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Homework answers / question archive / 1) An investment is expected to generate cash flows of $20000 next year (at time t=1), and $10000 in two years at time t=2
1) An investment is expected to generate cash flows of $20000 next year (at time t=1), and $10000 in two years at time t=2. After that, the annual cash flows generated by the investment will decrease forever at growth rate of -8% APR compounded annually. What is the present value of this stream of cash flows if r=10% APR compounded annually? (rounded to nearest 10th)
2) If you start depositing a constant $200 per month in a particular fund, starting next month, your advisor thinks you should have $936264.05 forty years later. What effective annual rate of return (EAR) is the advisor assuming that the fund will provide? (rounded to nearest basis point, as in "0.1234")
1) Computation of Present Value of the stream of Cash Flows:
Present Value of the stream of Cash Flows = Future Cash Flows * Present Value of Discounting Factor(rate%,time period)
= 20,000/1.1+10,000/1.1^2+51111.11/1.1^2
= $18,181.82 + $8,264.46 + $42,240.59
Present Value of the stream of Cash Flows = $68.686.87
Workings:
Value after year 2 = (Cash flow for year 2*Growth rate)/(Required return-Growth rate)
=10,000*(1-0.08)/(0.1-(0.08))
=9200/0.18
=51111.11
2) Computation of Effective Annual Rate of Return (EAR)
Given,
Monthly deposits = $200
Amount after 40 Years or Future Value = $936264.05
First we calculate Monthly Rate using Rate Function in Excel:
=rate(nper,pmt,-pv,fv)
Here,
Rate = Monthly Rate = ?
Nper = 40 years * 12 months = 480 months
PMT = $200
PV = 0
FV = 936264.05
Substituting the values in formula:
=rate(480,200,0,-936264.05)
Rate or Monthly Rate = 0.75%
So, monthly rate required is 0.75%
Effective Annual Rate (EAR) = (1 + Monthly Rate)^12 - 1 = (1+0.0075)^12 - 1 = 9.38%
So, effective annual rate of return (EAR) is the advisor assuming that the fund will provide is 9.38%.
