1) Las Paletas Corporation has two different bonds currently outstanding. Bond M
ID: 2708618 • Letter: 1
Question
1)
Las Paletas Corporation has two different bonds currently outstanding. Bond M has a face value of $10,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $1,200 every six months over the subsequent eight years, and finally pays $1,500 every six months over the last six years. Bond N also has a face value of $10,000 and a maturity of 20 years; it makes no coupon payments over the life of the bond. The required return on both these bonds is 6 percent compounded semiannually.
What is the current price of bond M and bond N? (Round your answers to 2 decimal places. (e.g., 32.16))
2)
A Japanese company has a bond outstanding that sells for 92 percent of its
Las Paletas Corporation has two different bonds currently outstanding. Bond M has a face value of $10,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $1,200 every six months over the subsequent eight years, and finally pays $1,500 every six months over the last six years. Bond N also has a face value of $10,000 and a maturity of 20 years; it makes no coupon payments over the life of the bond. The required return on both these bonds is 6 percent compounded semiannually.
Explanation / Answer
This is really just a net present value problem, simply discount all the bond payments and the redemption of the bond itself at maturity to a present value with the required rate of return which they conveniently provided as the nominal rate of 8% per annum compounded semi-annually which means that it's really 4% every six months.
As bond N pays no coupons, this is simple. As you know the future value equation is FV = PV * R^T therefore the amount of money you would have to save at a rate of 4% every six months such that you would have $29,500 in 48 six month periods (24 years) would be PV = $29,500 / 1.04^48 which is $4,489.75
Therefore the current price of bond N could be no more than $4,489.75 or you would not meet the required rate of 8% per annum compounded semi-annually.
With bond M, the process is similar but you must also consider all of the coupon payments as well. it's as if you were depositing money into a savings account at that 8% compounded semi-annually (4% per six months) rate in order to make each of the coupon payments and adding them up with what it would take to save up for the face value in 24 years (48 six month periods). Hence it is:
PV = $29,500 / 1.04^48 + $2,100 / 1.04^15 + $2,100 / 1.04^16 + $2,100 / 1.04^17 + ... + $2,100 / 1.04^34 + $2,700 / 1.04^35 + $2,700 / 1.04^36 + $2,700 / 1.04^37 + ... + $2,700 / 1.04^48
You can see that these are summations of finite geometric sequences and is really:
PV = $29,500 / 1.04^48 + $2,100 * ( summation of the term ( 1 / 1.04 )^n for n from 15 to 34 ) + $2,700 * ( summation of the term ( 1 / 1.04 )^k for k from 35 to 48 )
Applying the summation of a finite geometric sequence equation gives you:
PV = $29,500 / 1.04^48 + $2,100 * ( ( 1 - ( 1 / 1.04 )^35 ) / ( 1 - 1 / 1.04 ) - ( 1 - ( 1 / 1.04 )^15 ) / ( 1 - 1 / 1.04 ) ) + $2,700 * ( ( 1 - ( 1 / 1.04 )^49 ) / ( 1 - 1 / 1.04 ) - ( 1 - ( 1 / 1.04 )^35 ) / ( 1 - 1 / 1.04 ) )
PV = $28,487.32
Therefore bond M current price must be no more than $28,487.32 in order to give you the required return of 8% per annum compounded semi-annually.
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