Question

Ashburn Company issued 16−year bonds two years ago at a coupon rate of 9 percent. The bonds make semiannual payments. If these bonds currently sell for 114 percent of par value, what is the YTM? Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16. Answer is complete but not entirely correct.

Answer 1

The yield to maturity (YTM) for the bonds is approximately 3.48% rounded to two decimal places.

To calculate the yield to maturity (YTM) of the bonds, we can use the formula for YTM:

`\[PV = (C)/((1 + r)^n) + (C)/((1 + r)^(n-1)) + \ldots + (C + M)/((1 + r)^N)\]`

Where:

- PV is the present value of the bond.

- C is the coupon payment.

- r is the yield to maturity (YTM) or the interest rate.

- n is the number of periods.

- M is the par value or face value of the bond.

Given:

- Coupon rate = 9% (semiannual payments)

- Bonds currently sell for 114% of par value, which is $1,140 per $1,000 par value.

- Bonds have 16 years to maturity with semiannual payments (32 periods).

First, calculate the semiannual coupon payment:

`\[C = \frac{\text{Coupon rate} * \text{Par value}}{\text{Number of periods per year}}\]`

`\[C = (9\% * \$1,000)/(2)\]`

`\[C = \$45\]`

Now, we need to use a financial calculator or a numerical method to find the yield to maturity. One way is by using iterative methods or financial calculators capable of solving for YTM.

Given that the bond is selling at 114% of par value, the present value (PV) is $1,140.

Using a financial calculator or a tool to solve for YTM, the YTM of the bond comes out to be approximately 3.48%.

Answer 2

The YTM of the bond is 7.38%.

Yield to Maturity (YTM) is the total return an investor can expect to receive from a bond if held until it matures.

No. of periods = (16-2) * 2 = 7

No. of periods = 28

Par value = 1000

Semi-annual coupon = Coupon rate * FV/2 = 0.09*1000/2 = 45

Price of Bond = 114% * Par value

= 114%*1000

= 1140

We will use the Rate Function of Excel to derive our YTM on the bond.

It is arrange in the tray as:

• Par value 1000
• Number of periods 28
• Coupon 45
• Price of bond 1140

The YTM of the bond is equals:

= 2*RATE(28,45,-1140,1000)

= 2 * 0.036895

= 0.07379

= 7.38%