Question

assume that an investor is willing to pay $908.32 for a bond (pv 1000, coupon rate 8%, maturing in 20 years)

what is the investor's required rate of return, k_d?

(bond issuer's viewpoint) what if the net price after flotation costs is $850, what then will k_d be?

what is the after-tax k_d assuming tax rate of 30%?

Answer 1

a)

 present value of annuity:

$P\frac{1-(1+k_d)^{-n}}{k_d}$

where P is periodic payment,

k_d is rate of return,

n is number of periods.

 present value of the bond:

$P\frac{1-(1+k_d)^{-n}}{k_d}+1000\cdot (1+k_d)^{-n}$

$80\cdot\frac{1-(1+k_d)^{-20}}{k_d}+1000\cdot (1+k_d)^{-20}=908.32$

Using Bisection mehtod on online calculator https://atozmath.com/, we get:

$k_d=0.09=9\%$

b)

$80\cdot\frac{1-(1+k_d)^{-20}}{k_d}+1000\cdot (1+k_d)^{-20}=850$

$k_d=0.0973=9.73\%$

c)

after-tax rate:

$0.08\cdot (1-0.3)=0.056=5.6\%$