Assume the City of Tulsa, Oklahoma issued bonds 3 years ago as follows: 8.75% $150 million at 8.75%. The original maturity was 25 years, par value is $1,000, with interest paid annually. The original credit rating was A1/A+ by Moody's and S&P, respectively. If the rating agencies downgrade the credit ratings to A3/A-, investors will want a 9.10% return. What would happen to the price per bond if that happens today? (6 decimal places).

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TomShelby TomShelby · Answer 1 · 2019-07-30T15:45:27+02:00

Answer:

The bond will decrease by:

$27.019642

Their market value will be:

$972.980358

Explanation:

The price of the bond will decrease in order to increase the yield of the bond to 9.10%

We will calculate the present value of the annuity using the 9.10 rate compounding semiannually

[tex]C \times \frac{1-(1+r/2)^{-timex2} }{rate/2} = PV\\[/tex]

c= 1000 x 8.75%/2 = 1000 x 0.0875/2 = 43.75

time = 25 years - 3 = 22 years

rate 9.10% = 0.091

[tex]4375 \times \frac{1-(1+0.091/2)^{-22\times2} }{0.091/2} = PV\\[/tex]

PV = 825.798092

Then we calculate the present value of the redem of the bond:

[tex]\frac{Principal}{(1 + rate)^{time} } = PV[/tex]

Face value = 1,000

rate = 0.091

time = 22

[tex]\frac{1,000}{(1 + 0.91)^{22} } = PV[/tex]

PV = 147,182266

We add both to get the current PV at the new yield to maturity

825.798092 + 147,182266 = 972.980358

1000 - 972.980358 = ↓27.019642