Question

A 10-year $1,000 bond sells for $980, and the flotation costs are 2% of the par value. The coupon rate is 8%. Put in the values of the variables and calculate the before-tax cost of capital from this bond?

Coupon dollars (I) =   

Flotation costs in dollars (FC) =   

term (n) =   

Price (P) =   

Net proceeds (N_p) =   

r_d =   %

Answer 1

As the question is silent, on whether the bond pays annual or semi-annual coupons,

we shall calculate for both cases .

Before-tax cost of the bond=

Net proceeds=(( $ Coupon)*(1-(1+r)^-n)/r)+(FV/(1+r)^n)

Where,

Net proceeds= Selling price-Flotation cost,ie. 980-(1000*2%)= 960

Coupon amt.= (1000*8%)= $ 80 , if annual or   80/2= $ 40 ,if semi-annual coupon

n= no.of coupon periods, ie. 10 for annual & 10*2= 20 for semi-annual coupon bonds

So, substituting the values,

For annual coupon bonds

960=(80*(1-(1+r)^-10)/r)+(1000/(1+r)^10

Solving for r, we get the annual before-tax cost, r as:

8.61%

For semi-annual coupon bonds

960=(40*(1-(1+r)^-20)/r)+(1000/(1+r)^20

Solving for r, we get the annual before-tax semi-annual cost, r as:

4.3023%

Converting,

The annual before tax cost =

(1+4.3023%)^2-1=

8.79%

Before-tax cost of capital of this bond is its yield that equals the present net proceeds , to the present value of its future--- coupon +principal-at-maturity -- cash flows

	Coupons
	Annual	Semi-annual
Coupon dollars (I) =1000*8%=	80	40
Flotation costs in dollars (FC) =(1000*2%) =	20	20
term (n) =    10	10	10
Price (P) = 980	980	980
Net proceeds (N_p) =   980-20=	960	960
rd =   %   semi-annual		4.30%
Annual	8.61%	8.79%