发布时间 : 星期一 文章Fundamentals of Corporate Finance 3rd ed Jonathan Berk Ch4更新完毕开始阅读0454e40058f5f61fb6366680
46 Berk/DeMarzo/Harford ? Fundamentals of Corporate Finance, Third Edition, Global Edition
take our money to double, we can estimate the answer using the rule of 72: 72/10 ? 7.2, so the answer will be approximately 7.2 years.
?20000?ln?10000????7.27 N?ln?1.10?
Execute:
Using a financial calculator or Excel:
10 0 20000 ?10000 7.27 Excel Formula: ?NPER(RATE,PMT, PV, FV) ? NPER(0.10,0,–10000,20000)
Evaluate:
If you can earn 10% per year on the $10,000, it will double to $20,000 in 7.27 years. 37. Plan: Draw the timeline and determine the interest rate the bank is paying you. Execute:
0 –1,000 1 100 2 100 3 100
The payments are a perpetuity, so PV?100. r Setting the NPV of the cash flow stream equal to 0 and solving for r gives the IRR:
NPV?0?100100?1,000?r??10% r1,000
So the IRR is 10%.
Evaluate: The bank is paying you 10% on your deposit.
*38. Plan: Draw a timeline to show when the cash flows occur. Then determine how long the plant
will be in production. Also estimate the NPV of the project and hence whether or not it should be built.
Execute:
0 –10,000,000
1 2
1,000,000 – 1,000,000 – 50,000 50,000(1.05)
N 1,000,000 50,000(1.05)N – 1
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Chapter 4 Time Value of Money: Valuing Cash Flow Streams 47
The plant will shut down when:
1,000,000?50,000(1.05)N?1?01,000,000?2050,000(N?1)log(1.05)?log(20)(1.05)N?1?N ?
log(20)?1?62.4log(1.05) So the last year of production will be in year 62.
We now build an Excel spreadsheet with the cash flows to the 62 years.
A
B
C
D
E
F
G
BJ
BK
BL
1 2 G 1.05 3 R 0.06 4 5 6 T 0 1 2 3 4 5 60 61 62 7 8 ?10000000 1000000 1000000 1000000 1000000 1000000 1000000 1000000 1000000 9 ?50000 ?52500 ?55125 ?57881.3 ?60775.3 ?889485 ?933959 ?980657 10 ($10,000,000.00) 950000 947500 944875 942118.8 939224.7 110515 66040.71 19342.74 11 12 NPV $3,995,073.97 13 EXCEL NPV FORMULA ?B10?NPV(C3,C11:BL11)
The Net Present Value of the project is computed in cell B12.
Evaluate: So, the NPV?13,995,074?10,000?$3,995,074, and you should build it. *39. Plan: Draw a timeline to show when the cash flows will occur. Then determine how much you will have to put into the retirement plan annually to meet your goal.
Execute:
22 0 23 24 1 2 –C –C
65 66 67 43 44 45 –C 100 100
100 78 100
The PV of the costs must equal the PV of the benefits, so begin by dividing the problem into two parts: the costs and the benefits.
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48 Berk/DeMarzo/Harford ? Fundamentals of Corporate Finance, Third Edition, Global Edition
Costs: The costs are the contributions, a 43-year annuity with the first payment in one year:
PVcosts?C?1?1??? 0.07?(1.07)43?
Benefits: The benefits are the payouts after retirement, a 35-year annuity paying $100,000 per year with the first payment 44 years from today. The value of this annuity in year 43 is:
PV43?100,000?1?1???
0.07?(1.07)35? Solve for PV:
N
I/Y 7.00%
PV (1,294,767.23)
PMT 100,000
FV 0
Excel Formula
?PV(0.07,35,100000,0)
Given: 35
The value today is just the discounted value in 43 years:
PVbenefits??PV43(1.07)43100,000?1?1???
0.07(1.07)43?(1.07)35??70,581.24
Because the PV of the costs must equal the PV of the benefits (or equivalently, the NPV of the cash flow must be zero):
70,581.24?C?1?1??? 0.07?(1.07)43?
Solve for PV:
N
Given: 43
I/Y 7.00%
PV (70,581.24)
PMT 0
FV 1,294,767
Excel Formula
?PV(0.07,43,0,1294767.23)
Solving for C gives
C?70,581.24?0.071???1?(1.07)43? ???5,225.55PV 70,581.24
PMT (5,226)
FV 0
Excel Formula
?PMT(0.07,43,70581.24,0)
Solve for PMT:
N
Given: 43
I/Y 7.00%
? 2015 Pearson Education Limited
Chapter 4 Time Value of Money: Valuing Cash Flow Streams 49
Evaluate: You will have to invest $5,225.55 annually into the retirement plan to meet your goal.
40. We calculate the future value as FV = C × (1 + r)n. The initial amount C = $5,000 and the
interest rate r = 0.5% per month. Because we have a monthly interest rate, we also need to express the number of periods, n, in months, so n = 5 × 12 = 60. Thus,
FV = $5,000 × 1.00560 = $6,744.25
We will have $6,744.25 in the account in five years’ time.
41. The $5,000 cost is a monthly perpetuity. Using the perpetuity formula with monthly cash flows and the monthly interest rate, this cost has a present value of $5,000/0.005 = $1 million. 42. The most you can borrow is the PV of the payments you can afford. This is a PV of annuity
problem but with monthly payments and a monthly interest rate. CF = 200, r = 0.0075, n = 60
?C?1?200?1PV??1???9,634.67 ?1?n?60?r???1?r???0.0075???1.0075??? Or using the annuity calculator:
43. We want to compute the future value of our account balance. Let’s begin with the timeline over the next 46 months:
1 1,000 2 1,000
45 1,000 46 ? ? 2015 Pearson Education Limited
50 Berk/DeMarzo/Harford ? Fundamentals of Corporate Finance, Third Edition, Global Edition
Our charges correspond to a 45-month annuity. Therefore, using the FV of an annuity formula, the future value at the end of 45 months is: FV(Annuity) = $1,000 ×
11.0145?1? = $56,481.07 ?0.01Or using the annuity calculator:
Of course, we are not quite done. When we receive our statement in the 46th month, there will
be one more month’s worth of interest charged. Therefore, we will have a final balance of $56,481.07 × 1.01 = $57,045.89. Note that the future value formula for an annuity computes the future value as of the date of the last payment. In this question, we need to compute the future value one month after the final payment, which requires an additional calculation. (We could have alternatively computed the PV of the annuity, and then computed its future value 46 months in the future.)
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