Business 4179 Portfolio Management

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Business 4179 - Portfolio Management

• Chapter 2 - The Two Key Concepts in Finance
• SOLUTIONS to Questions and Problems

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K. Hartviksen
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Question 2 - 1

• With simple interest the effective rate of
  interest will equal the nominal rate.
• Any compounding will cause the effective rate to
  exceed the nominal rate.

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K. Hartviksen
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Question 2 - 2
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K. Hartviksen
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Question 2 - 3

• A future value can equal a present value only if
  there is no time value of money. (R0).
• Present values exceed future values only when
  interest rates are negative (Rlt0)

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K. Hartviksen
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Question 2 - 4

• If the first payment occurs immediately, it can
  be invested to earn interest over the first
  period. If it occurs at the end of the period,
  it cannot earn interest during that first period.

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K. Hartviksen
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Question 2 - 5

• This is best seen via a mathematical example.
• There is little difference between daily
  compounding and continuous compounding (for
  reasonable levels of interest rates).
• The difference increases with increases in the
  level of interest rates.
• Monthly versus annual compounding results in the
  greater difference.

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K. Hartviksen
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Question 2 - 6

• The statement is true.
• Consider the extremes. If R0, continuous
  compounding yields the same as simple interest.
• As R increases, the difference between simple
  interest and compound interest increases, too.

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K. Hartviksen
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Question 2 - 7

• False.
• Utility measures the combined influences of
  expected return and risk. A small sum of money
  to be received for certain has very little
  utility associated with it, whereas a small
  investment in a very risky venture, such as a
  lottery ticket, has considerable utility to some
  people.

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K. Hartviksen
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Question 2 - 8

• The answer depends on the individual, but many
  people will change their selection if the game
  can be played repeatedly.

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K. Hartviksen
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Question 2 - 9

• The answer depends on the individual.
• Because you incur the 50 cost despite the
  choice, it should not necessarily cause a person
  to change their selection.

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K. Hartviksen
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Question 2 - 10

• Yes.
• Set equations 2-9 and 2-11 equal to each other,
  cancel out the initial cash flow C, assume some
  initial value for N or for G and solve for
  the other variable.

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K. Hartviksen
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Question 2 - 11

• Mathematically, no, but practically speaking,
  yes, if the time period is long enough.
  Depending on the interest rate used, the present
  value of an annuity approaches some limit as the
  period increases.
• If the period is long enough, there is no
  appreciable difference between the two values.

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K. Hartviksen
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Chapter 2

• Problem Solutions

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Problem 2 - 1

• After the last payment to the custodian, the fund
  will have a zero balance. This means (PV
  payments in) - (PV payments out) 0, or
  equivalently,
• PV of payments in PV of payments out

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Problem 2 - 1...

• Payments out
• Multiply both sides of the equation by (1.08)26

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Problem 2 - 1...

• Payments in
• Let x the first payment
• Payments out Payments in

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Problem 2 - 3
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Problem 2 - 4
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Problem 2 - 5
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Problem 2 - 6
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Problem 2 - 7
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Problem 2 - 8
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Problem 2 - 9
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Problem 2 - 10
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Problem 2 - 11
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Problem 2 - 12
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Problem 2 - 13
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Problem 2 - 14
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Problem 2 - 15
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Problem 2 - 16
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Problem 2 - 17
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Problem 2 - 18
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Problem 2 - 19
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Problem 2 - 20

• Calculate the after-tax present value of the
  annuity due and compare it to the after-tax value
  of the lump sum, which is 1,026,100
• The after tax annuity payment would be
  250,000-75,305-10,000164,695
• The annuity is more valuable.