Business 5039, Fall 2004

Transcription

1 Business 5039, Fall 4 Assignment 3 Suggested Answers 1. Financial Planning Using the financial statements for Rosengarten, Inc., in Table 1, answer the following questions. a) 10 points) Construct Rosengarten s pro forma financial statements for 3 assuming that sales will be 20 percent greater than their 2 level. Use the following assumptions and guidelines: COGS is a constant fraction of sales. Net fixed assets are a constant fraction of total assets. Depreciation is a constant fraction of net fixed assets. The capital intensity ratio is not expected to change. The annual interest rate Rosengarten pays on its notes payable is 12% and the rate it pays on its long-term debt is 10%. The tax rate and the dividend payout ratio are not expected to change. Accounts payable are a constant fraction of sales. The current ratio must be at least 2.5 and the ratio must not exceed 0.5. Notes payable + Long-term debt Notes payable + Long-term debt + Total equity 1

2 Carefully explain each step of your solution and describe how Rosengarten will finance its expansion. All assets increase by 20%. Note that since the actual current ratio is 2.0, notes payable have to increase by less than 20% to get a current ratio of at least 2.5. In each answer, notes payable are such that the current ratio is exactly 2.5. Long-term debt and common stock is adjusted in a manner that makes total liabilities and equity equal to total assets and such that the debt ratio defined above is smaller than 0.5. The pro forma financial statements can be seen in Table 1. b) 10 points) Suppose the firm was operating at 80% capacity in 2 and that it will increase net fixed assets in 3 only if it has to. Construct Rosengarten s pro forma statements under this scenario using the assumptions in a) for all variables except total assets. That is, the capital intensity ratio will change here. Carefully explain each step of your solution. Full capacity sales when NFA = 2, 000 being FCSNFA = 2, 000) = 3, = 3, 750, there is no need to increase net fixed assets since expected sales are 3,600. This means that the depreciation expense will also remain constant. We need an extra assumption to increase current assets so let us assume that all current assets increase with sales. The solution to this question can be seen in Table 1, where notes payable are such that the current ratio is 2.5, long-term debt is such that debt over total capital is less than 0.5 and common stock is adjusted to balance the sheet. c) 10 points) Suppose the firm was operating at 90% capacity in 2 and that it will increase net fixed assets in 3 only if it has to. Construct Rosengarten s pro forma statements under this scenario using the assumptions in a) for all variables except total assets. That is, the capital intensity ratio will change here. Carefully 2

3 explain each step of your solution. Full capacity sales are then FCSNFA = 2, 000) = 3, = 3, 333 and thus net fixed assets have to be increased. Since we assume that the firm will be operating at full capacity sales in 3, the new level of net fixed assets is NFA 02 FCS 02 Sales 03 = 2, 000 3, 600 = 2, , 333 The rest of the solution can be seen in Table 1. d) 10 points) Suppose the firm was operating at 80% capacity in 2 but wants to operate at 90% capacity in 3. Construct Rosengarten s pro forma statements under this scenario using the assumptions in a) for all variables except total assets. That is, the capital intensity ratio will change here. Carefully explain each step of your solution. Net fixed assets in 3 will be Sales 03 /.9 Sales 02 /.8 NFA 02 = 3, 600/.9 2, 000 = 2, , 000/.8 The rest of the solution can be seen in Table Time Value of Money Consider an annuity which first payment, $, will be received one year from now, the annual interest rate being 6%. Find the present and future values of this annuity under the following conditions: a) 4 points) The annuity consists of 20 fixed annual payments and interest is compounded once a year. PV = 1 ) ) = $2, FV = )20 1) = $7,

4 b) 4 points) The annuity consists of 20 fixed annual payments and interest is compounded monthly. The effective annual rate of interest is then ) 12 1 = % 12 and thus: PV = 1 ) ) = $2, FV = )20 1) = $7, c) 4 points) The annuity consists of 20 annual payments increasing by 2% each year and interest is compounded annually. PV = 1 ) ) = $2, FV = ) ) 20 ) = $8, d) 4 points) The annuity consists of an infinity of annual payments decreasing by 5% each year and interest is compounded annually. Future value is not defined and PV =.06.05) =.11 = $1, e) 4 points) The annuity consists of an infinity of annual payments decreasing by 99.99% each year and interest is compounded every nanosecond. Future value is not defined and PV = e.06 1).9999) = e = $ Time Value of Money Bill Lesuk plans to retire in exactly 25 years. His goal is to create a fund that will pay $60,000 per year for 30 years. During his retirement years, Bill s money will be in an account expected to return, on average, 5% annually. 4

5 a) 5 points) How large must Bill s fund be after 25 years in order to make the desired payments throughout his retirement? PV = 60, ) ) = $922, b) 5 points) Suppose Bill makes equal monthly contributions to his retirement fund until the day he retires. What must each contribution be to meet his retirement goal if the quoted rate on his fund is 8% compounded monthly? C = 922, /12) )/.08/12) = $ c) 5 points) Suppose Bill makes equal daily contributions to his retirement fund until the day he retires. What must each contribution be to meet his retirement goal if the quoted rate on his fund is 8% compounded monthly? Since interest is compounded monthly, all that matters is the total monthly payment, which has to be as in b), i.e. $ There being, on average, 365/12 = days in a month, each daily payment should be C = = $ d) 5 points) Suppose Bill makes equal daily contributions to his retirement fund until the day he retires. What must each contribution be to meet his retirement goal if the quoted rate on his fund is 8% compounded daily? C = 922, /365) )/.08/365) = $31.65 e) 5 points) Suppose Bill makes monthly contributions to his retirement fund until the day he retires and each contribution is always 4% greater than the previous one. What must the first contribution be for Bill to meet his retirement goal if the quoted rate on his fund is 8% compounded monthly? 5

6 C 1 = 922, /12) ) ) /.08/12.04) = $

7 Rosengarten, Inc. Actual and Pro Forma Balance Sheets Assets Actual a) b) c) d) Cash Accounts receivable Inventory Total current assets 1,400 1,680 1,680 1,680 1,680 Net fixed assets 2,000 2,400 2,000 2,160 2,133 Total assets 3,400 4,080 3,680 3,840 3,813 Liabilities and Shareholders Equity Actual a) b) c) d) Accounts payable Notes payable Total current liabilities Long-term debt Common stock Accum. retained earnings 1,000 1,946 2,000 1,978 1,985 Total liabilities and equity 3,400 4,080 3,680 3,840 3,813 Rosengarten, Inc. Actual and Pro Forma Income Statements Actual a) b) c) d) Sales 3,000 3,600 3,600 3,600 3,600 COGS Depreciation EBIT 1,842 2,210 2,310 2,270 2,277 Interest Taxable income 1,720 2,103 2,223 2,173 2,190 Taxes 40%) Net income 1,032 1,262 1,334 1,304 1,314 Dividends Earnings retained , Table 1: Financial statements for Question 1. 7