Initial Cash Flow at Time 0 = -(Appraised Value of Land + Cost of Building Plant and Equipment + Net Working Capital)
Substituting values in the above formula, we get,
Initial Cash Flow at Time 0 = -(6,000,000 + 32,600,000 + 1,475,000) = -$40,075,000 (answer for Part a)
Part b)
Step 1: Calculate Weights of Different Sources of Finance
Market Value of Debt = Number of Bonds*Par Value*Current Selling Price Percentage = 245,000*1,000*105% = $257,250,000
Market Value of Common Stock = Number of Shares*Current Selling Price = 9,500,000*73.10 = $694,450,000
Market Value of Preferred Stock = Number of Shares*Current Selling Price = 465,000*83 = $38,595,000
Total Market Value of Firm = Market Value of Debt + Market Value of Common Stock + Market Value of Preferred Stock = 257,250,000 + 694,450,000 + 38,595,000 = $990,295,000
Now, we can calculate weights as follows:
Weight of Debt = Market Value of Debt/Total Market Value of Firm = 257,250,000/990,295,000
Weight of Equity = Market Value of Equity/Total Market Value of Firm = 694,450,000/990,295,000
Weight of Preferred Stock = Market Value of Preferred Stock/Total Market Value of Firm = 38,595,000/990,295,000
Step 2: Calculate After-Tax Cost of Debt
The after-tax cost of debt can be calculated with the use of Rate function/formula of EXCEL/Financial Calculator. The function/formula for Rate is Rate(Nper,PMT,-PV,FV) where Nper = Period, PMT = Payment (here, Coupon Payment), PV = Present Value (here, Current Selling Price) and FV = Future Value (here, Face Value of Bonds).
Here, Nper = 23*2 = 46, PMT = 1,000*6%*1/2 = $30, PV = 1,000*105% = $1,050 and FV = $1,000
Using these values in the above function/formula for Rate, we get,
Pre-Tax Cost of Debt = Rate(46,30,-1050,1000)*2 = 5.61%
After-Tax Cost of Debt = Pre-Tax Cost of Debt*(1-Tax Rate) = 5.61%*(1-22%) = 4.38%
Step 3: Calculate Cost of Preferred Stock
The cost of preferred stock is determined as below:
Cost of Preferred Stock = Annual Dividend/Current Stock Price*100 = (3.8%*100)/83*100 = 4.58%
Step 4: Calculate Cost of Equity
The cost of equity is arrived as below:
Cost of Equity = Risk Free Rate + Beta*(Market Risk Premium) = 2.9% + 1.2*(6%) = 10.10%
Calculate Discount Rate
The value of discount rate is calculated as follows:
Discount Rate = (Weight of Debt*After-Tax Cost of Debt + Weight of Preferred Stock*Cost of Preferred Stock + Weight of Equity*Cost of Equity) + Appropriate Risk Adjustment Factor
Substituting values in the above formula, we get,
Discount Rate = (257,250,000/990,295,000*4.38% + 38,595,000/990,295,000*4.58% + 694, 450,000/990,295,000*10.10%) + 1.5% = 9.90% (answer for Part b)
The after-tax salvage value of the plant is arrived as below:
Annual Depreciation = Cost of Plant and Equipment/Useful Life = 32,600,000/8 = $4,075,000
Book Value of Plant and Equipment After 5 Years = Cost of Plant and Equipment - Annual Depreciation*5 = 32,600,000 - 4,075,000*5 = $12,225,000
Loss on Sale of Plant and Equipment = Book Value of Plant and Equipment After 5 Years - Salvage Value = 12,225,000 - 5,200,000 = $7,025,000
After-Tax Salvage Value = Salvage Value + Loss on Sale of Plant and Equipment*Tax Rate = 5,200,000 + 7,025,000*22% = $6,745,500 (answer for Part c)
The annual operating cash flow (OCF) is determined as follows:
Sales Value (19,550*11,070)216,418,500
Less Variable Costs (19,550*9,700)189,635,000
Fixed Costs7,500,000
Depreciation4,075,000
EBT15,208,500
Less Taxes3,345,870
EAT11,862,630
Add Depreciation4,075,000
Operating Cash Flow$15,937,630
Answer for Part d) is $15,937,630.
The accounting break-even quantity is calculated as follows:
Accounting Break-Even Quantity = (Fixed Cost + Depreciation)/(Selling Price - Variable Cost)
Substituting values in the above formula, we get,
Accounting Break-Even Quantity = (7,500,000 + 4,075,000)/(11,070 - 9,700) = 8,449 units (answer for Part e)
IRR
IRR is the minimum rate of return acceptable from a project. It can be calculated with the use of IRR function/formula of EXCEL/Financial Calculator. The basic formula for calculating IRR is given below:
NPV = 0 = Cash Flow Year 0 + Cash Flow Year 1/(1+IRR)^1 + Cash Flow Year 2/(1+IRR)^2 + Cash Flow Year 3/(1+IRR)^3 + Cash Flow Year 4/(1+IRR)^4 + Cash Flow Year 5/(1+IRR)^5
IRR is calculated with the use of EXCEL as below:
Year Cash Flow 0 -40075000 15937630 15937630 15937630 15937630 30558130 33.16% 4 6 4 IRR 10
where
IRR = RR(B2:B7) = 33.16%
NPV
The NPV can be calculated with the use of following formula:
NPV = Cash Flow Year 0 + Cash Flow Year 1/(1+Discount Rate)^1 + Cash Flow Year 2/(1+Discount Rate)^2 + Cash Flow Year 3/(1+Discount Rate)^3 + Cash Flow Year 4/(1+Discount Rate)^4 + Cash Flow Year 5/(1+Discount Rate)^5
Substituting values in the above formula, we get,
NPV = -40,075,000 + 15,937,630/(1+9.90%)^1 + 15,937,630/(1+9.90%)^2 + 15,937,630/(1+9.90%)^3 + 15,937,630/(1+9.90%)^4 + (15,937,630 + 6,745,500 + 1,475,000 + 6,400,000)/(1+9.90%)^5 = $29,619,521.66
