HKM needs to raise 10 million for nancing an investment. The company plans to is
ID: 2633184 • Letter: H
Question
HKM needs to raise 10 million for nancing an investment. The company plans to issue ve-year
bonds with a face value of $1000, and a coupon rate of 6.5% (annual payments). The following
table summarizes the yield to maturity for ve year corporate bonds with the same maturity and
coupon rate (annual coupons) for various ratings of the bonds by a well known rating agency:
Rating AAA AA A BBB BB
Yield 6.20% 6.30% 6.50% 6.90% 7.50%
HKM has asked the same rating agency to give a rating for its bonds (and paid for it) but has
not yet received the rating.
(a) If the rating turns out to be AA what will the price of the bonds be?
(b) How many bonds will the company need to issue (if you nd a fraction, round to the nearest
whole number since the company cannot issue fractions of bonds)
(c) Finally when the company sells the bonds after they have been rated, the price of each bond
is $959.54.
(i) What is the yield to maturity on HKM bonds? (If you think that you are clever in the
way you are answering this question, explain what you do and why).
(ii) What is the likely rating of the bonds? Are they junk bonds?
Explanation / Answer
a)price of bond if AA is given=interest x pvaif@6.30 for five years + pv of maturity of bond
pviaf for five years =0.940+0.8884+0.8325+0.7381+0.7367=4.1313
price of bond= (1000 x 6.5%) x 4.1313=268.5 + 736.7 =1005.2
(present value of maturity= 1000 x disc factor @ 6.30% for 5th year =1000 x 0.7367=736.7)
b) no of bonds to be issued = 10m/1005.2=9948 bonds
c) YTM= [C+(f-p)/n]/(f+p)/2
C=interest, f=face vaue, p=price of bond
[65+(1000-959.54)/5]/1000+959.54/2
73/979.77=7.45%
The yield to maturity formula is used to calculate the yield on a bond based on its current price on the market. The yield to maturity formula looks at the effective yield of a bond based on compounding as opposed to the simple yield which is found using the dividend yield formula.
d)yes it is a junk bond according to standard and poor rating
the rating will be BB
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