公司理财计算题汇总

公司理财计算题汇总

金融工程三班 奚红胜

第四章：净现值：P73

Since this bond has no interim coupon payments, its present value 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 = $92.30 PV = $1,500,000 / 1.0827 = $187,780.23

a. At a discount rate 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 = $9,090.91 Option two: $20,000 / 1.15 = $12,418.43 Choose the second option. c. Option one: $10,000 / 1.2 = $8,333.33 Option two: $20,000 / 1.25 = $8,037.55 Choose 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 option 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 = 2

1 + r = 1.18921 r = 0.18921 = 18.921%

PV = $5,000,000 / 1.1210 = $1,609,866.18 a. $1,000 / 0.1 = $10,000

b. $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.

$2,420 / 0.1 = $24,200 is the value two years from now of

the perpetual stream. Thus, the value of the perpetuity is $24,200 / 1.12 = $20,000.

The 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; remember 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 more precise answer by interpolating between nine and ten percent. [ 10% [6.1446 a r b c 6.4 d

c.

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 solving the annuity formula for the interest rate. Sophisticated calculators can compute the rate directly as 9.0626%.

[Note: A standard financial calculator’s TVM keys can solve for this rate. With annuity

flows, the IRR key on “advanced” financial calculators is unnecessary.]

a.The annuity amount can 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 50.07

$17,824.65 = C (4.1002) C = $4,347.26

Thus, putting $4,347.26 into the 7% account each year will provide $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 = $17,824.65 The formula for future value of any annuity can be used to solve the problem (see

footnote 11 of the text).

Option one: This cash flow is an annuity due. To value 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 + $115,200 300.10

= $115,200 + $115,200 (9.4269)

= $1,201,178.88

Option 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 $72,759.60 [= $101,055 (1 - 0.28)].

Value

= $446,000 + $72,759.60 300.10

= $446,000 + $72,759.60 (9.4269)

= $1,131,897.47 Since option one has a higher PV, you should choose it. se the discount factors to discount the individual cash flows. Then compute the NPV 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. Thus, the appropriate annuity factor to use with them is 2.6198 (= 4.3553 - 1.7355).

Year Cash Flow Factor PV 1 $700 0.9091 $636.37 2 900 0.8264 743.76 3 1,000 4 1,000 2.6198 2,619.80 5 1,000 6 1,000 7 1,250 0.5132 641.50 8 1,375 0.4665 641.44 Total $5,282.87

NPV = -$5,000 + $5,282.87 = $282.87 Purchase the machine. 第五章：债券和股票定价：P95

The 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 use 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

40

is it 3%. PV=C Tr+F/(1+r)

a. $40 (19.7928) + $1,000 / 1.0440 = $1,000

Notice that whenever the coupon rate and the market rate are the same, the bond is priced at par.

b. $40 (17.1591) + $1,000 / 1.0540 = $828.41

Notice that whenever the coupon rate is below the market rate, the bond is priced below par. c. $40 (23.1148) + $1,000 / 1.0340 = $1,231.15

Notice that whenever the coupon rate is above the market rate, the bond is priced above

a. The semi-annual interest rate is $60 / $1,000 = 0.06. Thus, the effective

annual rate is 1.062 - 1 = 0.1236 = 12.36%.

b. c.

12

Price = $30 120.06 + $1,000 / 1.06 = $748.48 12Price = $30 120

.04 + $1,000 / 1.04= $906.15

Note: In parts b and c we are implicitly assuming that the yield curve is flat. That is,

the yield in year 5 applies for year 6 as well.

rice = $2 (0.72) / 1.15 + $4 (0.72) / 1.152 + $50 / 1.153 = $36.31 The number of shares you own = $100,000 / $36.31 = 2,754 shares

第六章：投资决策和其他方法：P121

a. Payback period of Project A = 1 + ($7,500 - $4,000) / $3,500 = 2 years

Payback period of Project B = 2 + ($5,000 - $2,500 -$1,200) / $3,000 = 2.43 years Project A should be chosen.

b.

NPVA = -$7,500 + $4,000 / 1.15 + $3,500 / 1.152 + $1,500 / 1.153 = -$388.96 NPVB = -$5,000 + $2,500 / 1.15 + $1,200 / 1.152 + $3,000 / 1.153 = $53.83

Project B should be chosen.

Average 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

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.

2 - $1,000 / (1 + r)3

- $1,000 / (1 + r)4 = 0 By 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 - $1,000 / 1.13 - $1,000 / 1.14= -$359.95 When r = 20%:

NPV = $5,000 - $2,500 / 1.2 - $2,000 / 1.22 - $1,000 / 1.23 - $1,000 / 1.24= $466.82 Yes, they are consistent with the choices of the IRR rule since the signs of the cash

flows change only once.

PI = $40,000 70.15

/ $160,000 = 1.04

consider

Since the PI exceeds one accept the project.

第七章：净现值和资本预算：P140

Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 1. Annual Salary Savings $120,000 $120,00$120,000 $120,000 $120,000

2. Depreciation 100,000 160,000 96,000 57,600 57,600 3. Taxable Income 20,000 -40,000 24,000 62,400 62,400 4. Taxes 6,800 -13,600 8,160 21,216 21,216 5. Operating Cash Flow 113,200 133,600 111,840 98,784 98,784

(line 1-4) 6. -100,000 Net working $100,000

capital

7. Investment 8. Total Cash Flow

$500,000 75,792* -$400,000 $113,200 $133,60$111,840 $98,784 $74,576

*75,792 = $100,000 - 0.34 ($100,000 - $28,800)

NPV = -$400,000+ $113,200 / 1.12 + $133,600 / 1.122 + $111,840 / 1.123 + $98,784 / 1.124 + $74,576 / 1.125

= -$7,722.52

Real interest rate = (1.15 / 1.04) - 1 = 10.58%

NPVA = -$40,000+ $20,000 / 1.1058 + $15,000 / 1.10582 + $15,000 / 1.10583 = $1,446.76

NPVB = -$50,000+ $10,000 / 1.15 + $20,000 / 1.152 + $40,000 / 1.153 = $119.17

Choose project A.

PV = $120,000 / {0.11 - (-0.06)}

= $705,882.35

t = 0 t = 1 $12,000 $6,000

t = 2 $6,000 t = 3 t = 4 t = 5 $6,000

$4,000 $12,000 $6,000

t = 6

$6,000

... ...

The present value of one cycle is:

4

PV = $12,000 + $6,000 30.06 + $4,000 / 1.06

= $12,000 + $6,000 (2.6730) + $4,000 / 1.064 = $31,206.37

The cycle is four years long, so use a four year annuity factor to compute the equivalent annual cost (EAC).

4

EAC= $31,206.37 / 0.06

= $31,206.37 / 3.4651

= $9,006 The present value of such a stream in perpetuity is

$9,006 / 0.06 = $150,100

第八章：公司战略和净现值分析：P154 The accounting break-even = (120,000 + 20,000) / (1,500 - 1,100) = 350 units

. The accounting break-even = 340,000 / (2.00 - 0.72)

= 265,625 abalones

b. [($2.00 300,000) - (340,000 + 0.72 300,000)] (0.65) = $28,600 This is the after tax profit.

本文来源：https://www.bwwdw.com/article/p0l4.html