Solutions - Midterm Review Class[2009]

Solutions - Midterm Review Class[2009] - Midterm Review...

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Midterm Review Class : TVM, Bonds, Stocks Future Value: FV = Investment × (1 + r) n Present Value: PV = Future Value (1 + r) n Example 1 (FV): How much can you accumulate in your savings account in 5 years if you deposit $100 today and the bank pays you a 3% annual interest rate? FV = 100 x (1.03) 5 = $115.93 Example 2 (P V): What is the value today of $100 to be received at the end of 5 years if the bank pays you a 3% annual interest rate? PV = 100 / (1.03) 5 = $86.26 Example 3 (PV): What is the present value of $100 to be deposited into a savings account today paying 8% annually, with semi-annual compounding, for two years? A) $85.48 B) $100 C) $116.00 D) $116.99 (Answer B: The present value of $100 today is $100!) Example 4: 0 1 2 3 r = 5% |-----------|-------------|-----------| $200 $400 $300 a) Compute FV at end of year 3 FV = 200x(1 .05) 2 + 400x(1.05) 1 + 300 = 220.5 + 420 + 300 = 940.5 b) Compute PV PV = 200 + 400 + 300 (1.05) 1 (1.05) 2 (1.05) 3 = 190.48 + 362.81 + 259.15 = 812.44 56916275ad478a3edc06671e75d8c3760b7fe85c.doc 1
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Example 5: Multiple Cash Flows In two years from today, the following cash flows will have a future value of $7,651.25: $500 today, $Y at the end of one year, and $5,000 at the end of two years. The annual interest rate is 5%. What is Y? A) $1,822.44 B) $1,850.00 C) $2,000.00 D) $2,126.25 Detailed solution : 0 1 2 r = 5% |-----------|------------| FV 2 = $7651.25 $500 “Y” $5000 You can use either Option a) FV formula and bring all cash flows to t=2 or Option b) PV formula and bring all cash flows to t=0 Option a) Bring all cash flows to t=2 (use FV or compound) 500(1 + r) 2 + Y(1 + r) 1 + 5000 = 7651.25 500(1.05) 2 + Y (1.05) + 5000 = 7651.25 551.25 + Y(1.05) + 5000 = 7651.25 Y(1.05) = 7651.25 – 5000 – 551.25 Y(1.05) = 2100 Y = 2100 / (1.05) Y = $2000 Option b) Bring all cash flows to t=0 (use PV and discount) 500 + Y/(1 + r) 1 + 5000/(1 + r) 2 = 7651.25/ (1 + r ) 2 500 + Y/(1.05) + 5000/(1.05) 2 = 7651.25/(1.05) 2 500 + Y/(1.05) + 4535.15 = 6939.91 Y/(1.05) = 6939.91- 4535.15 – 500.00 Y/(1.05) = 1904.76 Y = 1904.75 x (1.05) Y = $2000 56916275ad478a3edc06671e75d8c3760b7fe85c.doc 2
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– Cash flows start at end of first time period – Cash Flows start immediately PV Perpetuity (ordinary) = C r PV Perpetuity due = PV Ordinary Perpetuity x (1 +r) #43 Text (ch.4) Perpetuities: A bank will pay you $100 per year forever if you deposit $2500 in the bank today. a) If the first payment is made at the end of the first year, what interest rate is the bank paying? b) Using the interest rate calculated in (a), what is the value of the same perpetuity if
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Solutions - Midterm Review Class[2009] - Midterm Review...

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