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1、Chapter 2: Accounting Statements and Cash Flow2.10 AssetsCurrent assetsCash$ 4,000Accounts receivable 8,000Total current assets$ 12,000Fixed assetsMachinery$ 34,000Patents 82,000Total fixed assets$116,000Total assets$128,000Liabilities and equityCurrent liabilitiesAccounts payable$ 6,000Taxes payabl
2、e 2,000Total current liabilities$ 8,000Long-term liabilitiesBonds payable$7,000Stockholders equityCommon stock ($100 par)$ 88,000Capital surplus19,000Retained earnings 6,000Total stockholders equity$113,000Total liabilities and equity$128,0002.11One year agoTodayLong-term debt$50,000,000$50,000,000P
3、referred stock30,000,00030,000,000Common stock100,000,000110,000,000Retained earnings 20,000,000 22,000,000Total$200,000,000$212,000,0002.12Total Cash Flow of the Stancil CompanyCash flows from the firmCapital spending$(1,000)Additions to working capital (4,000)Total$(5,000)Cash flows to investors o
4、f the firmShort-term debt$(6,000)Long-term debt(20,000)Equity (Dividend - Financing) 21,000Total$(5,000)Note: This table isnt the Statement of Cash Flows, which is only covered in Appendix 2B, since the latter has the change in cash (on the balance sheet) as a final entry.2.13a.The changes in net wo
5、rking capital can be computed from:Sources of net working capitalNet income$100Depreciation50Increases in long-term debt 75Total sources$225Uses of net working capitalDividends$50Increases in fixed assets* 150Total uses$200Additions to net working capital$25*Includes $50 of depreciation. b.Cash flow
6、 from the firmOperating cash flow$150Capital spending(150)Additions to net working capital (25)Total$(25)Cash flow to the investorsDebt$(75)Equity 50Total$(25)Chapter 3: Financial Markets and Net Present Value: First Principles of Finance (Advanced)3.14 $120,000 - ($150,000 - $100,000) (1.1) = $65,0
7、003.15 $40,000 + ($50,000 - $20,000) (1.12) = $73,6003.16a.($7 million + $3 million) (1.10) = $11.0 millionb. i. They could spend $10 million by borrowing $5 million today.ii. They will have to spend $5.5 million = $11 million - ($5 million x 1.1) at t=1.Chapter 4: Net Present Value4.12a.$1,000 1.05
8、10 = $1,628.89b.$1,000 1.0710 = $1,967.15c.$1,000 1.0520 = $2,653.30d.Interest compounds on the interest already earned. Therefore, the interest earned in part c, $1,653.30, is more than double the amount earned in part a, $628.89.4.13Since this bond has no interim coupon payments, its present value
9、 is simply the present value of the $1,000 that will be received in 25 years. Note: As will be discussed in the next chapter, the present value of the payments associated with a bond is the price of that bond.PV = $1,000 /1.125 = $92.304.14PV = $1,500,000 / 1.0827 = $187,780.234.15a.At a discount ra
10、te of zero, the future value and present value are always the same. Remember, FV = PV (1 + r) t. If r = 0, then the formula reduces to FV = PV. Therefore, the values of the options are $10,000 and $20,000, respectively. You should choose the second option.b.Option one:$10,000 / 1.1 = $9,090.91Option
11、 two:$20,000 / 1.15 = $12,418.43Choose the second option.c.Option one:$10,000 / 1.2 = $8,333.33Option two:$20,000 / 1.25 = $8,037.55Choose the first option.d.You are indifferent at the rate that equates the PVs of the two alternatives. You know that rate must fall between 10% and 20% because the opt
12、ion you would choose differs at these rates. Let r be the discount rate that makes you indifferent between the options.$10,000 / (1 + r) = $20,000 / (1 + r)5(1 + r)4 = $20,000 / $10,000 = 21 + r = 1.18921r = 0.18921 = 18.921%4.16The $1,000 that you place in the account at the end of the first year w
13、ill earn interest for six years. The $1,000 that you place in the account at the end of the second year will earn interest for five years, etc. Thus, the account will have a balance of$1,000 (1.12)6 + $1,000 (1.12)5 + $1,000 (1.12)4 + $1,000 (1.12)3= $6,714.614.17PV = $5,000,000 / 1.1210 = $1,609,86
14、6.184.18a.$1.000 (1.08)3 = $1,259.71b.$1,000 1 + (0.08 / 2)2 3 = $1,000 (1.04)6 = $1,265.32c.$1,000 1 + (0.08 / 12)12 3 = $1,000 (1.00667)36 = $1,270.24d.$1,000 e0.08 3 = $1,271.25e.The future value increases because of the compounding. The account is earninginterest on interest. Essentially, the in
15、terest is added to the account balance at the end of every compounding period. During the next period, the account earns interest on the new balance. When the compounding period shortens, the balance that earns interest is rising faster.4.19The price of the consol bond is the present value of the co
16、upon payments. Apply the perpetuity formula to find the present value. PV = $120 / 0.15 = $8004.20a.$1,000 / 0.1 = $10,000b.$500 / 0.1 = $5,000 is the value one year from now of the perpetual stream. Thus, the value of the perpetuity is $5,000 / 1.1 = $4,545.45.c.$2,420 / 0.1 = $24,200 is the value
17、two years from now of the perpetual stream. Thus, the value of the perpetuity is $24,200 / 1.12 = $20,000.4.21Apply the NPV technique. Since the inflows are an annuity you can use the present value of an annuity factor.NPV= -$6,200 + $1,200 = -$6,200 + $1,200 (5.3349)= $201.88Yes, you should buy the
18、 asset.4.22Use an annuity factor to compute the value two years from today of the twenty payments. Remember, the annuity formula gives you the value of the stream one year before the first payment. Hence, the annuity factor will give you the value at the end of year two of the stream of payments. Va
19、lue at the end of year two= $2,000 = $2,000 (9.8181)= $19,636.20The present value is simply that amount discounted back two years.PV = $19,636.20 / 1.082 = $16,834.884.23The easiest way to do this problem is to use the annuity factor. The annuity factor must be equal to $12,800 / $2,000 = 6.4; remem
20、ber PV =C ATr. The annuity factors are in the appendix to the text. To use the factor table to solve this problem, scan across the row labeled 10 years until you find 6.4. It is close to the factor for 9%, 6.4177. Thus, the rate you will receive on this note is slightly more than 9%.You can find a m
21、ore precise answer by interpolating between nine and ten percent. 10% 6.1446 a r b c 6.4 d 9% 6.4177 By interpolating, you are presuming that the ratio of a to b is equal to the ratio of c to d.(9 - r ) / (9 - 10) = (6.4177 - 6.4 ) / (6.4177 - 6.1446)r = 9.0648%The exact value could be obtained by s
22、olving the annuity formula for the interest rate. Sophisticated calculators can compute the rate directly as 9.0626%.Note: A standard financial calculators TVM keys can solve for this rate. With annuity flows, the IRR key on “advanced” financial calculators is unnecessary.4.24a.The annuity amount ca
23、n be computed by first calculating the PV of the $25,000 which you need in five years. That amount is $17,824.65 = $25,000 / 1.075. Next compute the annuity which has the same present value.$17,824.65= C $17,824.65= C (4.1002) C= $4,347.26Thus, putting $4,347.26 into the 7% account each year will pr
24、ovide $25,000 five years from today.b.The lump sum payment must be the present value of the $25,000, i.e., $25,000 / 1.075 = $17,824.65The formula for future value of any annuity can be used to solve the problem (see footnote 11 of the text).4.25Option one: This cash flow is an annuity due. To value
25、 it, you must use the after-tax amounts. The after-tax payment is $160,000 (1 - 0.28) = $115,200. Value all except the first payment using the standard annuity formula, then add back the first payment of $115,200 to obtain the value of this option.Value= $115,200 + $115,200 = $115,200 + $115,200 (9.
26、4269)= $1,201,178.88Option two: This option is valued similarly. You are able to have $446,000 now; this is already on an after-tax basis. You will receive an annuity of $101,055 for each of the next thirty years. Those payments are taxable when you receive them, so your after-tax payment is $72,759
27、.60 = $101,055 (1 - 0.28).Value= $446,000 + $72,759.60 = $446,000 + $72,759.60 (9.4269)= $1,131,897.47Since option one has a higher PV, you should choose it.4.26Let r be the rate of interest you must earn.$10,000(1 + r)12= $80,000(1 + r)12 = 8r = 0.18921 = 18.921%4.27First compute the present value
28、of all the payments you must make for your childrens education. The value as of one year before matriculation of one childs education is$21,000 = $21,000 (2.8550) = $59,955.This is the value of the elder childs education fourteen years from now. It is the value of the younger childs education sixtee
29、n years from today. The present value of these is PV= $59,955 / 1.1514 + $59,955 / 1.1516 = $14,880.44You want to make fifteen equal payments into an account that yields 15% so that the present value of the equal payments is $14,880.44. Payment = $14,880.44 / = $14,880.44 / 5.8474 = $2,544.804.28Thi
30、s problem applies the growing annuity formula. The first payment is $50,000(1.04)2(0.02) = $1,081.60.PV= $1,081.60 1 / (0.08 - 0.04) - 1 / (0.08 - 0.04)1.04 / 1.0840 = $21,064.28This is the present value of the payments, so the value forty years from today is $21,064.28 (1.0840) = $457,611.464.29Use
31、 the discount factors to discount the individual cash flows. Then compute the NPV of the project. Notice that the four $1,000 cash flows form an annuity. You can still use the factor tables to compute their PV. Essentially, they form cash flows that are a six year annuity less a two year annuity. Th
32、us, the appropriate annuity factor to use with them is 2.6198 (= 4.3553 - 1.7355).YearCash FlowFactorPV1 $7000.9091$636.372 9000.8264743.7631,00041,0002.61982,619.8051,00061,00071,2500.5132641.5081,3750.4665641.44Total$5,282.87NPV= -$5,000 + $5,282.87= $282.87Purchase the machine.Chapter 5: How to V
33、alue Bonds and Stocks5.9The amount of the semi-annual interest payment is $40 (=$1,000 0.08 / 2). There are a total of 40 periods; i.e., two half years in each of the twenty years in the term to maturity. The annuity factor tables can be used to price these bonds. The appropriate discount rate to us
34、e is the semi-annual rate. That rate is simply the annual rate divided by two. Thus, for part b the rate to be used is 5% and for part c is it 3%. PV=C+F/(1+r)40a. $40 (19.7928) + $1,000 / 1.0440 = $1,000Notice that whenever the coupon rate and the market rate are the same, the bond is priced at par
35、. b. $40 (17.1591) + $1,000 / 1.0540 = $828.41Notice that whenever the coupon rate is below the market rate, the bond is priced below par.c. $40 (23.1148) + $1,000 / 1.0340 = $1,231.15Notice that whenever the coupon rate is above the market rate, the bond is priced above par.5.10a.The semi-annual in
36、terest rate is $60 / $1,000 = 0.06. Thus, the effective annual rate is 1.062 - 1 = 0.1236 = 12.36%.b.Price = $30 + $1,000 / 1.0612 = $748.48c.Price = $30 + $1,000 / 1.0412= $906.15Note: In parts b and c we are implicitly assuming that the yield curve is flat. That is, the yield in year 5 applies for
37、 year 6 as well.5.11Price = $2 (0.72) / 1.15 + $4 (0.72) / 1.152 + $50 / 1.153= $36.31The number of shares you own = $100,000 / $36.31 = 2,754 shares5.12Price = $1.15 (1.18) / 1.12 + $1.15 (1.182) / 1.122 + $1.152 (1.182) / 1.123 + $1.152 (1.182) (1.06) / (0.12 - 0.06) / 1.123 = $26.955.13Insert bef
38、ore last sentence of question: Assume that dividends are a fixed proportion of earnings.Dividend one year from now = $5 (1 - 0.10) = $4.50Price = $5 + $4.50 / 0.14 - (-0.10)= $23.75Since the current $5 dividend has not yet been paid, it is still included in the stock price.Chapter 6: Some Alternativ
39、e Investment Rules6.10a.Payback period of Project A = 1 + ($7,500 - $4,000) / $3,500 = 2 yearsPayback period of Project B = 2 + ($5,000 - $2,500 -$1,200) / $3,000 = 2.43 yearsProject A should be chosen.b.NPVA = -$7,500 + $4,000 / 1.15 + $3,500 / 1.152 + $1,500 / 1.153 = -$388.96NPVB = -$5,000 + $2,5
40、00 / 1.15 + $1,200 / 1.152 + $3,000 / 1.153 = $53.83Project B should be chosen.6.11a.Average Investment:($16,000 + $12,000 + $8,000 + $4,000 + 0) / 5 = $8,000Average accounting return:$4,500 / $8,000 = 0.5625 = 56.25%b.1.AAR does not consider the timing of the cash flows, hence it does not consider
41、the time value of money.2.AAR uses an arbitrary firm standard as the decision rule.3.AAR uses accounting data rather than net cash flows.6.12aAverage Investment = (8000 + 4000 + 1500 + 0)/4 = 3375.00Average Net Income = 2000(1-0.75) = 1500= AAR = 1500/3375=44.44% 6.13 a.Solve x by trial and error:-$
42、8,000 + $4,000 / (1 + x) + $3000 / (1 + x)2 + $2,000 / (1 + x)3 = 0x = 6.93%b.No, since the IRR (6.93%) is less than the discount rate of 8%.Alternatively, the NPV a discount rate of 0.08 = -$136.62.6.14a.Solve r in the equation:$5,000 - $2,500 / (1 + r) - $2,000 / (1 + r)2 - $1,000 / (1 + r)3 - $1,
43、000 / (1 + r)4 = 0By trial and error,IRR = r = 13.99%b.Since this problem is the case of financing, accept the project if the IRR is less than the required rate of return.IRR = 13.99% 10%Reject the offer.c.IRR = 13.99% 20%Accept the offer.d.When r = 10%:NPV = $5,000 - $2,500 / 1.1 - $2,000 / 1.12 -
44、$1,000 / 1.13 - $1,000 / 1.14 = -$359.95When r = 20%:NPV = $5,000 - $2,500 / 1.2 - $2,000 / 1.22 - $1,000 / 1.23 - $1,000 / 1.24 = $466.82Yes, they are consistent with the choices of the IRR rule since the signs of the cash flows change only once.6.15 PI = $40,000 / $160,000 = 1.04Since the PI excee
45、ds one accept the project.Chapter 7: Net Present Value and Capital Budgeting7.9Since there is uncertainty surrounding the bonus payments, which McRae might receive, you must use the expected value of McRaes bonuses in the computation of the PV of his contract. McRaes salary plus the expected value of his bonuses in years on
