Jallouk Corporation has two different bonds currently outstanding. Bond M has a face value of $20,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $3,000 every six months over the subsequent eight years, and finally pays $3,300 every six months over the last six years. Bond N also has a face value of $20,000 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 10 percent compounded semiannually.

What is the current price of bond M and bond N?

Current Price of Bond M is $28,406.72

Current Price of Bond N is $2,840.91

Explanation:

BOND M

PV of par paid at maturity is:

= Face Value / (1 + r) ^ n

where

r is rate which is 5% because it is semiannually so, in this the rate will be:

= 10 / 2

= 5%

n is number of years which is 40 because it is semiannually, so the number of years got doubled

= 20,000 / (1 + 0.05) ^ 40

= $2,840.92

PV of the 16 will be computed by using the Present Value annuity:

PVOA = PMT [ (1 - {1 / (1 + i) ^ n}) / i ]

where

Pmt is $3,000

n is 16 years

i is 0.05

= 3,000 [ (1 - {1 / (1 + 0.05) ^ 16}) / 0.05]

= 3,000 [ (1 - 0.45811) / 0.05]

= 3,000 * 10.8378

= $32,513.4

PV at t = 0

= 32,513.4 / 1.05 ^ 12

= $18,104.68

PV of the 12 year

where

pmt is $3,300

t = 14

= 3300 [ (1 - {1 / 1.05 ^12) } / 0.05]

= 3300 [ 0.44316 / 0.05]

= $29,248.56

PV at 12

= 29,248.56 / 1.05 ^12

= $7,461.12

PV of Bond M = $2,840.92 + $18,104.68 + $7,461.12

= $28,406.72

BOND N

The Present value of Bond N is computed by using the excel formula of present value:

=-PV (rate, nper, pmt, fv, type)

where

rate is 5%

nper is 40 because it is semiannually, so the number of years got doubled

pmt is 0

Fv is $20,000

Putting the values in the formula:

=-Pv (5%,40,0,20000,0)

= $2,840.91