Question

Jallouk Corporation has two different bonds currently outstanding. Bond M has a face value of $50,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $1,600 every six months over the subsequent eight years, and finally pays $1,900 every six months over the last six years. Bond N also has a face value of $50,000 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?

Answer 1

For Bond N compounded semi annually, current price of the bond N as it does not give any coupon payment, current price =

Face value/(1+ r/2%)^t*2

= $50000 / (1.05)⁴⁰

= $50000 ×0.14

= $ 7000

^​​​​​​​The current price of the bond N is $7000.

Calculating the present value of bond M:

Current price = Present value of all interest received + present value of face value of the bond

Present value of all interest received =

Let the maturity time be 40 years as compounded semiannually and required rate of return be 5%

$ 1600/ (1.05)¹³ + $1600/(1.05)¹⁴​​​​​​......$1600/(1.05)²⁸ + $1900/(1.05)²⁹ +........ + $1900/(1.05)⁴⁰

= 9655.8 + 4294 = $13949.8

Present value of face value= $50000/ (1. 05)⁴⁰

= $ 7000

So current price of bond M = $20949.8