Question

4. (30 pts) Proctor & Gamble (PG) is currently calculating the cost of capital for a major expan- sion program. We have the following information regarding the program: • The tax rate for the duration of the program is 25% • New 10-year coupon bonds will be issued - Similar 10-year, $1,000 par value, 8% coupon, semiannual noncallable bonds cur- rently sell for $898.54 - New bonds will be privately placed with no flotation cost • Common stock currently sells for $120 - Do = 2.98 and g = .055 - B=.5, r = .06, and MRP = .0975 - Bond-Yield Risk Premium = .06 • The target capital structure is 45% debt and 55% common equity With the above information, find PG's WACC with the following formula WACC = ward(1-1) + WpPp+ wers

Answer 1

(4) Calculation of WACC

WACC = (cost of equity x weight of equity + cost of debt (1-tax) x weight of debt)

WACC = (10.88% x 0.55) + (10.84% (1-tax) x 0.45)

WACC = (5.984%) + (10.84% (1-0.25) x 0.45)

WACC = (5.984% + 3.658%)

therefore WACC = 9.642%

Notes:

a) Calculation of cost of equity

Cost of equity could be found out using two approaches as per the information given in the question

Approach 1 : Cost of equity using capital asset pricing model

As per CAPM we have, Rf + Beta x Market risk premium

Risk free rate = 0.06 or 6%

MRP = 0.0975 or 9.75%

Beta = 0.5

CAPM = 6% + 0.5 x 9.75%

= 10.875% or 10.88%

Approach 2 : Cost of equity using gordon's growth rate model

As per gordon's model we have,

p0 = D0 (1+g) / Ke - g

where,

p0 = $120

D0 = 2.98

g = 0.055 or 5.5%

therefore, 120 = 2.98 (1+0.055) / Ke - 0.055

by solving the above formula, Ke or cost of equity will be 8.12%

Since the company is planning a major expansion program, hence it is a risky project and since it is a risky project the shareholders expectation will be higher and so should be the cost of capital, since risky projects should be discounted using higher discount rates hence the cost of equity will be 10.88%.

b) Calculation of cost of debt

Cost of debt could be found out using internal rate of return by applying hit and trial method

Case 1: Let IRR be 5%

We know that Net present value = Present value of cash inflows - Present value of cash outflows

Given:

Face Value = $1000

Coupon rate = 4% (since the payment is to be made semi annually, we will divide the coupon rate of 8% by 2)

Yield to maturity = 5% (since the payment is to be made semi annually, we will divide the Yield to maturity of 10% by 2)

Current value of bond = $898.54

maturity years = 20 yrs (since the payment is to be made semi annually, we will multiply the maturity yrs of 10 by 2)

898.54 = (40 x (PVAF 5% , 20yrs) + (1000 x (PVF 5%, 20th year)

898.54 = (40 x 12.46) + (1000 x 0.3769)

898.54 = (498.40 + 376.90)

therefore NPV = +23.24

Case 2: Let IRR be 2.5%

Face Value = $1000

Coupon rate = 4% (since the payment is to be made semi annually, we will divide the coupon rate of 8% by 2)

Yield to maturity = 2.5% (since the payment is to be made semi annually, we will divide the Yield to maturity of 5% by 2)

Current value of bond = $898.54

maturity years = 20 yrs (since the payment is to be made semi annually, we will multiply the maturity yrs of 10 by 2)

898.54 = (40 x (PVAF 2.5% , 20yrs) + (1000 x (PVF 2.5%, 20th year)

898.54 = (40 x 15.59) + (1000 x 0.610)

898.54 = (623.60 + 610)

therefore NPV = -335.06

Using the IRR method we have,

IRR = Lower rate + lower rate NPV / (Lower rate NPV - higher rate NPV ) x (Higher rate - Lower rate)

IRR = 2.5 + (335.06) / (-335.06 - 23.24) x (5% - 2.5%)

IRR = 4.84%

Now we will add the bond risk premium of 6% as given in the question and the effective pre - tax cost of debt will be (4.84% + 6%) that is 10.84%.