Question

Risky Corporation’s bonds are currently selling for $650 and bear a 5% coupon rate and $1,000 par value. If the bonds pay annual interest and have 12 years to maturity, what is the yield to maturity?

Answer 1

Answer:

YTM 10.18%

Explanation:

We can calculate the excel YTM using excel

The YTM will the rate which equals the present value of the bonds and the present value of the maturity

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

Coupon payment 50 (1,000 x 5% = 50)

time 12

$50 \times \frac{1-(1+YTM)^{-12} }{YTM} = PV$

PVc

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

Maturity   1,000.00

time   12.00

$\frac{1000}{(1 + YTM)^{12} } = PV$  

PVm

PV c + PV m = $650.0000

so we got that:

$50 \times \frac{1-(1+YTM)^{-12} }{YTM} + \frac{1000}{(1 + YTM)^{12} } = 650$  

on excel we will enter on A1 any number value

then on any other cell we will enter the formula for present value of the bond:

=PV(A1,12,50)+1,000/power(1+A1,12)

The we use goal seek on that cell to get 650 changing A1

this give us the rate which is

YTM = 0.101828014 = 10.18%

Because of how the formula for present value works is not possible to solve for rate with a given formula. There are formulas which give an approximation result but are not the excet formula.

the excel formula can only be achieve with trial and error, so we use excel to do it more quickly.