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KFA has issued a 100-year coupon bond with par of $1,000, and a 6.50% annual coupon...

KFA has issued a 100-year coupon bond with par of $1,000, and a 6.50% annual coupon paid semi-annually. Calculate its price for each of the following three YTM scenarios: 4.0%, 6.0%, and 8.0%.

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Expert Solution

Face Value = $1,000

Annual Coupon Rate = 6.50%
Semiannual Coupon Rate = 3.25%
Semiannual Coupon = 3.25% * $1,000
Semiannual Coupon = $32.50

Time to Maturity = 100 years
Semiannual Period = 200

If YTM is 4.00%:

Annual YTM = 4.00%
Semiannual YTM = 2.00%

Current Price = $32.50 * PVIFA(2.00%, 200) + $1,000 * PVIF(2.00%, 200)
Current Price = $32.50 * (1 - (1/1.02)^200) / 0.02 + $1,000 / 1.02^200
Current Price = $32.50 * 49.04734 + $1,000 * 0.01905
Current Price = $1,613.09

If YTM is 6.00%:

Annual YTM = 6.00%
Semiannual YTM = 3.00%

Current Price = $32.50 * PVIFA(3.00%, 200) + $1,000 * PVIF(3.00%, 200)
Current Price = $32.50 * (1 - (1/1.03)^200) / 0.03 + $1,000 / 1.03^200
Current Price = $32.50 * 33.24309 + $1,000 * 0.00271
Current Price = $1,083.11

If YTM is 8.00%:

Annual YTM = 8.00%
Semiannual YTM = 4.00%

Current Price = $32.50 * PVIFA(4.00%, 200) + $1,000 * PVIF(4.00%, 200)
Current Price = $32.50 * (1 - (1/1.04)^200) / 0.04 + $1,000 / 1.04^200
Current Price = $32.50 * 24.99020 + $1,000 * 0.00039
Current Price = $812.57

jeff jeffy answered 5 months ago
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