Question

Benson biometrics, inc. has outstanding $1,000 face value 8% coupon bonds that make semiannual payments and have fourteen years remaining to maturity. if the current price for these bonds is $1,118.74, what is the annualized yield to maturity?

Answer 1

YTM 6.681%

Step-by-step explanation:

The YTM be the rate at wich we discount the coupon payment and maturity to arrive at hte curernt price of the bonds.

he coupon payment present valeu will be of a single annuity

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

C 40.000 (1,000 x 8%/2)

time 28 (14 years x 2 payment er year)

YTM

Then, the maturity will be a lump sum:

`(Maturity)/((1 + rate)^(time) ) = PV`

Maturity 1,000.00

time 28.00

This two at he YTM should give the market price of 1,118.74

we write on excel on A1 as follow

=PV(A2;28;40)+100/power(1+A2;28)

Then, on A2 wetpe a numebr between 0 and 1

last, we use goal seek to get the value of 1,118.74 changing A2 to gethte YTM

0.033405627

Now, this will be the semiannual rate so we multiply by 2 and get the annualized yield to maturity at 6.681%