Bond value and time--Constant required returns Pecos Manufacturing has just issued a 15-year, 12% coupon interest rate, $1,000-par bond that pays interest annually. The required return is currently 14%, and the company is certain it will remain at 14% until the bond matures in 15 years. a. Assuming that the required return does remain at 14% until maturity, find the value of the bond with (1) 15 years, (2) 12 years, (3) 9 years, (4) 6 years, (5) 3 years, and (6) 1 year to maturity. b. Plot your findings on a set of "time to maturity (x axis)market value of bond (y axis)" axes constructed similarly to Figure 6.5 on page 246. c. All else remaining the same, when the required return differs from the coupon interest rate and is assumed to be constant to maturity, what happens to the bond value as time moves toward maturity? Explain in light of the graph in part b.

Question

Bond value and time--Constant required returns Pecos Manufacturing has just issued a 15-year, 12% coupon interest rate, $1,000-par bond that pays interest annually. The required return is currently 14%, and the company is certain it will remain at 14% until the bond matures in 15 years. a. Assuming that the required return does remain at 14% until maturity, find the value of the bond with (1) 15 years, (2) 12 years, (3) 9 years, (4) 6 years, (5) 3 years, and (6) 1 year to maturity. b. Plot your findings on a set of "time to maturity (x axis)market value of bond (y axis)" axes constructed similarly to Figure 6.5 on page 246. c. All else remaining the same, when the required return differs from the coupon interest rate and is assumed to be constant to maturity, what happens to the bond value as time moves toward maturity? Explain in light of the graph in part b.

Any clue how to start?

Answer 1

Part a

1) 877.2
2) 886.794
3) 901.07
4) 922.2
5) 953.56
6) 982.45

Answer 2

To start solving this problem, we need to use the concept of present value to find the value of the bond at different time points. The formula for calculating the present value of a bond is:

Bond Value = (Coupon Payment x [1 - (1 / (1 + r)^n)]) / r + (Par Value / (1 + r)^n)

Where:
Coupon Payment = Annual coupon interest rate x Par Value
r = Required return
n = Time to maturity in years
Par Value = $1,000 for this bond

Now, let's calculate the values of the bond at different time points:

a. Assuming the required return remains at 14% until maturity:
1. With 15 years to maturity:
Coupon Payment = 0.12 x $1,000 = $120
Bond Value = ($120 x [1 - (1 / (1 + 0.14)^15)]) / 0.14 + ($1,000 / (1 + 0.14)^15)

2. With 12 years to maturity:
Coupon Payment = 0.12 x $1,000 = $120
Bond Value = ($120 x [1 - (1 / (1 + 0.14)^12)]) / 0.14 + ($1,000 / (1 + 0.14)^12)

3. With 9 years to maturity:
Coupon Payment = 0.12 x $1,000 = $120
Bond Value = ($120 x [1 - (1 / (1 + 0.14)^9)]) / 0.14 + ($1,000 / (1 + 0.14)^9)

4. With 6 years to maturity:
Coupon Payment = 0.12 x $1,000 = $120
Bond Value = ($120 x [1 - (1 / (1 + 0.14)^6)]) / 0.14 + ($1,000 / (1 + 0.14)^6)

5. With 3 years to maturity:
Coupon Payment = 0.12 x $1,000 = $120
Bond Value = ($120 x [1 - (1 / (1 + 0.14)^3)]) / 0.14 + ($1,000 / (1 + 0.14)^3)

6. With 1 year to maturity:
Coupon Payment = 0.12 x $1,000 = $120
Bond Value = ($120 x [1 - (1 / (1 + 0.14))]) / 0.14 + ($1,000 / (1 + 0.14))

Now, plot your findings on a graph with "time to maturity" on the x-axis and "market value of the bond" on the y-axis.

c. On the graph, you will notice that as time moves towards maturity, the bond value decreases. This happens because as time passes, the remaining coupon payments become smaller in present value terms, and the discounted value of the par value at maturity also diminishes. As a result, the bond becomes less valuable to investors, leading to a decrease in its market value.

Answer 3

To begin, we can use the formula for the present value of a bond to calculate its value at different time periods:

PV = C × (1 - (1 + r)^-n) / r + M / (1 + r)^n

Where:
PV = Present value of the bond
C = Annual coupon payment
r = Required return rate
n = Time to maturity in years
M = Par (face) value of the bond

For part a, we can plug in the given values and calculate the bond value at different time periods:

(1) With 15 years to maturity:
PV = 120 × (1 - (1 + 0.14)^-15) / 0.14 + 1000 / (1 + 0.14)^15

(2) With 12 years to maturity:
PV = 120 × (1 - (1 + 0.14)^-12) / 0.14 + 1000 / (1 + 0.14)^12

(3) With 9 years to maturity:
PV = 120 × (1 - (1 + 0.14)^-9) / 0.14 + 1000 / (1 + 0.14)^9

(4) With 6 years to maturity:
PV = 120 × (1 - (1 + 0.14)^-6) / 0.14 + 1000 / (1 + 0.14)^6

(5) With 3 years to maturity:
PV = 120 × (1 - (1 + 0.14)^-3) / 0.14 + 1000 / (1 + 0.14)^3

(6) With 1 year to maturity:
PV = 120 × (1 - (1 + 0.14)^-1) / 0.14 + 1000 / (1 + 0.14)^1

For part b, plot the bond value at each time period on a graph with the time to maturity on the x-axis and the market value of the bond on the y-axis.

For part c, analyze the graph from part b. As time moves towards maturity, the bond value moves closer to its face value (par value). This is because, as the bond approaches maturity, there is less uncertainty about receiving the periodic coupon payments and the repayment of the bond's face value. Therefore, the bond value increases and approaches its par value.