Present Value of Growth - Math Problem Example

Number: Lecturer: Word Count: Campus of Study: Topic: Problem The principal amount borrowed is 500,000(P) for a period of 20(N) years. The given nominal interest rate is 10% (j). With these details, we can calculate the effective annual interest rate(i) from, =[1 + (.1/12)] 12- 1 =10.47% This is the effective annual interest rate. We can now calculate the monthly interest from i*=0.1047/12 =0.8725% The total number of periods(n) is 20*12=240 periods Monthly Repayment C is calculated suing the formula, 500,000= C/.008725[1 – 1 / (1 + 0.008725)240] C=4,981.83 Hence the monthly repayment is $4,981.83 Case 1: After 5 years, the balance owed(P) will be present value of the future payments. P=4981.83/0.008725[1–1/(1 + 0.008725)180] =451,440.90 The Effective Annual Interest Rate i can be computed from the new nominal rate(12%): i=[1+(.12/12)]12-1 =12.68% The monthly interest Rate i is (0.1268/12)=1.06% and the number of periods n is 180(12*15). The new monthly instalment is, 451,440.90=C/0.0106[1–1/(1+0.0106)180] C=$5,628.90 The monthly instalment is increased to $5,628.90 Case 2: The monthly instalment is 4,981.83 and the balance owed is 451,440.90 and the monthly nominal interest rate is 1.06%. New loan term period n is obtained from, =log[4981.83/(4981.83 – 451440.90*0.0106)]/log(1.0106) =306.6 The new loan term period is 25 years and 7 months. Problem 2: The monthly cash flow(C) is estimated as $500,000. The required rate of return(p) is 10% and inflation rate(i) is 4%. Case 1: Based on rate of return i) When the project generates cash flows forever, the Present value can be calculated from, PV=C/(p-i) =8,333,333.33 ii) When the project generates cash flows for 20 years, the Present Value is given by, PV =500,000[(1.04)/1.1)+(1.04/1.1)2..(1.04/1.1)20] =500,000 [11.687] = 5,843,500 The value of the building is after 20 years is 5million. Its Present value is, Complex value after 20 years V = 5,000,000 / (1.1)20 = 743,218.14 Present Value of Total Cash flows is $6,586,720(5,843,500+743,220). Therefore, when the project generates cash flows forever, 8.33 million can be invested, whereas when the cash flows are generated for 20 years, 6.586 million can be invested. Case 2: Real Rate of Interest Real rate of interest includes both the required rate of return and the effects of inflation. Hence this can be taken as the real rate of return required from the project. It is calculated as, r=(1+p)/(1+i)–1 =(1.1/1.04)–1 =5.77% i) When the cash flows are generated forever, the present value using the real rate of interest is given by, PV=C/ r =500,000/0.0577 =8,665,511.27 ii) When the cash flows are generated for 20 years, the Present Value using the real rate of interest is given by, PV=500,000/0.0577[1–1/(1.0577)20] =5,843,595.12 The building value is 743,218.14 after 20 years, as calculated in case1. Present Values of total cash flows is $6,586,820(5,843,600+743,220). Therefore, when the project generates cash flows forever, 8.66million can be invested, whereas when the cash flows are generated for 20 years, 6.586million can be invested. Problem 3: Given that Newcastle Ltd is all equity financed and the cost of capital Ke is 15%. Tax rate T is assumed to be 40% and the equity capital is taken as Ec. The amount of debt is 50% of equity and hence Debt D=0.5Ec and the cost of Debt Kd=10%. The total value of the company will increase by 50% and hence the total value of assets is 1.5Ec(Ec+0.5Ec). Argument 1: Reduction in Company’s cost of capital by debt. The Company’s cost of capital can be computed using the weighted average cost of capital (WACC). WACC = Kd(1–T)(D/V)+Ke(E/V) = [0.1 (1-0.40) (0.5Ec/1.5Ec)]+[0.15 (Ec/1.5Ec)] = 12% Therefore the company’s cost of capital has been reduced to 12% when the company borrows debt at a rate of 10%. Argument 2: NPV of rejected projects are favourable Based on the new WACC, the required rate of return (i.e., the company’s cost of capital) has been reduced to 12%. Hence the PV of future cash flows will differ from earlier. This can be illustrated using the following example. Case 1: Initially, a project which requires an investment of $280,000 and which will generate a cash flow of $50,000 for the next 10 years was rejected. This was because the NPV was negative (as shown below) as the cost of capital was 15%. PV of cash flows = 50,000/0.15 [1 – 1/ (1.15)10] = 250,938.43 NPV = 250,938.43–280,000 = -29,061.57 Case 2: Under the new capital structure, cost of capital is 12%. PV of cash flows = 50,000/0.12[1 – 1/ (1.12)10] = 282,511.15 NPV = 282,511.15–280,000 = +2,511.15 Under the modified capital structure, the NPV is positive for the project which was earlier rejected. Rationale: The consultant’s view cannot be accepted without taking into account a number of other factors. These are listed below. The value of the assets is taken from the book value of the assets. The debt borrowed is also taken as 50% of this value. However, the best practise to calculate the cost of capital is to consider the market value of the assets, in which case, the difference can be significant. The calculations do not take into account, the possible changes in the cost of capital due to inflation and other external factors, which is a drawback in most cases. The WACC is calculated using only the cost of debt and the cost of equity. It is important to note that raising capital via. Debt increases the beta value of the company, i.e., the risk of investing is increased, as the company is obligated to pay the debt. Hence the cost of equity is also increased due to this change in capital structure. Problem 4: Manufacturing Company: Boral Ltd. Stock Code: BLD.AX Balance Sheets for the last 3 years: Period ending 30-Sep-07 30-Sep-06 30-Sep-05 Current Assets 1451 76.20 42.10 Total Assets 5816.60 5587 5104.30         Short-term debt 25.60 1 25.10 Long-term debt 1492.40 1653.10 1410.50 Total debt 1518 1654.40 1435.60         Total liabilities 2829.30 2832 2632.10         Net Assets 2987.30 2755 2472.20 Net Tangible Assets 2647 2402.1 2180.60 (http://au.finance.yahoo.com/q/abs?s=BLD.AX) Bank: Commonwealth Bank of Australia Stock Code: CBA.AX Balance Sheets for the last 3 years: Period ending 30-Sep-07 30-Sep-06 30-Sep-05 Short-term money 10108 2063 1869 Loans 299779 259307 217888 Net Debt 289671 257244 216019 (http://au.finance.yahoo.com/q/abs?s=CBA.AX) Capital Structure Comparison: From the balance sheets, it is evident that the capital structures of the two companies are completely different. The assets and liabilities of the Commonwealth Bank are monetary in nature. Debt Ratio: The debt ratio of Boral limited is computed as the ratio of total debt to total assets which is equal to (1518/5816.60) 26.1%. This is lesser when compared to the Commonwealth bank which has a higher debt ratio. Also, the Commonwealth bank of Australia has lesser short term money and in order to compute the liquidity position of the bank, the cash as well as the loans and deposits are to be considered. The gearing ratio of the bank has to be much higher, as the entire operation of the bank involves taking deposits and lending loans. However the gearing ratio of Boral cannot go much higher as it will affect the debt rating of the company. Assets Comparison: From the balance sheets, it is evident that Boral Limited has a number of non-tangible assets whereas all the assets and liabilities are monetary in nature. The banks normally seek and increase liabilities in order to build the assets. However manufacturing companies tend to build assets and thrive to increase the value. Problem 5: Case Study: Cole Sports a) Dividend Payments and Stock Valuation: As there are opportunities for business development with the additional capital raised by making the company public, it is essential to estimate the business growth. This will give an estimate on the earnings per share. Based on the earnings, the plowback rate can be computed for continuous growth. Hence from the earnings per share and the plowback rate, the dividend payments can be forecast during the growth period. Case 1: Assuming that the business can expand for the next 6 years and the growth in earnings to be 50% every year, the earnings per share is calculated. The plowback rate is currently 70%. If this is increased to 80% for the next 6 years, the dividend payments can be computed. Period 2008 2009 2010 2011 2012 2013 EPS ($) 3.00 4.50 6.75 10.13 15.19 22.78 Plowback% 80% 80% 80% 80% 80% 80% Div($) 0.60 0.90 1.35 2.03 3.04 4.56 The cost of capital is the sum of the cost of raising equity and the current cost of capital. This can be taken as 12%. At the end of 6 years, when there are no opportunities for expansion, a fixed dividend of $6 can be given to the share holders forever. Value of stock after 6 years =Dividend/rate =6/0.12 =50 From these values, the current value of the stock can be computed as, Present Value =(0.60/1.12)+(0.90/1.122)…+(4.56+50/1.126) =0.54+0.72+0.96+1.29+1.73+27.64 =32.88 Therefore, the current market price of the share is 32.88 and this would put the Price/Earning ratio of the company at 16.44 and hence outruns the competitor. Case 2: When there are opportunities for 8 years, then the dividend payments can be calculated using the same assumptions as case 1. Period 2008 2009 2010 2011 2012 2013 2014 2015 EPS ($) 3.00 4.50 6.75 10.13 15.19 22.78 34.17 51.26 Plowback% 80% 80% 80% 80% 80% 80% 80% 80% Div($) 0.60 0.90 1.35 2.03 3.04 4.56 6.83 10.25 Assuming that a constant dividend of $9 is paid to perpetuity after 8 years, Present value of Stock =0.54+0.72+0.96+1.29+1.73+2.31+3.09+34.43 =45.07 Based on these assumptions, the market price can be set as $45.07. From Case1 and Case2, the price of the stock can be set somewhere between $32.88 and $45.07. b) Present Value of growth opportunities is the rise in stock price due to the plowback of income into the business for growth. Growth rate can be computed from current return on equity and the plowback rate which is estimated to be 10.2% If this growth rate is taken for perpetuity, Current Value of Stock =0.60/(0.12–0.102) =33.33 Stock Value (No growth) = 13.17 (Book Value) This indicates that the present value of growth opportunities is $20.16 per share, i.e., the value of PVGO is 40.32million. Read More