Please provide a step by step solution for this problem. Thank you! The I Corpor
ID: 2620450 • Letter: P
Question
Please provide a step by step solution for this problem.
Thank you!
The I Corporation has an obligation to pay $1 million in 10 years. The want to invest money now that it will be sufficient to meet this obligation. The purchase of a zero- coupon bond would provide a solution; but such zeros are not available in the exact required maturity now. Instead the I Corporation is planning to select from the 3 corporate bonds shown below. The prices of bonds are given as percent of par. COUPON RATE(%)MATURITY(YRS)PRICE 30 10 20 YIELD(%) BOND1 6 BOND211 BOND39 69.04 113.1 100.00 Discuss how the I Corporation will choose and what is going to ultimately the bond portfolio of their choice,Explanation / Answer
Zero coupon Bond Value = F/ (1+r)^t
F= Face value of Bond= $1,000,000
r= Rate of Yield = 9%
t= time to maturity = 10years
Therefore Zero coupon Bond value at present = 1,000,000/ (1+0.09)^10
= $422,410.81
This ZCB is not available in the market hence; we need to construct a portfolio which has maturity value of $1,000,000 after 10 years.
BOND#1
Coupon Rate = 6%
Maturity =30 Years
Price (p) = $69.04
Yield =9%
PVIF (9%, 30) = 0.0754
PVAF (9%,30) = 10.2737
Therefore Present Value (PV) = 69.04 = Coupon Amt* PVAF (9%,30) + Redemption Amount * PVAF (9%,30)
BOND#2
Coupon Rate = 11%
Maturity =10 Years
Price (p) = $113.1
Yield =9%
PVIF (9%, 10) = 0.4224
PVAF (9%, 10) = 6.4177
Therefore Present Value (PV) = Coupon Amt* PVAF (9%,30) + Redemption Amount * PVAF (9%,30)
BOND#3
Coupon Rate = 9%
Maturity =20 Years
Price (p) = $100
Yield =9%
PVIF (9%, 20) = 0.1784
PVAF (9%, 20) = 9.1285
Therefore PV = Coupon Amt* PVAF (9%, 20) + Redemption Amount * PVAF (9%, 20)
Now there is two options for the investor to choose, they are such as;
Option
Price
PV
1
69.04
69.1822
2
113.1
112.8347
3
100
100
Total
422410.807
422410.807
Alternative -1
Therefore, 69.04*x+113.1*(1-x)= 69.1822*x+112.8347 *(1-x)
Alternative -2
Alternatively, we can purchase Bond#3 which has same yield rate for the same maturity period.
Option
Price
PV
1
69.04
69.1822
2
113.1
112.8347
3
100
100
Total
422410.807
422410.807
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