Question 1

Given the opportunity to invest in one of the three bonds listed below,which would you purchase? Assume an interest rate of 7%.

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Question 2

Suppose that a bond that will mature in two years has a face value of $1000 and 20% coupon rate.The one year spot market interest rate is 13% and the expected second period's forward rate is 12%.According to the expectation hypothesis,the two year spot rate is:
A) 11.50%
B) 9.12%
C) 12.74%
D) 7.00%

Accepted Answer

The expectation hypothesis suggests that the future long-term interest rates can be approximated by the current short-term interest rates and the expected future short-term rates. To find the two-year spot rate under the expectation hypothesis, we use the formula that equates the present value of cash flows from holding two one-year bonds sequentially to the present value of holding one two-year bond. Given a 20% coupon rate on a $1000 face value bond, the annual coupon payment is $200. The one-year spot rate is 13%, and the expected second period's forward rate is 12%.The calculation involves finding the rate $r$ that satisfies the equation:$$1000 = \frac{200}{(1+0.13)} + \frac{1200}{(1+r)^2}$$However, the above calculation is not directly needed for this question. Instead, we use the relationship between spot and forward rates to find the two-year spot rate. The formula to link one-year spot rate ($S_1$), the two-year spot rate ($S_2$), and the one-year forward rate one year from now ($F_{1,2}$) is:$$(1 + S_1)(1 + F_{1,2}) = (1 + S_2)^2$$Given $S_1 = 0.13$ and $F_{1,2} = 0.12$, we solve for $S_2$:$$(1 + 0.13)(1 + 0.12) = (1 + S_2)^2$$$$1.13 \times 1.12 = (1 + S_2)^2$$$$1.2656 = (1 + S_2)^2$$Taking the square root of both sides:$$1 + S_2 = \sqrt{1.2656}$$$$S_2 = \sqrt{1.2656} - 1$$$$S_2 \approx 0.1274 \text{ or } 12.74\%$$Therefore, according to the expectation hypothesis, the two-year spot rate is approximately 12.74%.

Question 3

A number of publicly traded firms pay no dividends yet investors are willing to buy shares in these firms.How is this possible? Does this violate our basic principle of stock valuation? Explain.

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Question 4

Given the following set of spot rates:

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Question 5

Suppose that a bond that will mature in three years is now traded at $99.83.The annual coupon payment is $5.635.Its yield to maturity is
A) 3.42%
B) 5.10%
C) 5.69%
D) 7.20%

Accepted Answer

To find the yield to maturity, we need to solve for the interest rate that makes the present value of the bond's cash flows equal to the current market price of $99.83. Using a financial calculator or spreadsheet, we get a yield to maturity of 5.69%. Therefore, the correct answer is (C).

Question 6

The expectations hypothesis states that the forward rate over second period is:
A) set to the spot rate expected to prevail over the second period.
B) equal to the first period spot rate.
C) always greater than the spot rate in period one.
D) always greater than the period 3 forward rate.

Accepted Answer

The expectations hypothesis states that the forward rate for the second period is equal to the expected spot rate for that period. Therefore, choice A is correct. Choice B is incorrect because it suggests that the forward rate for the second period is equal to the first period spot rate, which is not necessarily true under the expectations hypothesis. Choice C is incorrect because the forward rate for the second period can be lower than or equal to the spot rate in period one, depending on expectations about future interest rates. Choice D is incorrect because there is no general relationship between the second period forward rate and the third period forward rate under the expectations hypothesis.

Question 7

A forward rate prevailing from period three through to period four can be:
A) readily observed in the market place.
B) extracted from high coupon bonds.
C) extracted from spot rates with 2 and 3 year maturities.
D) extracted from spot rates with 3 and 4 years to maturity.

Accepted Answer

A forward rate prevailing from period three through to period four can be extracted from spot rates with 3 and 4 years to maturity using the formula: (1 + r4)^4 = (1 + r3)^3 * (1 + f34). Therefore, the correct answer is D, which matches the maturities required for the calculation. A, B and C do not provide the correct combinations of spot rates to extract the forward rate.

Question 8

The liquidity preference hypothesis explains that the 2^nd year forward rates are set higher than the expected spot rate over year two because: A) of a downward sloping yield curve. B) of long term rates being greater than short term rates. C) investors must be induced to buy the riskier two year bond. D) two year bonds are less risk than one years bonds when rates are higher.

Accepted Answer

The liquidity preference hypothesis states that investors have a preference for more liquid shorter-term investments, which leads to a higher demand for shorter-term bonds. To induce investors to buy longer-term bonds, these bonds must offer a higher yield, resulting in higher forward rates than expected spot rates. Therefore, the correct answer is C, as investors must be induced to buy the riskier two-year bond.

Question 9

In the above problem,the yield to maturity of the 2 year bond is:
A) 21%.
B) 18%.
C) 12%.
D) 11%.

Accepted Answer

Using the formula for yield to maturity:

$1,000 = \frac{\$50}{(1+i)^1} + \frac{\$1,050}{(1+i)^2}$

Simplifying, we get:

$1,000 = \frac{\$50}{(1+i)} + \frac{\$1,050}{(1+i)^2}$

$0 = \frac{\$50}{(1+i)} + \frac{\$1,050}{(1+i)^2} - \$1,000$

Solving for i using a financial calculator or spreadsheet, we get i = 17.93%.

Therefore, the yield to maturity of the 2 year bond is 18%.

Question 10

Show that a firm with earnings of $10,000 a year in perpetuity would be better off paying all earnings in dividends rather than investing 25% of its earnings (also in perpetuity)in projects earning 14% if its discount rate is 15%.

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Question 11

The market rate of interest on 2 year bonds is 6.25% while the rate on a one year bond maturing on one year is 5.50%.The forward rate on a one year bond one year from now is 6.5%.The liquidity premium to induce investors to hold the 2 year bond is:
A) 0.250%.
B) 0.005%.
C) 0.125%.
D) 0.500%.

Accepted Answer

The answer of The market rate of interest on 2...

Question 12

Suppose that there are three zero coupon bonds with maturity date 1 year,2 year and 3 year respectively.The current price of the 1 year,2 year and 3 year bonds respectively are $826.45,$718.18 and $640.66 respectively.The yield to maturity of the first year bond is:
A) 21%.
B) 18%.
C) 12%.
D) 11%.

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Question 13

In the above example,the price of the bond is
A) $1121
B) $1000
C) $1325
D) $1200

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Question 14

What can you deduce about forward rates of interest if the liquidity-preference hypothesis of the term structure is correct?
A) The forward rate is less than investor's expectations of next years one year interest rate.
B) The forward rate is greater than investor's expectations of next years one year interest rate.
C) The forward rate is equal to investor's expectations of next years one year interest rate.
D) The forward rate is equal to the risk-free interest rate.

Accepted Answer

The liquidity-preference hypothesis suggests that investors demand a premium for holding longer-term bonds, implying that forward rates are higher than what investors actually expect future short-term rates to be. This is because investors perceive longer-term investments as riskier and demand a higher return for committing their money for a longer period.

Question 15

Explain why some bond investors are subject to liquidity risk and/or default risk.How does each of these risks affect the yield of a bond?

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The answer of Explain why some bond investors are subject...

Question 16

Suppose that an investor disagrees with market expectations and feels that the forward rate prevailing in the market is higher than what it should be,then the investor can make profit by:
A) selling a bond now and buying it up later.
B) selling a bond now
C) buying a bond now
D) buying a bond now and selling it later.

Accepted Answer

If the investor feels that the forward rate is too high, they expect interest rates to decrease in the future. Buying a bond now at the higher interest rate and selling it later when interest rates decrease will result in a profit for the investor.

Question 17

Which of the following amounts is closest to the present value of a bond with coupon payment of $80 and a face value of $1,000? Interest payments are made at the end of each of 2 years,and the bond matures in 2 years.The spot interest rate for the first year is 10%,and the spot interest rate for the second year is 12%.
A) $910
B) $934
C) $949
D) $1,000

Accepted Answer

To calculate the present value of the bond, we need to calculate the present value of each coupon payment and the face value, and then add them up. Using the formula for present value of a future payment, we get:

PV of first coupon payment = $80/1.10 = $72.73
PV of second coupon payment = $80/((1.10)(1.12)) = $63.51
PV of face value = $1000/((1.10)(1.12)) = $797.19

Thus, the present value of the bond is:

PV = $72.73 + $63.51 + $797.19 = $933.43

The closest amount to this is $934, so the correct answer is B.

Question 18

Term structure refers to:
A) how interest rates vary over different structures of bonds.
B) how interest rates vary over different structures of corporate securities.
C) how interest rates vary over time with otherwise identical bonds.
D) the maturity dates of a bond issue.

Accepted Answer

Term structure refers to how interest rates vary over time with otherwise identical bonds. It is also referred to as the yield curve, which shows the relationship between bond yields and maturities.

Question 19

Which of the following statements is true?
A) The spot rate is a weighted average of the yields to maturity.
B) The spot rate is always higher than the yield to maturity.
C) The yield to maturity is a weighted average of spot rates.
D) The yield to maturity is always higher than the spot rate.

Accepted Answer

The yield to maturity is calculated as a weighted average of the spot rates for each coupon payment date. Therefore, statement C is true. Statements A, B, and D are false.

Question 20

Given r₁ = .050 and r₂ = .054,what can you deduce about investor's expectations of future short-term interest rates if the expectations hypothesis is correct? A) Investors expect future short-term rates to be greater than current short-term rates. B) Investors expect future short-term rates to be less than current short-term rates. C) Investors expect future short-term rates to be equal to current short-term rates. D) Investors expect future short-term rates to be higher than current forward rates.

Accepted Answer

The expectations hypothesis states that long-term interest rates are a predictor of future short-term interest rates. If the current long-term interest rate (represented by r₁) is lower than the future long-term interest rate (represented by r₂), then investors are expecting future short-term rates to be greater than current short-term rates. Therefore, A is the correct choice.

Quiz 6: How to Value Bonds and Stocks

Given the opportunity to invest in one of the three bonds listed below,which would you purchase? Assume an interest rate of 7%.

Suppose that a bond that will mature in two years has a face value of $1000 and 20% coupon rate.The one year spot market interest rate is 13% and the expected second period's forward rate is 12%.According to the expectation hypothesis,the two year spot rate is:

A number of publicly traded firms pay no dividends yet investors are willing to buy shares in these firms.How is this possible? Does this violate our basic principle of stock valuation? Explain.

Given the following set of spot rates:

Suppose that a bond that will mature in three years is now traded at $99.83.The annual coupon payment is $5.635.Its yield to maturity is

The expectations hypothesis states that the forward rate over second period is:

A forward rate prevailing from period three through to period four can be:

The liquidity preference hypothesis explains that the 2nd year forward rates are set higher than the expected spot rate over year two because:

In the above problem,the yield to maturity of the 2 year bond is:

Show that a firm with earnings of $10,000 a year in perpetuity would be better off paying all earnings in dividends rather than investing 25% of its earnings (also in perpetuity)in projects earning 14% if its discount rate is 15%.

The market rate of interest on 2 year bonds is 6.25% while the rate on a one year bond maturing on one year is 5.50%.The forward rate on a one year bond one year from now is 6.5%.The liquidity premium to induce investors to hold the 2 year bond is:

Suppose that there are three zero coupon bonds with maturity date 1 year,2 year and 3 year respectively.The current price of the 1 year,2 year and 3 year bonds respectively are $826.45,$718.18 and $640.66 respectively.The yield to maturity of the first year bond is:

In the above example,the price of the bond is

What can you deduce about forward rates of interest if the liquidity-preference hypothesis of the term structure is correct?

Explain why some bond investors are subject to liquidity risk and/or default risk.How does each of these risks affect the yield of a bond?

Suppose that an investor disagrees with market expectations and feels that the forward rate prevailing in the market is higher than what it should be,then the investor can make profit by:

Term structure refers to:

Which of the following statements is true?

Given r1 = .050 and r2 = .054,what can you deduce about investor's expectations of future short-term interest rates if the expectations hypothesis is correct?

The liquidity preference hypothesis explains that the 2^nd year forward rates are set higher than the expected spot rate over year two because:

Given r₁ = .050 and r₂ = .054,what can you deduce about investor's expectations of future short-term interest rates if the expectations hypothesis is correct?