Question

Jallouk Corporation has two different bonds currently outstanding Bond a face value of $20,000 and matures in 20 yearsThe bond makes no payments for the first six yearsthen pays $ 1300 every six months over the subsequent eight yearsand finally pays $1,600 every six months over the last six years. Bond N also has a face value of 20,000 and a maturity of yearsmakes no coupon payments over the of the bond. The required return on both these bonds is 8 percent compounded semiannually What is the current price of Bond M and Bond N? Do round intermediate calculations and round your answers to 2 decimal places

Answer 1

Answer : Calculation of Current Price

Current price of the bond is sum of present value of Coupon payment and maturity value received over the life of Bond

Current Price of Bond M

It can be calculated using PV function of Excel :

For the purpose of calculation of present value we will first calculate the present value of  $1,600 every six months over the last six years to year 14 (20 - 6)

=PV(rate,nper,pmt,fv)

where rate is the rate of interest per period i.e 8% / 2 = 4% (Given that the rate is compounded semiannually)

nper is the number of periods i.e 6 * 2 = 12 (Multiplies by 2 as semiannual compounding)

pmt is the periodic payment i.e 1600

fv is the face value or future value i.e 20000

=PV(4%,12,-1600,-20000)

Present value at year 14 is 27508.06

Now we will calculate present value of $ 1300 every six months over the subsequent eight years to year 6

=PV(rate,nper,pmt,fv)

where rate is the rate of interest per period i.e 8% / 2 = 4% (Given that the rate is compounded semiannually)

nper is the number of periods i.e 8 * 2 = 16 (Multiplies by 2 as semiannual compounding)

pmt is the periodic payment i.e 1300

fv is the face value or future value i.e 27508.06 (calculated above)

=PV(4%,16,-1300,-27508.06)

Present value at year 6 is 29834.76

Now we will calculate present value of Bond at year 0 or current Bond Price

=PV(rate,nper,pmt,fv)

where rate is the rate of interest per period i.e 8% / 2 = 4% (Given that the rate is compounded semiannually)

nper is the number of periods i.e 6 * 2 = 12 (Multiplies by 2 as semiannual compounding)

pmt is the periodic payment i.e 0

fv is the face value or future value i.e 29834.76 (calculated above)

=PV(4%,12,0,-29834.76)

Present value at year 0 is 18634.70

Current Bond Price of Bond M is 18634.70

Calculation of Current Bond Price of Bond N

=PV(rate,nper,pmt,fv)

where rate is the rate of interest per period i.e 8% / 2 = 4% (Given that the rate is compounded semiannually)

nper is the number of periods i.e 20 * 2 = 40 (Multiplies by 2 as semiannual compounding)

pmt is the periodic payment i.e 0 (as no coupon payments)

fv is the face value or future value i.e 20000

=PV(4%,40,0,-20000)

Current Bond Price of N is 4165.78