Seventeen years ago, Rickety Airlines sold an $800 million bond issue to finance
ID: 2760812 • Letter: S
Question
Seventeen years ago, Rickety Airlines sold an $800 million bond issue to finance the purchase of new jet airliners. These bonds were issued in $1,000 denominations with an original maturity of 20 years and a coupon rate of 6.00%. (Show all calculations.)
Determine the value today of one of these bonds to an investor who requires a 12.00% rate of return on these securities.
Determine the value today of one of these bonds to an investor who requires a 4.00% rate of return on these securities.
Determine the value today of one of these bonds to an investor who requires a 15.00% rate of return on these securities.
Describetherelationshipbetweenaninvestorsrequiredreturnandvaluation of a bond.
Explanation / Answer
Solution:
Value of Bond as on today is calculated by following romular:
Value of Bond as on today = Interest x PVIFA(Required rate of return, n) + Maturity Value x PVIF(Required return, n)
Case 1
Investor’s required rate of return = 12%
Coupon Interest = $1,000 x 6% = $60
No. of payments (n) = 20
No of payments left = 3 (Hence Present Value Interest Factor is taken for 3 years only)
Value of Bond as on today = $60 x PVIFA (12%, 3) + $1,000 x PVIF (12%, 3)
= ($60 x 2.40183) + ($1,000 x 0.71178) = $144.11 + $711.78 = $855.89 or $855.90
Case 2
Investor’s required rate of return = 4%
Number of payments left = 3 (Hence Present Value Interest Factor is taken for 3 years only)
Value of Bond as on today = $60 x PVIFA (4%, 20) + $1,000 x PVIF (4%, 20)
= ($60 x 2.775) + ($1,000 x 0.889) = $166.50 + $889 = $1,055.50
Case 3
Investor’s required rate of return = 15%
No of payments left = 3 (Hence Present Value Interest Factor is taken for 3 years only)
Value of Bond as on today = $60 x PVIFA (15%, 3) + $1,000 x PVIF (15%, 3)
= ($60 x 2.2832) + ($1,000 x 0.6575) = $137 + $657.50 = $794.50
Describe the relationship between an investors required return and valuation of a bond:
Some basic rules which should be remembered with regard to bonds are:
Hence, we can say that there is inverse relationship between Market Value of Bond as on today and investors required rate of return. When Required rate of return exceeds coupon rate, it means the investor wants higher return and that is the reason bonds sell at discount and vice-versa.
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