The Morgan Corporation has two different bonds currently outstanding. Bond M has
ID: 2773955 • Letter: T
Question
The Morgan Corporation has two different bonds currently outstanding. Bond M has a face value of $30,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $2,400 every six months over the subsequent eight years, and finally pays $2,700 every six months over the last six years. Bond N also has a face value of $30,000 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.
The Morgan Corporation has two different bonds currently outstanding. Bond M has a face value of $30,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $2,400 every six months over the subsequent eight years, and finally pays $2,700 every six months over the last six years. Bond N also has a face value of $30,000 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
Theoritacally current price of the bond is nothing but the present value of interest payments made and the present value of maturity proceeds.
Current price of Bond M:
In the current case Bond M makes no interest payments instead it makes periodic payments as stated, so, the present value of these payments is nothing but the price of the bond.
As the interest rate is semi anually compounding, the present value factor is calculated by using formula 1/(1+i)n
Where i is the interest rate=6%/2 =3% as it is semi annual.
n=the number of half years with in the said period.
so, for the first half year present value factor =1/(1+.03)
For the second half year present value factor=1/(1+.03)2
For the third half year present value factor=1/(1+i)3 so on and so forth.
Therefore current price of Bond M=$32,891.04.
Current price of Bond N:
Current price of bond N is the maturity value of the bond * Present value factor of the 40 the period from the above table.
=$30,000 * 1/(1+.03)40
=$30,000*0.306556841
=$9,196.71.
Therefore, current price of the bond N=$9,196.71..
Number of half years in 20 years tenure Present value factor Payments made Present value of payments made 1 0.970873786 $0.00 2 0.942595909 $0.00 3 0.915141659 $0.00 4 0.888487048 $0.00 5 0.862608784 $0.00 6 0.837484257 $0.00 7 0.813091511 $0.00 8 0.789409234 $0.00 9 0.766416732 $0.00 10 0.744093915 $0.00 11 0.722421277 $0.00 12 0.70137988 $0.00 13 0.68095134 $2,400.00 $1,634.28 14 0.661117806 $2,400.00 $1,586.68 15 0.641861947 $2,400.00 $1,540.47 16 0.623166939 $2,400.00 $1,495.60 17 0.605016446 $2,400.00 $1,452.04 18 0.587394608 $2,400.00 $1,409.75 19 0.570286027 $2,400.00 $1,368.69 20 0.553675754 $2,400.00 $1,328.82 21 0.537549276 $2,400.00 $1,290.12 22 0.521892501 $2,400.00 $1,252.54 23 0.506691748 $2,400.00 $1,216.06 24 0.491933736 $2,400.00 $1,180.64 25 0.477605569 $2,400.00 $1,146.25 26 0.463694727 $2,400.00 $1,112.87 27 0.450189056 $2,400.00 $1,080.45 28 0.437076753 $2,400.00 $1,048.98 29 0.424346362 $2,700.00 $1,145.74 30 0.41198676 $2,700.00 $1,112.36 31 0.399987145 $2,700.00 $1,079.97 32 0.388337034 $2,700.00 $1,048.51 33 0.377026247 $2,700.00 $1,017.97 34 0.3660449 $2,700.00 $988.32 35 0.355383398 $2,700.00 $959.54 36 0.345032425 $2,700.00 $931.59 37 0.334982937 $2,700.00 $904.45 38 0.325226152 $2,700.00 $878.11 39 0.315753546 $2,700.00 $852.53 40 0.306556841 $2,700.00 $827.70 Total $32,891.04