# Valuation of bonds under different interest rates

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? Anna Hegg has been considering investing in the bonds of Atilier Industries. The bonds were issued 5 years ago at their $1000 par value and have exactly 25 years remaining until they mature. They have an 8% coupon interest rate, are convertible into 50 shares of common stock, and can be called at any time at $1080. Moody's rates the bond Aa. Atilier industries, a manufacturer of sporting goods, recently acquired a small athletic-wear company that was in financial distress. As a result of the acquisition, Moody's and other rating agencies are considering a ratings change for Atilier bonds. Recent economic data suggest that expected inflation, currently at 5%pa, is likely to increase to 6% pa.

? Anna remains interested in the Atilier bond but is concerned about inflation, a potential rating change, and maturity risk. To get a feel for the potential impact of these factors on the bond value, she decided to apply the valuation techniques she learned before.

? Requirements:

a) If the price of a common stock into which the bond is convertible rises to $30 per share after 5 years, and the issuer calls the bonds at $1080, should Anna let the bond be called away from her or should she convert it into common stock?

b) For each of the following required returns, calculate the bond's value, assuming annual interest. Indicate whether the bond will sell at a discount, at a premium, or at par value.

1. Required return is 6%

2. Required return is 8%

3. Required return is 10%

c) Repeat the calculations in part (b), assuming that interest is paid semi-annually and that semi-annual required returns are one-half of those shown. Compare and discuss differences between bond values for each required return calculated here and in part b under the annual versus semi-annual payment assumptions.

d) If Anna buys the bond today at its $1000 par value and holds it for exactly 3 years, at which time the required return is 7%, how much of a gain of loss will she experience in the value of the bond (ignoring interest already received and assuming annual interest)?

e) Rework part (d), assuming that Anna holds the bond for 10 years, and sells it when the required return is 7%. Compare your finding to that in part (d), and comment on the bond's maturity risk.

f) Assume that Anna buys the bond at its last price of 98.38, and holds it until maturity. What will her yield to maturity be, assuming annual interest?

g) After evaluating all of the issues raised above, what recommendations would you give Anna with regard to her proposed investment in the Atilier Industries bonds?

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? Anna Hegg has been considering investing in the bonds of Atilier Industries. The bonds were issued 5 years ago at their $1000 par value and have exactly 25 years remaining until they mature. They have an 8% coupon interest rate, are convertible into 50 shares of common stock, and can be called at any time at $1080. Moody's rates the bond Aa. Atilier industries, a manufacturer of sporting goods, recently acquired a small athletic-wear company that was in financial distress. As a result of the acquisition, Moody's and other rating agencies are considering a ratings change for Atilier bonds. Recent economic data suggest that expected inflation, currently at 5%pa, is likely to increase to 6% pa.

? Anna remains interested in the Atilier bond but is concerned about inflation, a potential rating change, and maturity risk. To get a feel for the potential impact of these factors on the bond value, she decided to apply the valuation techniques she learned before.

? Requirements:

a) If the price of a common stock into which the bond is convertible rises to $30 per share after 5 years, and the issuer calls the bonds at $1080, should Anna let the bond be called away from her or should she convert it into common stock?

Annie should convert the bonds. The value of the stock if the bond is converted is:

50 shares x $30 per share = $1,500

while if the bond was allowed to be called in the value would be on $1,080

b) For ...

#### Solution Summary

The solution explains how to find the price of a bond given different required returns.