above.

16. When the face value is higher than the bond price, the bond is trading:

1. At a premium

2. At par

3. At a discount

4. All of the above are possible

5. None of the Above

17. A bond is trading at a premium when:

1. Its coupon rate is lower than the YTM

2. Its coupon rate is equal to the YTM

3. Its coupon rate is higher than the YTM

4. None of the Above

18. Suppose you have a 20-year bond paying 8% semiannual coupon, with face value of US$1,000. Assuming that YTM is 7%, 8% and 9%, calculate the bond price over time, that is, as we approach maturity.

As we approach maturity, what happens to the price of the bond?

Hint: Leaving the maturity date constant, change the settlement date by one year at a time to reflect the passage of time.

1. The bond price converges toward the face value.

2. The bond price diverges from its face value.

3. The bond can converge or diverge depending on whether it is premium or discount.

4. There is no clear pattern in how the bond price moves over time.

19. When comparing the time path of a premium, par and discount bond, the discounted coupon payment is the highest for:

1. Premium bond

2. Par bond

3. Discount bond

4. None of the above, they cross