Question 1

If the nominal rate is 4.5% and the inﬂation rate is 1.8%, determine the real rate.

Accepted Answer

The answer of If the nominal rate is 4.5% and...

Question 2

Ajax Corporation issued 10,000 units of $1,000 face value bonds that mature in 20 years and have a 4% coupon rate that is paid semi-annually. If the bonds were sold at 96.5% of their face value,
Calculate the yield to maturity on the date of the issue.

Accepted Answer

The yield to maturity is the annual rate of return an investor can expect to receive if they hold the bond until maturity. It is calculated using the following formula:YTM = (C + (FV - PV) / N) / ((FV + PV) / 2)where:C = the annual coupon paymentFV = the face value of the bondPV = the present value of the bondN = the number of years to maturityIn this case, the annual coupon payment is $40 (4% of $1,000), the face value of the bond is $1,000, the present value of the bond is $965 (96.5% of $1,000), and the number of years to maturity is 20. Plugging these values into the formula, we get:YTM = (40 + (1000 - 965) / 20) / ((1000 + 965) / 2)= (40 + 35 / 20) / ((1000 + 965) / 2)= (40 + 1.75) / ((1965) / 2)= 41.75 / 982.5= 0.0425= 4.25%Therefore, the yield to maturity on the date of the issue is 4.25%.

Question 3

ABC Corporation has 4-year, 5% annual coupon bonds outstanding. Given a 6.5% yield to maturity, determine the duration of these bonds.

Accepted Answer

To calculate the duration of a bond, we use the formula:

Duration = (1 + (1 / y)) * ((PV of all future cash flows) - (Face value / (1 + y)^n)) / (PV of bond * y)

where y represents the yield to maturity, n represents the number of periods, and PV represents the present value.

First, we need to calculate the present value of the bond, which is the sum of the present values of all the coupon payments and the face value:

PV of bond = (50 / (1 + 0.065)^1) + (50 / (1 + 0.065)^2) + (50 / (1 + 0.065)^3) + (1,000 / (1 + 0.065)^4) 
PV of bond = 1,754.25

Next, we need to calculate the present value of all the future cash flows weighted by their time until payment. We can break this down into two parts: the present value of the coupon payments and the present value of the face value:

PV of coupon payments = (1 / (1 + 0.065)^1) * 50 + (2 / (1 + 0.065)^2) * 50 + (3 / (1 + 0.065)^3) * 50 
PV of coupon payments = 132.91

PV of face value = (4 / (1 + 0.065)^4) * 1,000 
PV of face value = 743.80

So the present value of all future cash flows is:

PV of all future cash flows = PV of coupon payments + PV of face value
PV of all future cash flows = 876.71

Now we can plug in all the values into the duration formula:

Duration = (1 + (1 / 0.065)) * ((876.71) - (1,000 / (1 + 0.065)^4)) / (1,754.25 * 0.065) 
Duration = 2.90

Therefore, the duration of the bond is 2.90 years, which corresponds to answer choice C.

Question 4

The outstanding bonds of Jacksen Global Freight carry an 8% coupon and have a current market price of $1,054. These semiannual bonds mature in 20 years and have a face value of $1,000. What
Is the current annual yield on these bonds?

Accepted Answer

The current annual yield is calculated as the annual coupon payment divided by the current market price. The annual coupon payment is 8% of the face value, which is $80. The current market price is $1,054. Thus, the current annual yield is ($80 / $1,054) * 100 = 7.48%.

Question 5

If the nominal rate is 5.5%, and the real rate is 1.5%, determine the inﬂation rate.

Accepted Answer

The Fisher equation relates nominal rates, real rates, and inflation: (1 + nominal rate) = (1 + real rate) * (1 + inflation rate). Solving for the inflation rate gives approximately 3.94%.

Question 6

A bond that pays interest annually yields an 8.5% rate of return. The inﬂation rate for the same period is 4.6%. What is the actual real rate of return on this bond?

Accepted Answer

The real rate of return can be calculated by subtracting the inflation rate from the bond's rate of return. Therefore, the real rate of return on this bond is 8.5% - 4.6%, which equals 3.9%. However, since the bond pays interest annually, we need to use the annual compound interest formula to calculate the actual real rate of return. This formula is (1 + real rate of return)^1 = 1 + (nominal rate of return - inflation rate)^1. Plugging in the numbers, we get (1 + real rate of return)^1 = 1 + (0.085 - 0.046)^1, which simplifies to (1 + real rate of return)^1 = 1.039. Solving for the real rate of return, we get 1 + real rate of return = 1.0373. Subtracting 1 from both sides, we get the real rate of return to be 0.0373, or 3.73%. Therefore, the best choice is B.

Question 7

Which one of the following bonds has the greatest interest rate risk?

Accepted Answer

Zero-coupon bonds have higher interest rate risk compared to coupon bonds of the same maturity because they do not pay interest until maturity. Among the options, the 20-year, zero-coupon bond (C) has the longest duration, making it the most sensitive to changes in interest rates.

Question 8

If investors require a 7% nominal return and the expected inﬂation rate is 3%, what is the expected real return?

Accepted Answer

Real return = (1 + nominal return) / (1 + inflation rate) - 1 
Real return = (1.07 / 1.03) - 1 = 0.0388 or 3.88%

Question 9

The yield to maturity on a bond is currently 6.48%. The real rate of return is 2.87%. What is the rate of inﬂation?

Accepted Answer

The Fisher Effect states that the nominal interest rate is equal to the real interest rate plus the expected inflation rate.
Therefore, Nominal Interest Rate = Real Interest Rate + Inflation Rate
In this case, we can use the Fisher Effect formula to solve for the inflation rate:
6.48% = 2.87% + Inflation Rate
Inflation Rate = 6.48% - 2.87%
Inflation Rate = 3.61%
Therefore the correct answer is B.

Question 10

Baker's Men's Wear has a 5.5%, semiannual coupon bond outstanding with a current market price of $978.90. The bond has a par value of $1,000 and a yield to maturity of 5.76%. How many years is It until this bond matures?

Accepted Answer

The correct answer is A because the bond has a yield to maturity of 5.76%, which is greater than the coupon rate of 5.5%. This means that the bond is selling at a discount, and the number of years until maturity can be calculated using the following formula:Number of years until maturity = (Par value - Current market price) / (Coupon payment * (1 - (1 + Yield to maturity / 2)^(-2 * Number of years until maturity)))Plugging in the given values, we get:Number of years until maturity = (1000 - 978.90) / (55 * (1 - (1 + 0.0576 / 2)^(-2 * Number of years until maturity)))Solving for the number of years until maturity, we get:Number of years until maturity = 11.10 years

Question 11

ABC Corporation has 3-year, 7% annual coupon bonds outstanding. Given an 8.5% yield to maturity, determine the duration of these bonds.

Accepted Answer

The answer of ABC Corporation has 3-year, 7% annual coupon...

Question 12

Micalah's Crafts needs $225,000 today to purchase some new equipment. They are planning on issuing 10-year bonds with a 6% coupon rate and semi-annual interest payments. The current
Market rate of interest is 6.5%. How many bonds must Micalah's Crafts sell to raise the money they
Need?

Accepted Answer

To find the number of bonds needed, calculate the present value of a bond using the market rate (6.5%) as the discount rate. The bond's coupon rate is 6%, so it pays $30 every six months. The present value of these payments and the face value (assumed $1,000) must equal the market price. Solving this, the price is less than $1,000, so more than 225 bonds are needed. 234 bonds will cover the $225,000 needed.

Question 13

Ajax Corporation issued 10,000 units of $1,000 face value bonds that mature in 20 years and have a 4% coupon rate that is paid semi-annually. If the bonds were sold at 96.5% of their face value,
Calculate the yield to maturity at the end of year 8.

Accepted Answer

Step 1: Calculate the present value of the bond using the given information.

Coupon payment per period = 4% * $1,000 * 0.5 = $20
N = 20 years * 2 = 40 semi-annual periods
i/y = ?
FV = $1,000

Using the present value of an annuity formula:

PV of annuity = $20 * [1 - 1/(1 + i/y)^N] / (i/y) = $20 * [1 - 1/(1 + i/y)^40] / (i/y)
PV of face value = $1,000 * 0.965 = $965

PV of bond = PV of annuity + PV of face value = $20 * [1 - 1/(1 + i/y)^40] / (i/y) + $965

Step 2: Use a financial calculator or trial and error method to find the yield to maturity (IRR) that makes the present value of the bond equal to the selling price.

Selling price = $1,000 * 0.965 = $965
PV of bond = PV of annuity + PV of face value = $20 * [1 - 1/(1 + i/y)^40] / (i/y) + $965
Solve for i/y = 4.38%

Therefore, the yield to maturity at the end of year 8 is 4.38%, which is closest to choice C (4.38%).

Question 14

Ajax Corporation issued 10,000 units of $1,000 face value bonds that mature in 20 years and have a 4% coupon rate that is paid semi-annually. If the bonds were sold at 103.5% of their face value,
Calculate the yield to maturity at the end of year 4.

Accepted Answer

Step 1: Calculate the price of the bond
The bonds were sold at 103.5% of their face value, so the price per bond is:

Price per bond = $1,000 × 1.035 = $1,035

Since there are 10,000 bonds, the total price of the bonds issued is:

Total price of bonds = $1,035 × 10,000 = $10,350,000

Step 2: Calculate the annual coupon payment
The coupon rate is 4%, which is paid semi-annually. Therefore, the annual coupon payment is:

Annual coupon payment = $1,000 × 4% × 2 = $80

Step 3: Calculate the yield to maturity
We can use trial and error or a financial calculator to find the yield to maturity. Using trial and error, we find that a yield of approximately 3.71% gives a price close to the actual price of the bond:

N = 16 (since there are 20 years to maturity and coupons are paid semi-annually, there are 2 × 20 = 40 semi-annual periods over the life of the bond, and 4 years have passed, so there are 2 × 4 = 8 semi-annual periods remaining)
I/Y = 3.71% (guess)
PMT = $80 (semi-annual coupon payments)
FV = $1,000 (face value at maturity)
PV = -$1,035 (negative since this is a cash outflow)
Solve for I/Y = 3.71%

Therefore, the yield to maturity at the end of year 4 is approximately 3.71%. The closest answer choice is D, 3.71%.

Question 15

Calculate the duration of an 8% coupon bond that makes annual coupon payments that is currently priced at $950 and has three years left to maturity.

Accepted Answer

To calculate the duration of the bond, we need to use the formula:

Duration = (Present Value of Future Cash Flows / Bond Price) x (Weighted Average Time to Receive Cash Flows)

The present value of future cash flows for an 8% coupon bond with three years left to maturity that makes annual coupon payments is:

PV = (0.08 x 1000) / (1 + r) + (0.08 x 1000) / (1 + r)^2 + (0.08 x 1000 + 1000) / (1 + r)^3

where r is the required rate of return or yield to maturity.

Using trial and error, we find that the yield to maturity is approximately 9.7312%. Plugging this rate into the formula above, we get:

PV = (0.08 x 1000) / (1 + 0.097312) + (0.08 x 1000) / (1 + 0.097312)^2 + (0.08 x 1000 + 1000) / (1 + 0.097312)^3 = 950

The duration is then:

Duration = (950 / 950) x [(1 x 1) + (2 x 1) + (3 x 1)] = 2.8 years

Therefore, the best choice is C) 2.8 years.

Question 16

This morning, Marty bought a 4% coupon bond at par value. The bond pays semi-annual interest and has twenty years to maturity. By what percentage will the price of Marty's bond change if
Market interest rates rise by 1.5% tonight?

Accepted Answer

When market interest rates rise, bond prices fall. The bond's duration and the change in interest rates can be used to estimate the price change. A 1.5% increase in rates significantly impacts a long-term bond like this, resulting in an approximate 18.06% decrease in price.

Question 17

Ajax Corporation issued 10,000 units of $1,000 face value bonds that mature in 20 years and have a 4% coupon rate that is paid semi-annually. If the bonds were sold at 96.5% of their face value,
Calculate the yield to maturity at the end of year 4.

Accepted Answer

The answer of Ajax Corporation issued 10,000 units of $1,000...

Question 18

Ajax Corporation issued 10,000 units of $1,000 face value bonds that mature in 20 years and have a 4% coupon rate that is paid semi-annually. If the bonds were sold at 103.5% of their face value,
Calculate the yield to maturity at the end of year 10.

Accepted Answer

Step 1: Calculate the annual coupon payment:
Coupon rate = 4%
Face value = $1,000
Annual coupon payment = Coupon rate x Face value = 4% x $1,000 = $40
Semi-annual coupon payment = $40/2 = $20

Step 2: Calculate the semi-annual yield to maturity after 10 years using the bond pricing formula:
N = 20 x 2 = 40 (number of semi-annual periods)
PV = -$1,035 (cost of the bond)
PMT = $20 (semi-annual coupon payment)
FV = $1,000 (face value of the bond)
Using a financial calculator or Excel, we can solve for the semi-annual yield to maturity (YTM) to be 1.789%

Step 3: Convert the semi-annual yield to maturity to an annual yield to maturity:
Yield to maturity = 2 x Semi-annual yield to maturity = 2 x 1.789% = 3.578%

Therefore, the yield to maturity at the end of year 10 is 3.58%, which is closest to option B) 3.58%.

Question 19

Ajax Corporation issued 10,000 units of $1,000 face value bonds that mature in 20 years and have a 4% coupon rate that is paid semi-annually. If the bonds were sold at 103.5% of their face value,
Calculate the yield to maturity on the date of the issue.

Accepted Answer

The answer of Ajax Corporation issued 10,000 units of $1,000...

Question 20

Ajax Corporation issued 10,000 units of $1,000 face value bonds that mature in 20 years and have a 4% coupon rate that is paid semi-annually. If the bonds were sold at 103.5% of their face value,
Calculate the yield to maturity at the end of year 8.

Accepted Answer

The yield to maturity (YTM) calculation involves determining the interest rate that equates the present value of future cash flows (coupon payments and face value at maturity) to the bond's current price. Given the bond's price at 103.5% of face value, semi-annual coupon payments, and the remaining 12 years to maturity, the YTM is approximately 3.64%.

Quiz 7: Interest Rates and Bond Valuation

If the nominal rate is 4.5% and the inﬂation rate is 1.8%, determine the real rate.

Ajax Corporation issued 10,000 units of $1,000 face value bonds that mature in 20 years and have a 4% coupon rate that is paid semi-annually. If the bonds were sold at 96.5% of their face value, Calculate the yield to maturity on the date of the issue.

ABC Corporation has 4-year, 5% annual coupon bonds outstanding. Given a 6.5% yield to maturity, determine the duration of these bonds.

The outstanding bonds of Jacksen Global Freight carry an 8% coupon and have a current market price of $1,054. These semiannual bonds mature in 20 years and have a face value of $1,000. What Is the current annual yield on these bonds?

If the nominal rate is 5.5%, and the real rate is 1.5%, determine the inﬂation rate.

A bond that pays interest annually yields an 8.5% rate of return. The inﬂation rate for the same period is 4.6%. What is the actual real rate of return on this bond?

Which one of the following bonds has the greatest interest rate risk?

If investors require a 7% nominal return and the expected inﬂation rate is 3%, what is the expected real return?

The yield to maturity on a bond is currently 6.48%. The real rate of return is 2.87%. What is the rate of inﬂation?

Baker's Men's Wear has a 5.5%, semiannual coupon bond outstanding with a current market price of $978.90. The bond has a par value of $1,000 and a yield to maturity of 5.76%. How many years is It until this bond matures?

ABC Corporation has 3-year, 7% annual coupon bonds outstanding. Given an 8.5% yield to maturity, determine the duration of these bonds.

Micalah's Crafts needs $225,000 today to purchase some new equipment. They are planning on issuing 10-year bonds with a 6% coupon rate and semi-annual interest payments. The current Market rate of interest is 6.5%. How many bonds must Micalah's Crafts sell to raise the money they Need?

Ajax Corporation issued 10,000 units of $1,000 face value bonds that mature in 20 years and have a 4% coupon rate that is paid semi-annually. If the bonds were sold at 96.5% of their face value, Calculate the yield to maturity at the end of year 8.

Ajax Corporation issued 10,000 units of $1,000 face value bonds that mature in 20 years and have a 4% coupon rate that is paid semi-annually. If the bonds were sold at 103.5% of their face value, Calculate the yield to maturity at the end of year 4.

Calculate the duration of an 8% coupon bond that makes annual coupon payments that is currently priced at $950 and has three years left to maturity.

This morning, Marty bought a 4% coupon bond at par value. The bond pays semi-annual interest and has twenty years to maturity. By what percentage will the price of Marty's bond change if Market interest rates rise by 1.5% tonight?

Ajax Corporation issued 10,000 units of $1,000 face value bonds that mature in 20 years and have a 4% coupon rate that is paid semi-annually. If the bonds were sold at 96.5% of their face value, Calculate the yield to maturity at the end of year 4.

Ajax Corporation issued 10,000 units of $1,000 face value bonds that mature in 20 years and have a 4% coupon rate that is paid semi-annually. If the bonds were sold at 103.5% of their face value, Calculate the yield to maturity at the end of year 10.

Ajax Corporation issued 10,000 units of $1,000 face value bonds that mature in 20 years and have a 4% coupon rate that is paid semi-annually. If the bonds were sold at 103.5% of their face value, Calculate the yield to maturity on the date of the issue.

Ajax Corporation issued 10,000 units of $1,000 face value bonds that mature in 20 years and have a 4% coupon rate that is paid semi-annually. If the bonds were sold at 103.5% of their face value, Calculate the yield to maturity at the end of year 8.