Absalom Motors\'s 9% coupon rate, semiannual payment, $1,000 par value bonds tha
ID: 2637498 • Letter: A
Question
Absalom Motors's 9% coupon rate, semiannual payment, $1,000 par value bonds that mature in 10 years are callable 9 years from now at a price of $1,100. The bonds sell at a price of $1,520, and the yield curve is flat. Assuming that interest rates in the economy are expected to remain at their current level, what is the best estimate of the nominal interest rate on new bonds? Round your answer to two decimal places.
The real risk-free rate is 3%. Inflation is expected to be 3% this year, 5% next year, and then 4% thereafter. The maturity risk premium is estimated to be 0.0007 x (t - 1), where t = number of years to maturity. What is the nominal interest rate on a 7-year Treasury security? Round your answer to two decimal places.
Explanation / Answer
1)
The bond is selling at a large premium, which means that its coupon rate is much higher than the going rate of interest.
Therefore, the bond is likely to be called. The possibility to be called is more likely than to remain outstanding untill maturity.
Thus it is appropriate to calculate Yield to call.
Calculation of yield to call:
NPER =
10
periods
PV =
-1,520
PMT (9% p.a.)=
220
for 6 months
$205.19
$34.20
FV =
1,100
YTC =?
Solve for YTC using Rate
YTC =
12.9715%
12.97% per period or 12.97% x 2 = 25.943 p.a.
This would be close to the going rate and Absalom Motors would have to pay this rate on the new bonds.
2)
Treasury securities do not have DRP or LP
r = r* + IP + MRP + DRP + LP.
r = r* + IP + MRP
r* = 0.03.
IP = [0.03 + 0.05 + (4)(0.05)]/7 = 0.04
MRP = 0.0007(6) = 0.0042.
rT7 = 0.03 + 0.04 + 0.0042 = 0.0742 = 7.42%.
1)
The bond is selling at a large premium, which means that its coupon rate is much higher than the going rate of interest.
Therefore, the bond is likely to be called. The possibility to be called is more likely than to remain outstanding untill maturity.
Thus it is appropriate to calculate Yield to call.
Calculation of yield to call:
NPER =
10
periods
PV =
-1,520
PMT (9% p.a.)=
220
for 6 months
$205.19
$34.20
FV =
1,100
YTC =?
Solve for YTC using Rate
YTC =
12.9715%
12.97% per period or 12.97% x 2 = 25.943 p.a.
This would be close to the going rate and Absalom Motors would have to pay this rate on the new bonds.