A
4-6A Cash budget) The sharpe corporations projected sales for the eight months of 200 are as follows: January 90,000, february 120,000, march 135,000, april 240,000, ,may 300,000 june 270,000 july 225,000 august 150,000. Of sharpes sales, 10 percent is for cash, another 60 percent is collected in the month following sale. November and December sales for 2003 were 220,000 and 175,000 respectively. Sharpe purchases its raw materials two months in advance of its sales equal to 60 percent of their final sales price. The supplier is paid one month after it makes delivery. For example purchases for april sales are made in February and payment is made in march. In addition sharpe pays 10,000 per month for rent and 20,000 each month for other expenditures. Tax prepayments of 22,500 are made each quarter, beginning in march. The companys cash balance at December 31, 2003 was 22,000 a minimum balance of 15,000 must be maintained at all times. Assume that any short term financing needed to maintain the cash balance is paid off in the month following the month of financing if sufficient funds are available. Interest on short-term loans 12 percent is paid monthly. Borrowing to meet estimated monthly cash needs takes place at the beginning of the month. Thus if in the month of april the firm expects to have a need for an additional 60,500, these funds x 1/12 x 60,500 owed for april and paid at the beginning of may. a. Prepare a cash budget for sharpe covering the first seven months of 2004. b. B. sharpe has 200,000 in notes payable due in july that must be repaid or renegotiated for an extension. Will the firm have ample cash to repay the notes.
Please see the attached excel sheet
5-1 a to what amount will the following investments accumulate? a.5,000 invest D for 10 years at 10 percent compounded annually b. 8,000 invested for 7 years at 8 percent compounded annually c. 775 invested for 12 years at 12 percent compounded annually d. 21,000 invested for 5 years at 5 percent compounded annually.
5-1. a. FVn = PV (1 + i)n
FV10 = $5,000(1 + 0.10)10
FV10 = $5,000 (2.594)
FV10 = $12,970
b. FVn = PV (1 + i)n
FV7 = $8,000 (1 + 0.08)7
FV7 = $8,000 (1.714)
FV7 = $13,712
c. FV12 = PV (1 + i)n
FV12 = $775 (1 + 0.12)12
FV12 = $775 (3.896)
FV12 = $3,019.40
d. FVn = PV (1 + i)n
FV5 = $21,000 (1 + 0.05)5
FV5 = $21,000 (1.276)
FV5 = $26,796.00
5-2A. (Compound value solving for n) How many years will the following take?
a. $500 to grow to $1,039.50 if invested at 5 percent compounded annually
b. $35 to grow to $53.87 if invested at 9 percent compounded annually
c. $100 to grow to $298.60 if invested at 20 percent compounded annually
d. $53 to grow to $78.76 if invested at 2 percent compounded annually
(a) FVn = PV (1 + i)n
$1,039.50 = $500 (1 + 0.05)n
2.079 = FVIF 5%, n yr.
Thus n = 15 years (because the value of 2.079 occurs in the 15 year row of the 5 percent column of Appendix B).
(b) FVn = PV (1 + i)n
$53.87 = $35 (1 + .09)n
1.539 = FVIF 9%, n yr.
Thus, n = 5 years
(c) FVn = PV (1 + i)n
$298.60 = $100 (1 + 0.2)n
2.986 = FVIF 20%, n yr.
Thus, n = 6 years
(d) FVn = PV (1 + i)n
$78.76 = $53 (1 + 0.02)n
1.486 = FVIF 2%, n yr.
Thus, n = 20 years
5-4a (present value) what is the present value of the following future amounts? A .800 to be received 10 years from now discounted back to the present at 10 percent. b. 300 to be received 5 years from now discounted back to the present at 5 percent. c.1,000 to be received 8 years from now discounted back to the present at 3 percent. d. 1,000 to be received 8 years from now discounted back to the present at 20 percent
5-4. a. PV = FVn [pic]
PV = $800 [pic]
PV = $800 (0.386)
PV = $308.80
b. PV = FVn [pic]
PV = $300 [pic]
PV = $300 (0.784)
PV = $235.20
c. PV = FVn [pic]
PV = $1,000 [pic]
PV = $1,000 (0.789)
PV = $789
d. PV = FVn [pic]
PV = $1,000 [pic]
PV = $1,000 (0.233)
PV = $233
Chapter 5: 5-5A (compound annuity) what is the accumulated sum of each of the following streams of payments? a.$500 a year for 10 years compounded annually at 5 percent b. $100 a year for 5 years compounded annually at 10 percent c. $35 a year for 7 years compounded annually at 7 percent d. $25 a year for 3 years compounded annually at 2 percent
5-5. a. FVn = PMT [pic]
FV = $500 [pic]
FV10 = $500 (12.578)
FV10 = $6,289
b. FVn = PMT [pic]
FV5 = $100 [pic]
FV5 = $100 (6.105)
FV5 = $610.50
c. FVn = PMT [pic]
FV7 = $35 [pic]
FV7 = $35 (8.654)
FV7 = $302.89
d. FVn = MT [pic]
FV3 = $25 [pic]
FV3 = $25 (3.060)
FV3 = $76.50
Chapter 5: 5-6A (present value of an annuity) what is the present value of the following annuities? a. 2,500 a year for 10 years discounted back to the present at 7 percent. b. $70 a year for 3 years discounted back to the present at 3 percent c. C. $280 a year for 7 years discounted back to the present at 6 percent d. D. $500 a year for 10 years discounted back to the present at 10 percent.
5-6. a. PV = PMT [pic]
PV = $2,500 [pic]
PV = $2,500 (7.024)
PV = $17,560
b. PV = PMT [pic]
PV = $70 [pic]
PV = $70 (2.829)
PV = $198.03
c. PV = PMT [pic]
PV = $280 [pic]
PV = $280 (5.582)
PV = $1,562.96
d. PV = PMT [pic]
PV = $500 [pic]
PV = $500 (6.145)
PV = $3,072.50
5-9A. (Compound interest with nonannual periods)
a. Calculate the future sum of $5,000, given that it will be held in the bank five years at an
annual interest rate of 6 percent.
b. Recalculate part (a) using a compounding period that is (1) semiannual and
(2) bimonthly.
c. Recalculate parts (a) and (b) for a 12 percent annual interest rate.
d. Recalculate part (a) using a time horizon of 12 years (annual interest rate is still 6 percent).
e. With respect to the effect of changes in the stated interest rate and holding periods on
future sums in parts (c) and (d), what conclusions do you draw when you compare these
figures with the answers found in parts (a) and (b)?
(a) FVn = PV (1 + i)n
FV5 = $5,000 (1 + 0.06)5
FV5 = $5,000 (1.338)
FV5 = $6,690
(b) FVn = PV (1 + )mn
FV5 = $5,000 (1 + )2X5
FV5 = $5,000 (1 + 0.03)10
FV5 = $5,000 (1.344)
FV5 = $6,720
FVn = PV (1 + )mn
FV5 = 5,000 (1 + )6X5
FV5 = $5,000 (1 + 0.01)30
FV5 = $5,000 (1.348)
FV5 = $6,740
(c) FVn = PV (1 + i)n
FV5 = $5,000 (1 + 0.12)5
FV5 = $5,000 (1.762)
FV5 = $8,810
FV5 = PV mn
FV5 = $5,000 2X5
FV5 = $5,000 (1 + 0.06)10
FV5 = $5,000 (1.791)
FV5 = $8,955
FV5 = PV mn
FV5 = $5,000 6X5
FV5 = $5,000 (1 + 0.02)30
FV5 = $5,000 (1.811)
FV5 = $9,055
(d) FVn = PV (1 + i)n
FV12 = $5,000 (1 + 0.06)12
FV12 = 5,000 (2.012)
FV12 = $10,060
(e) An increase in the stated interest rate will increase the future value of a given sum. Likewise, an increase in the length of the holding period will increase the future value of a given sum.
Chapter 15
15-5. A manager in your firm decides to employ break-even analysis. Of what shortcomings should this manager be aware?
15-5. The most important shortcomings of break-even analysis are:
(1) The cost-volume-profit relationship is assumed to be linear over the entire range of output.
(2) All of the firm's production is assumed to be salable at the fixed selling price.
(3) The sales mix and production mix is assumed constant.
(4) The level of total fixed costs and the variable cost to sales ratio is held constant over all output and sales ranges.
15-8. Break-even analysis assumes linear revenue and cost functions. In reality, these linear functions over large output and sales levels are highly improbable. Why?
15-8. As the sales of a firm increase, two things occur that bias the cost and revenue functions toward a curvilinear shape. First, sales will increase at a decreasing rate. As the market approaches saturation, the firm must cut its price to generate sales revenue. Second, as production approaches capacity, inefficiencies occur that result in higher labor and material costs. Furthermore, the firm's operating system may have to bear higher administrative and fixed costs. The result is higher per unit costs as production output increases.
15-9A. (Fixed costs and the break-even point) A & B Beverages expects to earn $50,000 next year after taxes. Sales will be $375,000. The store is located near the shopping district surrounding Blowing Rock University. Its average product sells for $27 a unit. The variable cost per unit is $14.85. The store experiences a 40 percent tax rate.
a. What are the store’s fixed costs expected to be next year?
b. Calculate the store’s break-even point in both units and dollars.
15-9A.
(a) {S- (VC + F)} (1-T) = $50,000
[pic] = $50,000
[S – VC - } (1 – T) = $50,000
{$375,000 - $206,250 – F} (0.6) = $50,000
($168,750 - F) (0.6) = $50,000
F = $85,416.67
(b) QB = [pic] = [pic] = [pic] = 7,030 units
S* = [pic] = [pic] = $189,815
15-12A. (Break-even point) You are a hard-working analyst in the office of financial operations for a manufacturing firm that produces a single product. You have developed the following cost structure information for this company. All of it pertains to an output level of 10 million units.
Using this information, find the break-even point in units of output for the firm.
Return on operating assets = 25%
Operating asset turnover = 5 times
Operating assets = $20 million
Degree of operating leverage = 4 times
15-12A. Given the data for this problem, several approaches are possible for finding the break-even point in units. The approach below seems to work well with students.
Step (1) Compute the operating profit margin:
Operating Profit Margin x Operating Asset Turnover = Return on operating assets
(M) x (5) = 0.25
M = .05
Step (2) Compute the sales level associated with the given output level:
[pic]= 5
Sales = $100,000,000
Step (3) Compute EBIT:
(.05) ($100,000,000) = $5,000,000
Step (4) Compute revenue before fixed costs. Since the degree of operating leverage is 4 times, revenue before fixed costs (RBF) is 4 times EBIT as follows:
RBF = (4) ( ($5,000,000) = $20,000,000
Step (5) Compute total variable costs:
(Sales) - (Total variable costs) = $20,000,000
$100,000,000 - (Total variable costs) = $20,000,000
Total variable costs = $80,000,000
Step (6) Compute total fixed costs:
RBF - Fixed costs = $5,000,000
$20,000,000 - fixed costs = $5,000,000
Fixed costs = $15,000,000
Step (7) Find the selling price per unit, and the variable cost per unit:
P = [pic]= $10.00
V = [pic]= $8.00
Step (8) Compute the break-even point:
QB = [pic] = [pic] = [pic] = 7,500,000 units
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