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1)
1). Kellog Co. issues $100,000 total of bonds with a maturity of 5 years, which pay 3% interest annually. The bond yield to maturity is 3.5%.
What is the price of ONE bond today?
PV of interest payments ?
PV of maturity amount ?
Present price of the bond ?
This bonds sells at a Discount or Premium ?
2). January 2019, Hertz Company issues $1 million of 8% coupon bonds due January 2034, this bonds pay interest semiannually. If the yield to maturity on the bonds is 7%, what is the selling price of the bonds?
PV of interest payments ? PV of maturity amount ?
Present price of the bond ?
3). May, 2019, Aflec Company issues $5 million of bonds which pay $50 interest semiannually on each bond. The bonds are to be redeemed in May, 2029. If the yield to maturity on these bonds is 9%, what is the selling price of the bonds?
PV of interest payments ?
PV of maturity amount ?
Present price of the bond ?
Expert Solution
1). Computation of the price of one bond:-
PV of interest payments = C*((1-1/(1+rate)^n)/rate)
Here,
C = Coupon payment = $1,000*3% = 30
PV of interest payments = $30*((1-1/(1+3.5%)^5)/3.5%)
= $30*4.515
= $135.45
PV of maturity amount = Face value / (1+rate)^n
= $1,000/(1+3.5%)^5
= $1,000/1.188
= $841.97
Present price of the bond = PV of interest payments + PV of maturity amount
= $135.45 + $841.97
= $977.42
The bond is selling on discount because the coupon rate is lower than the yield to maturity so the bond price is lower than the face value.
2). Computation of the selling price of bond:-
PV of interest payments = C*((1-1/(1+rate)^n)/rate)
Here,
Rate = 7%/2 = 3.5% (semiannual)
C = Coupon payment = $1,000,000*8%/2= $40,000
n = (2019 - 2034)*2 = 30 periods semiannual)
PV of interest payments = $40,000*((1-1/(1+3.5%)^30)/3.5%)
= $40,000*18.392
= $735,681.82
PV of maturity amount = Face value / (1+rate)^n
= $1,000,000/(1+3.5%)^30
= $1,000,000/2.808
= $356,278.41
Present price of the bond = PV of interest payments + PV of maturity amount
= $735,681.82 + $356,278.41
= $1,091,960.23
The bond is selling at premium because the coupon rate is higher than the yield to maturity so the selling price is higher than the face value.
3). Computation of the selling price of bond:-
PV of interest payments = C*((1-1/(1+rate)^n)/rate)
Here,
n = (May 2019 to May 2029)*2 = 10*2 = 20 periods (semiannual)
Rate = 9%/2 = 4.5% (semiannual)
PV of interest payments = $50*((1-1/(1+4.5%)^20)/4.5%)
= $50*13.008
= $650.40
PV of maturity amount = Face value / (1+rate)^n
= $1,000/(1+4.5%)^20
= $1,000/2.412
= $414.64
Present price of the bond = PV of interest payments + PV of maturity amount
= $650.40 + $414.64
= $1,065.04
The bond is selling at premium because the coupon rate is higher than the yield to maturity so the selling price is higher than the face value.
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