6. Suppose $200 million of Mortgage Backed Bonds (MBB’s) are issued against a $3

Question

6. Suppose $200 million of Mortgage Backed Bonds (MBB’s) are issued against a $300 million pool of mortgages, in denominations of $10,000 for a period of 10 years. The bonds carry a coupon of 8% payable annually. Assume the securities receive the highest possible rating. a. What is the price of the security, assuming the issuer and underwriter agree that the rate of return required to sell the bonds is 9% ? b. At what percent of par value is the price of the security? c. If the required rate of return is also 9% two years after the issue, what is the price of this security, and what is the percent of par value? d. Answer parts a, b, c again, this time assuming the rate of return (i.e., yield to maturity) is 7%.

Explanation / Answer

To compute the intrinsic value/ price of a bond, we discount the cash flows from the bond at the required rate of return. The bond will be have annual coupons of $10000 x 8%, i.e., $800 and also a redeemable amount of par value of $10000.

At 9%

a) Price = $800 x PVIFA (9%, 10) + $10000 x PVIF (9%, 10) = $800 x 6.41765770099 + $10000 x 0.42241080687 = $9358.23

b) Percentage of par value = ($9358.23 / 10000) * 100 = 93.5823%

c) Two yeaars after the issue would mean that 2 coupon payments have been made and their are 8 coupon payments remainings. So, we compute the value using 8 years now instead of 10.

Price = $800 x PVIFA (9%, 8) + $10000 x PVIF (9%, 8) = $800 x 5.53481911463 + $10000 x 0.50186627965 = $9446.52

Percentage of par value = (9446.52 / 10000) * 100 = 94.4652%

At 7%

We use the discount rate of 7% instead of 9%.

a) Price = $800 x PVIFA (7%, 10) + $10000 x PVIF (7%, 10) = $800 x 7.02358154071 + $10000 x 0.5083492921 = $10702.36

b) Percentage of par value = (10702.36 / 10000) * 100 = 107.0236%

c) Two years after the issue would mean that 2 coupon payments have been made and their are 8 coupon payments remainings. So, we compute the value using 8 years now instead of 10.

Price = $800 x PVIFA (7%, 8) + $10000 x PVIF (7%, 8) = $800 x 5.97129850606 + $10000 x 0.58200910453 = $10597.13

Percentage of par value = (10597.13 / 10000) * 100 = 105.9713%

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