Given Bond Quote Information:

• Coupon Rate = 6.850%
• Maturity = May 2032
• Last Price = 93.231
• Change in Price = 1.650
• Yield = 7.482%

1. Yield to Maturity (YTM) Calculation:

To calculate the Yield to Maturity (YTM), we use the following formula:

$P = \frac{C}{(1 + YTM)^1} + \frac{C}{(1 + YTM)^2} + \dots + \frac{C + F}{(1 + YTM)^n}$

Where:

• $P$ = Current price of the bond (Last Price) = 93.231
• $C$ = Annual coupon payment = Coupon Rate $\times$ Face Value (assumed to be 100) = $6.850 \% \times 100 = 6.850$
• $F$ = Face value (assumed to be 100)
• $n$ = Number of years to maturity = May 2032 - current year
• $YTM$ = Yield to maturity (what we need to calculate)

We will solve for $YTM$, but it typically requires iterative numerical methods, so we can approximate by using the given information.

The bond's quoted yield is $7.482\%$, and since the price is close to par value (around 93), this is approximately the Yield to Maturity.

Thus, the YTM ≈ 7.482%.

2. Current Yield Calculation:

The Current Yield is calculated using the formula:

$\text{Current Yield} = \frac{\text{Annual Coupon Payment}}{\text{Current Price}} \times 100$

Where:

• Annual Coupon Payment = $6.850$ (from the coupon rate)
• Current Price = $93.231$

$\text{Current Yield} = \frac{6.850}{93.231} \times 100 = 7.347\%$

Summary:

• Yield to Maturity (YTM) ≈ 7.482%
• Current Yield = 7.347%

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Would you like further details or clarification?

Related Questions:

1. What factors influence the yield to maturity of a bond?
2. How does bond rating affect its yield and price?
3. How would the YTM change if the bond price increased to par value?
4. What is the difference between nominal yield, current yield, and YTM?
5. How does the time to maturity impact the volatility of a bond's price?

Tip:

The YTM incorporates both interest payments and any gain or loss if the bond is held until maturity, while the current yield only considers the coupon payments in relation to the current bond price.