Question

Assume that you have the following information:- Market Info:- Real interest rate = 2.0%; Expected inflation = 4.0%; Rm = 12.0%; Tax = 30.0%. Com. Stock info:- Par value = $1.0 ; Market value (price) = ?? ; Beta = 1.60 ; No. of outstanding shares = 1,000,000.0 ; EPS $3.0 ; pay-out ratio = 30.0%; Growth in EPS & Dividends = 5.0% ; Preferred Stock info:- Par value = $100.0; Dividend per share = 10.0%; Rp=8.0%; No. of outstanding shares = 100,000.0; Price = ???? Bonds info:- Par value = $1,000.0; Coupon interest = 4.0% ; YTM = 6.0%; Time to maturity = 20 years ; No. of bonds = 100.0; Price = ???

1- Calculate the WACC using historical weights in the capital structure.

2 - Calculate the WACC using market weights in the capital structure.

when you calculate write the formulas and equation not just a table

show your calculations step by step

Answer 1

Answer to the question:

1) Calculation of WACC using Historical Weight in capital structure:

Particulars	Rate	Historical Value	Weight	Weight * Rate
Debt	2.80%	$100,000	0.009	0.0252
Equity	18.61%	$1,000,000	0.090	1.6749
Preference share	8%	$10,000,000	0.901	7.208
				8.9081

Hence WACC using historical value weight = 8.9081% i.e. approximately equal to 8.91%

2) Calculation of WACC using market value Weight in capital structure:

Particulars	Rate	Market Value	Weight	Weight * Rate
Debt	2.80%	$75,000	0.0038	0.01064
Equity	18.61%	$6,950,000	0.3560	6.62516
Preference share	8%	$12,500,000	0.6402	5.1216
				11.7574

Hence WACC using market value weight = 11.7574% i.e. approximately equal to 11.76%

Note 1: Calculation of cost of equity and market value of the equity share

Par Value = $1

Beta = 1.60         

Number of share = 1,000,000

EPS = $3.0

DPS = 30% of EPS = $0.90

Growth = 5%

Real Risk free Interest rate = 2%

Inflation = 4%

Therefore nominal Risk Free interest rate(RF) = 1 + Real / 1 + Inflation

                                                                                    = 1.02 / 1.04

                                                                                    = 0.9808%

Market rate(RM) = 12%

Tax = 30%

Cost of equity as per CAPM = RF + (RM – RF)*Beta

                                                        = 0.9808 + (12-0.9808)*1.60

                                                        = 18.61%

Market price per share = D1 / Re-growth

                                                = $0.90* 1.05 / 0.1861 – 0.05

                                                = 0.945 / 0.1361

= $6.95 per share

Value of equity share for historical weight = 1,000,000 * $1 per share

    = $1,000,000

Value of equity share for market weight = 1,000,000 * $6.95 per share

    = $6,950,000

Note 2: Calculation of market value of the preference share

Par value = $100

Dividend per share = 10% i.e. $10 per share

Rate of preference share = 8%

Number of shares = 100,000

Rate of preference share = Dividend / Market price

        0.08 = $10 / Market price

Therefore market price = $125 per share

Value of preference share for historical weight = 100,000 * $100 per share

    = $10,000,000

Value of preference share for market weight = 1,000,000 * $125 per share

    = $12,500,000

Note3: Calculation of market value of the Debt

Par Value = $1000

Coupon = 4%

YTM = 6%

Time to maturity = 20 years

Number of bonds = 100

Cost of debt = Interest (1-tax)

                        = 4% (1-.30)

                        =2.80%

YTM = Interest + (Face value – Market Price) /20

                      (Face Value + Market Price)/2

0.06 = 40 + (1000 – X) /20

                (1000+X)/2

On solving the above we get that X = $750 per bond

Value of bonds for historical weight = 100 * $1000 per bond

    = $100,000

Value of preference share for market weight = 100 * $750 per share

    = $75,000