Financial Calculations - Beta Books New Investment, the Lease Payment, the Capital Gain or Loss on Each Debenture - Assignment Example

Financial Calculations Student’s Name Institutional Affiliation Financial Calculations Question 1 Units sales at $180 each (P) Number of units 9000 (Q) Variable cost per unit $95 (V) Fixed operating cost $550000 per annum (F) Outstanding debt of $1500000 at an interest cost of 8% per annum 50000 ordinary shares (N) Interim dividend at $1 per share Tax at 30% 10% increase in sales Degree of Operating Leverage (Cengage Learning, 2010) Where Q(P-V)-F= Earnings before interest and tax (EBIT) (Cengage Learning, 2010) Therefore, Degree of Financial Leverage (DFL) (Cengage Learning, 2010) Where EPS is earnings per share and I is interest paid. Hence, Combining degree of operating leverage (DOL) and degree of financial leverage (DFL) give degree of total leverage (DTL). Therefore, (Cengage Learning, 2010) Question 2 a) Beta Books new investment Let state 1 be when share price is $10.25 and state 2 when share price is $11.25. The average payment to old shareholders will be The Beta Books should make the investment because it will boost the company’s earnigs b) The time to make the investment The investment should be made before the share market learns the true value of the company existing assets to allow the company raise more money when it becomes known. c) Given a choice the new investment should be made by issuing shares and foregoing debt. It will be self-financing without external obligations. Question 3 Previous Years % Sales Forecast Values % Sales Forecast Values Sales 1500 - 1725 Retained Earnings 130 30.95% of net income 149.5 Costs 900 60% 1035 Dividends 290 69.05% of net income 333.5 Tax rate 0.3 30% of taxable income 207 Assets Liabilities/Equity Current Assets Current Liabilities Cash 160 10.67% 184 Creditors 300 20% 345 Debtors 440 29.33% 506 Short Term Notes 100 N/A 100 Inventory 600 40% 690 Non-Current Assets Non-Current Liabilities PP&E 1800 120% 2070 Debentures 800 N/A 800 Total Assets 3000 3450 Owner’s Equity Retained Profits 1000 N/A 1149.50 Ordinary Shares 800 N/A 800 Total 3000 3195 Calculations for various entries are done below; Sales forecast is 15% increase Percentage sales are calculated by dividing values that affected by sales by the current sales. For example, cost as a percentage of sales The percentage for tax rate is determined using the taxable income, which gives 30%. Retained earnings and dividends respective percentages are determined by using net income. a) External financing required (EFN) is the forecasted total assets minus forecasted total liability/equity b) c) At a capacity of 85% S0 = Current Sales, S1 = Forecasted Sales g = the forecasted growth rate is Sales, A*0 = Assets (at time 0) which vary directly with Sales, L*0 = Liabilities (at time 0) which vary directly with Sales, PM = Profit Margin = (Net Income)/(Sales), and b = Retention Ratio = (Addition to Retained Earnings)/(Net Income). Since SFC is greater than the forecast sales, the above formula is used, but only the total current assets are used in the calculations. Extra funding not needed in this case. Question 4 Previous years % Sales Forecast values % Sales Forecast values Sales 520 120% 624 Retained Earnings 62 73.81% 74.4 Costs 400 76.92% 480 Dividends 22 26.19% 26.4 Tax rate 0.3 30% of taxable income 43.20 Assets Liabilities/Equity Current Assets Current Liabilities Cash 200 38.46% 240 Creditors Debtors Short Term Notes Inventory Non-Current Assets Non-Current Liabilities PP&E 300 57.69 360 Debentures 250 N/A 250 Total Assets 500 600 Owners’ Equity Retained Profits 250 N/A 324.4 Ordinary Shares   500 574.4 Sales forecast is 20% increase, which is calculated as; a) External financing required (EFN) is the forecasted total assets minus forecasted total liability/equity b) Addition to retain earnings is given as: c) The Sustainable Growth Rate (SGR) Where d-dividend payout ratio and ROE-return on equity d) The sustainable growth rate has been calculated with values considering sales growth of 20%. Therefore, external funding needed is equal to that needed at a sales forecast of 20% increase, which is $25.6. e) At the growth rate where no external funding is required, the total assets will equal the total liability/equity. Given that before a growth rate, Total assets equals total liability/equity. Therefore, external funding will not be required at no growth rate or at zero (0) rate. Question 5 Sales 900 Costs 500 Taxable Income 400 Tax 120 Net Profit 280 Assets Current Assets 500 Non-Current Assets 600 1100 Liabilities/Equity Debt 700 Equity 400 1100 Retained Earnings 150 Dividends 130 a) The total assets-to-sales ratio consistent with a growth in sales of 15% At sales growth of 15%, Sales forecast Current assets as a percentage of sales Forecast current assets Non-current assets as a percentage of sales Forecast non-current assets Forecast total assets=575+690=$1265 The total assets-to-sales ratio consistent with a growth in sales of 15% The total assets-to-sales ratio=1.22 b) The debt/equity ratio consistent with a growth in sales of 15% Debt as a percentage of sales Forecast debt The debt/equity ratio consistent with a growth in sales of 15% c) The net profit margin ratio consistent with a growth in sales of 15% Cost as a percentage of sales Forecast costs Net forecast sales Tax as a percentage of taxable income Forecast tax Question 6 a) The lease payment Lease amount (PV) is assumed to be the cost of purchase of the equipment at $1000000. The residual payment (FV)=$70000 Where N=period in years, i=interest on income, Pyr=yearly lease payments Rearranging the equation, Therefore, b) The company to either purchase or lease the asset Cost purchasing the equipment by acquiring the loan Interest (I) charged on the loan for five years It is cheaper to buy the new equipment than to lease one. Therefore, the company should purchase the equipment. Question 7 Ben owns 800 shares in Black Enterprises whose current share price (cum rights) is $3 per share. Black Enterprises wishes to raise $3 million through a rights issue at a subscription price of $2.40. They currently have issued 10 million shares. a) The value of a right to buy 1 new share The number of rights needed is calculated first. b) The ex-rights share price The ex-rights shares for the stockholder will be Therefore, c) The value of the investment cum rights and ex-rights Before the right issues the value Ben investment was After the issue, the prices will fall but Ben will hold the rights and his investment become Question 8 Calculate the current price and the duration of the following debentures, each of which has a face value of $1000. Assume that coupon payments are made at the end of each year. Debenture Term to Maturity (Years) Coupon Rate (%) A 3 12 B 2 10 C 4 9 D 5 11 E 8 13 F 7 14 The current market interest rate is 9 per cent. a) The price of these bonds at 9% Where c coupon rate, F face value, r prevailing market rate, t time period over the term of the bond Price of bond is given as Present value of interest payments + present value of face value of a bond Bond A Bond B Bond C Bond D Bond E Bond F b) The duration of these bonds at 9% Assuming the bonds was issued on 01/01/2015. The calculations are done using excel formula. The calculations are for Macaulay Duration. Duration for Bond A =DURATION("01/01/2015","01/01/2018",0.12,0.09,1,1)=2.701 Duration for Bond B =DURATION("01/01/2015","01/01/2017",0.1,0.09,1,1)=1.910 Duration for Bond C =DURATION("01/01/2015","01/01/2019",0.09,0.09,1,1)=3.531 Duration for Bond D =DURATION("01/01/2015","01/01/2020",0.11,0.09,1,1)=4.138 Duration for Bond E =DURATION("01/01/2015","01/01/2023",0.13,0.09,1,1)=5.674 Duration for Bond F =DURATION("01/01/2015","01/01/2022",0.14,0.09,1,1)=5.118 c) The price of these debentures would be if the market interest rate increased to 12 percent. Bond A Bond B Bond C Bond D Bond E Bond F d) The capital gain or loss on each debenture Where Po initial stock price and P1 stock price after interest changes e) The duration of these bonds at 11% Assuming the bonds was issued on 01/01/2015. The calculations are done using excel formula. The calculations are for Macaulay Duration. Duration for Bond A =DURATION("01/01/2015","01/01/2018",0.12,0.11,1,1)=2.694 Duration for Bond B =DURATION("01/01/2015","01/01/2017",0.1,0.11,1,1)=1.908 Duration for Bond C =DURATION("01/01/2015","01/01/2019",0.09,0.11,1,1)=3.515 Duration for Bond D =DURATION("01/01/2015","01/01/2020",0.11,0.11,1,1)=4.102 Duration for Bond E =DURATION("01/01/2015","01/01/2023",0.13,0.11,1,1)=5.549 Duration for Bond F =DURATION("01/01/2015","01/01/2022",0.14,0.11,1,1)=5.027 f) The findings The interest rates have direct effect on the bond prices, as the interest increases, the bond prices reduces. The duration of the bond is also affected by the market interest rates. As the interest rate increases, the duration reduces slightly. Question 9 Debenture Face Value $2000 Coupon Rate 11% 35% probability that rates will fall to 9% 65% probability that rates will increase to 12% Par value $1900 a) Calculate the Market Price of the Non-Callable Debenture b) What would the coupon rate need to be for the debentures to sell at par? For callable debentures, c) The cost of the call provision Question 10 Face value $400000 Yielding 10.25% per annum 180 days to maturity a) At no interest rate, the maturity value equals the face value, which is $400000.00. The price of the note (P) will be at a discounted price, Where S=maturity value, r=yielding rate, t=period in years Therefore, b) The interest for 180 days will be the difference between the face value and the price of the note Where I=interest, P=price of the note, t=time in years The interest rate equals the yielding rate. Question 11 The Miller-Orr Model Target cash balance (Z) Where TC=transaction costs of buying or selling, v=standard deviation, r=daily rate, L=Lower limit Upper limit for the cash account (H) Where Z=target cash balance, L=lower limit Question 12 Quantity=80000 liters per year Ordering cost=$220 per order Cost of carrying the inventory=$1.20 per liter per year a) The economic order quantity (EOQ) b) The order cost c) The ordering days Taking 365 days in a year, d) The holding cost e) f) The annual total cost g) Lead time=20 days Question 13 Annual demand=20000 units Ordering cost=$2 per unit Carrying cost=$0.50 per unit The cost per unit=$10 Question 14 Calculate the Black—Scholes price for a call option with the following features: share price $24.00, exercise price $23.00, term to expiry 1 year, risk-free interest rate 5.25 per cent per annum (compounding annually) and volatility (variance) 0.07 per annum. The Black-Scholes Model: European options formula Where C= theoretical call value S =current stock price N= cumulative normal standard distribution t=time K=option strike price r=risk free interest v=the volatility S=$24, K=$23, r=0.0525, v=0.07 Calculating terms in the formula Substituting N(d1) and N(d2) in the original formula Question 15 Determining the profit and/or loss to the following: 1 Call Options- Buyer/Holder and Seller/Writer Market Price $10.25 Exercise Price $9.25 Call Premium $0.75 When the holder exercise the right to buy, The holder will make a profit of $0.25. 2 Put Options- Buyer/Holder and Seller/Writer Market Price $9.25 Exercise Price $10.75 Call Premium $0.80 When the holder exercise the right to sell, The holder will make a profit of $0.70. Question 16 Cash Price per Unit $ 59.00 Variable Cost per Unit $ 28.00 Current Quantity Sold per Month 1000 Quantity Sold under New Policy 1180 Monthly Required Return 2.5% Terms 30 days The company is planning to switch from a cash basis to offering credit terms. a) The cost of switching using both the One Shot Approach and the Accounts Receivable Approach. One Shot Approach The cost of the switch=current revenue + the cost of producing extra 180 units under the new policy b) If the new Credit price was set at $64 per Unit and 2% of sales were uncollectable, the NPV of the switch is calculated as follows; There is a discount rate (d) of Since 2% (u) will not be collected, the amount collected will be Where P-cash price, P’-credit price, Q-current quantity, Q’-quantity under new policy c) The default rate that makes NPV equal to zero. Rearranging the equation gives The default rate (u) would be d) The NPV associated with a One-Time Sale. Where: v = variable cost per unit u = probability of default P = Current Price r = Monthly requiredreturn e) The percentage chance the company would have of collecting given the one time sale extension of credit. The percentage chance is one minus the probability of the default at one-time sale. Hence, f) The NPV associated with a repeat sale Question 17 (a) The gain from the merger The annual savings from the merger is $270000 per year. (b) The net cost of the cash offer The cash offer is $5.9 million The combined value of the two companies 50% holding will be c) The net cost of the share alternative This amount is similar to the net cost of the cash offer, which is $850000 d) The NPV of the acquisition under: The cash offer NPV=850000/0.01=$85000000 The share offer Similarly, NPV=850000/0.01=$85000000 Question 18 a) The gain from the takeover; and b) The maximum price that Endeavour should be prepared to pay for Beard's shares. The maximum would be the total share price minus the gain= ($5million×2)-270000=$9730000 References Cengage Learning (2010). Degree of leverage. Retrieved from http://www.cengage.com/resource_uploads/downloads/0324594690_163047.pdf Read More