Answer to Question #199626 in Economics for Kamlesh Pandey

Question

Please explain the below calculation of Pretax cost of Debentures ?

WACC as per book value weights

Book value of Equity & Retained Earnings = Rs.15 crores+ Rs.20 crores =Rs.35 crores

Book Value of preference Shares = Rs. 1 crores

Book Value of Debentures =Rs. 10 crores

Book value of Term loan = Rs.12.5 crores

Cost of Equity = Next year Dividend/Share price + growth rate =3.6/40+0.07 = 0.1600 or 16.00%

Cost of Preference Shares = Dividend/ market price of Preference Share = Rs.100*12%/Rs.75 = 0.1600 or 16.00%

Pretax cost of Debentures(r) is given by (assuming annual coupon)

11.5/r*(1-1/(1+r)^6)+100/(1+r)^6 =80

Solving r =0.1708 or 17.08%

Answer 1

annual coupon=11.5

maturity=6 years

the nominal price of Debentures=100

discount rate (cost of Debentures)=r

Sold price=80

Formula:

$annual\ coupon/(1+r)+ annual\ coupon/(1+r)^2...annual\ coupon/(1+r)^6+the\ nominal\ price/(1+r)^6= sold\ price$

$annual\ coupon*(\frac{1}{1+r}+...+\frac{1}{(1+r)^6})+the\ nominal\ price/(1+r)^6= sold\ price$

sum of geometric progression: $\frac{\frac{1}{1+r}*(1-\frac{1}{1+r}^6)}{1-\frac{1}{1+r}}=\frac{\frac{1}{1+r}*(1-\frac{1}{1+r}^6)}{\frac{1+r-1}{1+r}}=\frac{1-\frac{1}{1+r}^6}{r}$

$\frac{11.5*(1-\frac{1}{1+r}^6)}{r}+\frac{100}{\frac{1}{1+r}^6}=80$

r=0.1708 or 17.08%