Question

Hagelin Co. wants to issue new 15-year bonds for some much-needed expansion projects. The company currently has 8 percent coupon bonds on the market that sell for $1,090, make semiannual payments, and mature in 15 years. Both bonds have a par value of $1,000. What coupon rate should the company set on its new bonds if it wants them to sell at par? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

YTM 7.02%

Explanation:

we will calcualte the YTM of the current bonds to know the market rate.

Issuing the bonds at this rate will put them at par value.

The YTM is the one which mades the future coupon payment and maturity equal to the market price.

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

Coupon payment: 1,000 x 8%/2 =  40

time 30 (15 years x 2 payment)

$40 \times \frac{1-(1+r)^{-30} }{r} = PV$

PV coupon

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity  1,000.00

time   30.00

$\frac{1000}{(1 + r)^{30} } = PV$  

PV maturity  355.24

PV coupon +  PV maturity = 1,090

For maths reason the only way to solve for rate is with trial and error

we can, however use excel to do it more quickly than by hand:

we write on A1 cell 0.1

en on B1 cell: =PV(A1,30,40)

on C1 cell= 1,000/power(1+A1;1/30)

on D1 =B1+C1

What we are doing is expressing the formulas on excel

then we use goal seek on D1

w e want it on 1090 cahnging the cell A1 which is the rate

this give us the semiannual rate of :

0.035100422

we multiply by 2 to get the annual rate:

0.070200843

YTM = 7.02%

we need to issue the bond at this rate.