Question

A firm is engaged in the production and packaging of sausages. The possibility of expanding its
production facilities through a total investment of € 1,200,000 with a 5-years duration is being
considered. The characteristics of financing this investment are presented as follows:
i. The 300,000€ is extracted from the company's increase in share capital. The share price is
5€, the current dividend is 0.25€ and the annual growth rate of these shares is estimated
at 8%. The valuation model is this of stable dividend growth.
ii. The € 600,000 is extracted from a 5-year bond loan, with a face value of € 1,000 and an
interest rate of 8% on issue. At the time of issue, the bond price was 1,000 euro.
iii. The rest amount will be covered by a 5-year bank loan with a fixed interest rate of 6%. The
tax rate is 29%.
Α. Considering that the new investment belongs to the same risk category as the existing firm’s assets
and that the market is in equilibrium, calculate:

A1. The cost of the equity.
Α2. The pre-tax cost of the bond loan.
Α3. The Weighted Average Cost of Capital of the investment (WACC).
Β. In the above investment, at the beginning of the third year, the share price is € 3, the dividend of
the current year is 0.2€, with 7% growth rate in the future, while the bond price in the secondary
market is €948. Calculate the new (at the beginning of the third year):
B1. Cost of the equity.
B2. Pre-tax cost of the bond loan.
B3. The Weighted Average Cost of Capital of the investment (WACC)
C. In another scenario, assume that ABC has set a target of 9% weighted average cost of capital
(WACC). We assume that Company has two sources of funding: equity and debt. In addition, we
assume that the company displays before tax 7% cost of debt and 11% cost of equity. The tax rate is
29%. Estimate which percentage of total capital should be equity and which percentage should be debt
in order the company to achieve the desired WACC.

Answer 1

A	Total Capital Required for Expanding Production Facilities	€   1,200,000.00
	Source of finance -
	New Share Capital	€       300,000.00
	Bond Issue , 5 year	€       600,000.00
	Bank Loan	€       300,000.00
	Share Price (Po)	€                    5.00
	Current Dividend (D)	€                    0.25
	Annual growth rate (g)	8.00%
	Bond Face value	€           1,000.00
	Bond Price at the time of issue	€           1,000.00
	Interest rate of Bond	8.00%
	Fixed Interest rate-Bank Loan	6.00%
	Tax rate	29%
A1	Cost of Equity
	According to Gordon's Model, Cost of Equity(Ke) can be calculated with following formula $k_{e} = \frac{D}{Po} + g$ Ke = 0.25/5 + 0.08	Where, D = Dividend Po = Share price g = growth rate
	Cost of Equity (Ke)	13.00%

A2	Pre-tax cost of Bond Loan
	Yield rate is cost of bond for company and when Face value and Price of Bond is equal then Yield rate also equal to interest (coupon) rate of Bond. Therefore,
	Pre-tax cost of Bond Loan	8.00%

A3	Weighted Average cost of Capital (WACC)
	Post-tax WACC = $k_{e}*W_{e} + K_{b}*W_{b}+K_{d}*W_{d}$	Where, W = Weights Kd = post tax cost of Loan Kb = post tax cost of Bond
	Post-tax cost of Bond = Kb(1-t)	5.68%
	Post-tax cost of Loan = Kd(1-t)	4.26%
	Source of Finance	Weight(W)	Cost(C)	W*C
	Equity	0.25	13.00%	0.0325
	Bond	0.5	5.68%	0.0284
	Bank Loan	0.25	4.26%	0.0107
	Post-tax WACC			7.16%

B	At the beginning of third year
	Price of share (P)	3
	Dividend (D)	0.2
	Growth rate (g)	7%
	Bond Price in secondary market	948
	Maturity of bond	5 years
	At the Beginning of 3rd year
B1	Cost of Equity
	According to Gordon's Model, Cost of Equity(Ke) can be calculated with following formula $k_{e} = \frac{D}{Po} + g$ Ke = 0.2/3 + 0.07
	Cost of Equity (Ke)	13.67%
B2	Pre-tax cost of Bond Loan (Kb)
	Yield rate is cost of bond for company .Yield to Maturity (YTM) is rate at which Present value of future cash flow equals to current bond price. We can calculate Yield rate with following formula $Price of Bond = \frac{80}{(1+YTM)^1}+\frac{80}{(1+YTM)^2}+\frac{1080}{(1+YTM)^2}$ Alternatively, can be calculated with "=irr" formula in excel. Please refer below image for calculation of yield rate.
	Pre-tax cost of Bond Loan	10.09%

C7 End of year Price at 3rd year beginning Cash Flow 948 80 80 1080 4 4 10.09%)

Formula reference -

C7 xIRR(C3:C6) End of year Price at 3rd year beginnin Cash Flow 948 80 80 1080 4 4 IRR(C3:C6)

B3	Weighted Average cost of Capital (WACC)
	Post-tax WACC = $k_{e}*W_{e} + K_{b}*W_{b}+K_{d}*W_{d}$
	Post-tax cost of Bond = Kb(1-t)	7.17%
	Post-tax cost of Loan = Kd(1-t)	4.26%
	Source of Finance	Weight(W)	Cost(C)	W*C
	Equity	0.25	13.67%	0.0342
	Bond	0.5	7.17%	0.0358
	Bank Loan	0.25	4.26%	0.0107
	Post-tax WACC			8.07%

C	Target WACC	9%
	Cost of Equity (ke)	11%
	post-tax cost of debt (kd) = 7%(1-0.29)	4.97%
	Weight of Equity	W1
	Weigh of Debt	(1-W1)
	Target WACC = Ke*W1 + Kd*(1-W1) 0.09 = 0.11*W1 + 0.0497(1-W1) 0.09 = 0.11W1 + 0.0497% - 0.0497W1 0.0603W1 = 0.0403 W1 = 0.0403/0.0603 W1 = 0.67
	W1	0.67
	W2	0.33

ePo 80 1080 80 Priceo fBond C7 End of year Price at 3rd year beginning Cash Flow 948 80 80 1080 4 4 10.09%)