Question

A 25-year maturity bond with par value $1,000 makes semiannual coupon payments at a coupon rate of 8%.

**a.** Find the bond equivalent and effective
annual yield to maturity of the bond if the bond price is $950.
**(Round your intermediate calculations to 4 decimal places.
Round your answers to 2 decimal places.)**

Bond equivalent yield to maturity | % |

Effective annual yield to maturity | % |

Answer #1

Par Value = $1,000

Current Price = $950

Annual Coupon Rate = 8.00%

Semiannual Coupon Rate = 4.00%

Semiannual Coupon = 4.00% * $1,000

Semiannual Coupon = $40

Time to Maturity = 25 years

Semiannual Period = 50

Let Semiannual YTM be i%

$950 = $40 * PVIFA(i%, 50) + $1,000 * PVIF(i%, 50)

Using financial calculator:

N = 50

PV = -950

PMT = 40

FV = 1000

I = 4.24%

Semiannual YTM = 4.24%

Equivalent YTM = 2 * Semiannual YTM

Equivalent YTM = 2 * 4.24%

Equivalent YTM = 8.48%

Effective YTM = (1 + Semiannual YTM)^2 - 1

Effective YTM = (1 + 0.0424)^2 - 1

Effective YTM = 1.0866 - 1

Effective YTM = 0.0866 or 8.66%

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