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 ye