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Suppose you are offered two bonds
Suppose you are offered two bonds. The first bond is a one-year bond paying a coupon of $100 and an unknown face value at the end of the year. The second bond is a consol (perpetuity) offering an annual payment of $50. Give all answers to two decimals. 1st attempt Part 1 (1 point) See Hint Suppose the interest rate is 10% and the face value of the bond is $800. The most you should be willing to pay for the one-year bond is $
Part 2 (1 point) See Hint Suppose the interest rate is 10%. The most you should be willing to pay for the perpetuity is $ Part 3 (1 point) See Hint , you would be indifferent between buying the one-year Suppose the interest rate is 10%. If the bond had a face value of $ bond and buying the perpetuity. Part 4 (1 point) See Hint %, you would be indifferent between Suppose the face value on the one-year bond is $800. If the interest rate were buying the one-year bond and buying the perpetuity.
Expert Solution
Ans. Price of the one year bond, P1 = (Coupon (C1) + Face Value(F))/(1+interest rate(r))
and price of the consol, P2 = Coupon(C2)/interest rate(r)
a) At r = 10% and F = $800,
P1 = (100+800)/(1+0.10) = $818.1818
b) At r = 10%,
P2 = 50/0.10 = $500
c) At r = 10%,
P1 = (100 + F)/(1+0.10) and P2 = 50/0.10 = $500
For the two bonds to become indifferent,
P1 = P2
=> (100+F)/1.1 = 500
=> P1 = $450
d) At F = $800,
P1 = (100+800)/(1+r) and P2 = 50/r
If the two bonds become indifferent,
P1 = P2
=> 900/(1+r) = 50/r
=> r = 0.058823 or 5.8823%
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