Question

Mobius is issuing 16-year, semiannual coupon, bonds for $938 to fund new projects. The expected yield to maturity on these bonds is 9%. What is the coupon rate on these bonds.

Answer 1

HI

Bond: A bond is debt instrument issued by government or corporate to raise funds. A holder of the bond receives periodic payment known as coupon payment and par value at the end of maturity. Usually par value of bond is $1,000

Price of bond: Price of bond is present value of all its future cash flows discounted by the interest rate known as “Yield to maturity”. If coupon is paid annually and coupon percentage is 8% , then at $1,000 par value, periodic coupon payment is $80.

Price of bond = PV(coupon payment) + PV(par value)

Semi Annual Payment: Most bonds pay semiannual coupon payment to its holder. So, if coupon rate is shown as 8%. Then semiannual coupon payment will be 1000*8%/2= $40

Yield to Maturity: Yield to maturity is total return that bond holder will be getting over the course of bond.

Given:

Coupon Rate =?

Years left to maturity t = 16 years

Current selling price P =$938

YTM=9%

Since face value F is not given, we assume that it is $1,000.

Also, since company making semiannual payment so per period coupon payment, so semiannual YTM = 9%/2 =4.5%

Period to Maturity = 16*2 = 32

Formula for present value:

Present Value P= C*(1-(1/(1+YTM)) ^t)/YTM + 1000*(1/(1+YTM) ^t)

938 = C*(1-(1/(1+0.045)) ^32)/0.045 + 1000*(1/(1+0.045) ^32)

938 = C*16.79 + 244.5

C        = $41.31

Since this is semiannual coupon payment so

And Coupon Rate = 41.31*2/1000 = 8.26%