Question

Cost of debt using both methods​ (YTM and the approximation​ formula)   ​Currently, Warren Industries can sell 20 dash year​, ​$1 comma 000​-par-value bonds paying annual interest at a 11​% coupon rate. Because current market rates for similar bonds are just under 11​%, Warren can sell its bonds for ​$1 comma 060 ​each; Warren will incur flotation costs of ​$20 per bond. The firm is in the 29​% tax bracket.

a.  Find the net proceeds from the sale of the​ bond, Upper N Subscript d.

b.  Calculate the​ bond's yield to maturity​ (YTM​) to estimate the​ before-tax and​ after-tax costs of debt.

c.  Use the approximation formula to estimate the​ before-tax and​ after-tax costs of debt.

Answer 1

a.Net proceeds from the sale of the​ bond :

Current selling price-Flotation cost

ie. 1060-20= 1040 /bond

b.Calculation of the​ bond's yield to maturity​ (YTM​) to estimate the​ before-tax and​ after-tax costs of debt:

We need to use the formula to find the Price/PV of the bond & plu-in all known values.

(PV/Price-Flot.cost)= (Pmt.*(1-(1+r)^-n)/r)+(FV/(1+r)^n)

where, net proceeds = $ 1040/ bond

Pmt.=annual coupon pmt.= 1000*11%= $ 110

r= annual yield/market interest rate= to be found out---??

n=no. of annual coupon periods= 20

FV= Face value of the bond= $ 1000

Now,putting values in the formula,

we get the before-tax yield on the bond as

1040=(110*(1-(1+r)^-20)/r)+(1000/(1+r)^20)=

r= 10.5136%

After-tax cost of the bond= Before-tax cost*(1-Tax rate)

ie. 10.5136%*(1-29%)=

7.46%

ANSWER:

BT cost= 10.51% &

AT cost=7.46%

c.Using the approximation formula to estimate the​ before-tax and​ after-tax costs of debt

Before-tax YTM= ((C+(FV-Price)/n)/((FV+Price)/2)

BT YTM = the annual befor-tax yield to be found out-- ??

c= annual coupon pmt.= 1000*11%=110

price= net proceeds = 1060-20=1040

FV=face value of the bond= $ 1000

So, putting values in the formula,

BT YTM=(110+((1000-1040)/20))/((1000+1040)/2)

10.59%

After-tax cost of the bond= Before-tax cost*(1-Tax rate)

ie. 10.59%*(1-29%)=

7.52%

ANSWER:

BT cost= 10.59% &

AT cost=7.52%