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4. (4 points)
(a) Assume that a one year bond that has no interest coupon payment with a maturity value (face value) of $1,000 sold for $900. Show the interest rate that this bond will pay when it matures.
(b) If the prices of similar bonds are selling next month for $950, show the interest rate that these bonds pay when they mature.

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Paramjeet Chawla
Paramjeet ChawlaLv8
28 Sep 2019

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Related questions

(a) Assume that a one year bond that has no interest coupon payment with a maturity value (face value) of $1,000 sold for $800. What is the interest rate that this bond will pay when it matures? Please show how you got your answer.


(b) If the prices of similar bonds are selling next month for $70, what is the interest rate that these bonds pay now when they mature. Please show how you got your answer.

(c) Please describe the relationship between bond prices and interest rates. Use the numbers above to support your answer.

5. Consider the following bonds that pay annual coupons (the next coupon will be paid in one year). Find the present value of each bond assuming a par value of $1,000 and a relevant interest rate of 4%.

Bond

A

B

C

Coupon rate

3%

4%

5%

Time to maturity

1 year

2 years

3 years

This assignment requires the following knowledge: For k different events, if the probability that each of them happens is p (0 < p < 1) and all events happen independently, the probability that all events happen together is p^k.
1. Five firms, namely A, B, C, D and E, issue discounted bonds with face value $1,000 and maturity 5 years in the market. All firms are pretty risky and each of them has a chance of 0.5 of collapse during the five years (thus bankrupted and can not pay back the bond accordingly). The bonds are all sold at an interest rate of 50% (the value is not surprising due to the extremely high risk of default).
(1) What is the present value of the bond given the interest rate, the face value and the maturity? Hint: we temporarily do not consider the issue of default.
(2) Say now you buy one bond from each of the five firms, what is the total amount you lend out today? Eventually only one firm does not fail and pays back the bond, what is the money you collect back 5 years later? You gain or loss in this case? If more than one firm pays back the bond, will you get more money back?
(3) What is the chance (probability) that you get nothing back assuming that firms fail independently? Together with the answer in (2), is it a good deal to buy one bond from each of the five firms?
(4) Repeat (2) and (3) with the only difference that now you buy 5 bonds from a single firm.
(5) Now we assume that the five firms all have similar businesses in Greece (and those are their only businesses), therefore, all firm fail together if the economy in Greece fails. Will you answer in (3) change?

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