Answer to Question #189701 in Financial Math for sanny

Question

Priyo Prangon Group has the following capital structure, which it considers optimal:

Mortgage Bonds, ($1000 par) $ 30,000,000

Preferred stock, ($100 par) $ 25,000,000

New Common stock ($40 par) $ 50,000,000

Retained earnings $ 30,000,000

$ 135,000,000

Company issued l,000 tk; 8.5%, 15-year bond whose net proceeds are Tk. 955.The tax rate is

35%. Company has preferred stock that pays a $15 dividend per share and sells for $150 per share in

the market. Company’s stock is $165. The dividend to be paid at the end of the coming year is $18

per share and is expected to grow at a constant annual rate of 6% and its flotation cost is 4%. Assume

the Government Treasury bill rate (risk free rate) is 7%. The Abul Khair Group stock’s beta

coefficient (β) is 1.5 and the rate of return on the market portfolio is 12%

Answer 1

calculate the weighted average cost of capital

he weighted average cost of capital is the overall capital of the company based on the weights. The main objective of the company is to reduce the cost of capital to a certain level where the shareholders could maximize the value. Higher the value of shareholders more profitability will be there. The amount is raised through internal sources or the external sources and will select the source that decreases the value.

$cost\space of \space debt\space capital=\frac{Face\space value \space(1-tax\space value)+\frac{Face\space value-issue\space price}{maturity\space period}}{\frac{Face\space value+Issue\space price}{2}}$

$=\frac{\$1000\times 8.5\%(1-3.5\%)+\frac{\$1000-\$955}{15}}{\frac{\$1000+\$955}{2}}$

$=\frac{\$55.25+\$3}{\$977.5}$

$=5.95\%$

$Cost\space of\space preference\space capital=\frac{Dividend}{Market price}\times 100$

$=\frac{\$15}{\$150}\times100$

$=10\%$

$Cost \space Equity Capital(DDM \space method)$

$\frac{Dividend\space for\space next\space year}{market\space }+growth\space rate.$

$\frac{\$18}{\$165-\$40\times4\%}+6\%$

$=\frac{\$18}{\$163.4-\$40\times4\%}+6\%$

$=17.02\%$

$Cost\space retained \space earnings$

$=\frac{Dividend\space\space\space year}{market\space price}+Growth\space rate$

$=\frac{\$18}{\$165}+6\%$

$=16.91\%$

Calculation of weighted average cost of capital;

$=cost\space of\space equity\times weights+cost\space of\space Retained\space \space earnings\times weights$

$=17.02\%\times \frac{50}{135}+10\%\times\frac{25}{135}+5.95\%\times \frac{30}{135}+16.91\%\times \frac{30}{135}$

$=6.3037\%+1.8519\%+1.3222\%+3.7578\%$

$=13.2356\%$