E-text responses



E-text responses

P4–2

Future value calculation Without referring to tables or to the preprogrammed function on your financial calculator, use the basic formula for future value along with the given interest rate, i, and the number of periods, n, to calculate the future value interest factor in each of the cases shown in the following table. Compare the calculated value to the value in Appendix Table A–1.

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Case

A FVIF 12%,2 periods = (1 +.12)2 = 1.254

B FVIF 6%,3 periods = (1 +.06)3 = 1.191

C FVIF 9%,2 periods = (1 +.09)2 = 1.188

D FVIF 3%,4 periods = (1 + .03)4 = 1.126

P4–3

Future value tables Use the future value interest factors in Appendix Table A–1 in each of the cases shown in the table on the facing page to estimate, to the nearest year, how long it would take an initial deposit, assuming no withdrawals,

a. To double.

b. To quadruple.

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Case A

a. 2 = 1 x (1 + .07)n b. 4 = 1 x (1 + .07)n

2 = (1.07)n 4 = (1.07)n

Log(2) = n x Log(1.07) Log(4) = n x Log(1.07)

n= Log(2)/Log(1.07) = 10.24 n= Log(4)/Log(1.07) = 20.49

Nearest to 10 years Nearest to 20 years

Case B

a. 2 = 1 x (1 + .40)n b. 4 = 1 x (1 + .40)n

2 = (1.40)n 4 = (1.40)n

Log(2) = n x Log(1.40) Log(4) = n x Log(1.40)

n= Log(2)/Log(1.40) = 2.06 n= Log(4)/Log(1.40) = 4.12

Nearest to 2 years Nearest to 4 years

Case C

a. 2 = 1 x (1 + .20)n b. 4 = (1 + .20)n

2 = (1.20)n 4 = (1.20)n

Log(2) = n x Log(1.20) Log(4) = n x Log(1.20)

n= Log(2)/Log(1.20) = 3.80 n= Log(4)/Log(1.20) = 7.60

Nearest to 4 years Nearest to 8 years

Case D

a. 2 = 1 x (1 +.10)n b. 4 = (1 +.10)n

2 = (1.10)n 4 = (1.10)n

Log(2) = n x Log(1.10) Log(4) = n x Log(1.10)

n= Log(2)/Log(1.10) = 7.27 n= Log(4)/Log(1.10) = 14.54

Nearest to 7 years Nearest to 15 years

P12–4

Breakeven analysis Barry Carter is considering opening a music store. He wants to estimate the number of CDs he must sell to break even. The CDs will be sold for $13.98 each, variable operating costs are $10.48 per CD, and annual fixed operating costs are $73,500.

a. Find the operating breakeven point in number of CDs.

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b. Calculate the total operating costs at the breakeven volume found in part a.

Total operating costs = FC + (Q x VC)

Total operating costs = $73,500 + (21,000 x $10.48)

Total operating costs = $293,580

c. If Barry estimates that at a minimum he can sell 2,000 CDs per month, should he go into the music business?

2,000 x 12 = 24,000 CDs per year. 2,000 records per month exceeds the operating breakeven by 3,000 records per year. Barry should go into the CD business.

d. How much EBIT will Barry realize if he sells the minimum 2,000 CDs per month noted in part c?

EBIT = (P x Q) - FC - (VC x Q)

= ($13.98 x 24,000) - $73,500 - ($10.48 x 24,000)

= $335,520 - $73,500 - $251,520

= $10,500

P12–19

EBIT–EPS and capital structure Data-Check is considering two capital structures.

The key information is shown in the following table. Assume a 40% tax rate.

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a. Calculate two EBIT–EPS coordinates for each of the structures by selecting any two EBIT values and finding their associated EPS values.

Using $50,000 and $60,000 EBIT:

| |Structure A | |Structure B | |

|EBIT |$50,000 |$60,000 |$50,000 |$60,000 |

|Less: Interest | 16,000 | 16,000 | 34,000 | 34,000 |

|Net profits before taxes |$34,000 |$44,000 |$16,000 |$26,000 |

|Less: Taxes | 13,600 | 17,600 | 6,400 | 10,400 |

|Net profit after taxes |$20,400 |$26,400 |$9,600 |$15,600 |

| | | | | |

|EPS (4,000 shares) |$5.10 |$6.60 | | |

|EPS (2,000 shares) | | |$4.80 |$7.80 |

Financial breakeven points:

Structure A Structure B

$16,000 $34,000

b. Plot the two capital structures on a set of EBIT–EPS axes.

EPS ($)

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EBIT ($)

c. Indicate over what EBIT range, if any, each structure is preferred.

If EBIT is expected to be below $52,000, Structure A is preferred. If EBIT is expected to be above $52,000, Structure B is preferred.

d. Discuss the leverage and risk aspects of each structure.

Structure A has less risk and promises lower returns as EBIT increases. B is more risky since it has a higher financial breakeven point. The steeper slope of the line for Structure B also indicates greater financial leverage.

e. If the firm is fairly certain that its EBIT will exceed $75,000, which structure would you recommend? Why?

If EBIT is greater than $75,000, Structure B is recommended since changes in EPS are much greater for given values of EBIT.

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