Question

1. You expect to receive a lump sum amount of $20,000 fifty years from now. But...

1. You expect to receive a lump sum amount of $20,000 fifty years from now. But you want that money now. So what is the present value of that sum if the current discount rate is 7.5%? Assume annual compounding.

2. You have just purchased a $1,500 five year certificate of deposit (CD) from a savings bank which will pay 3.5% interest compounded monthly. What will that CD be worth at maturity?

3. Calculate the present value of an ordinary annuity with ten annual payments of $2,700 if the appropriate interest rate is 5.5% compounded annually.

4. Twenty-five years ago, you purchased 100 shares of XYZ, Inc. for $8 per share. XYZ paid out no cash dividends during this period of time, but it did split its shares many times increasing your position to 9,600 shares (that’s correct: ninety-six hundred). If the current market price of XYZ is $12, what is your estimate of the average annual (implicit) rate of return R% on your investment in XYZ?    In other words, by how much (percentage-wise) did the value of your position in XYZ change each year on average?

Please show formulas and work. Thank you!

Homework Answers

Answer #1

QUESTION 1

This question is a simple application of time value of money concept. The basic TVM function: FV = PV * (1 + r)n

We need to calculate PV, when FV = $20,000, r = 7.5%, n = 5

PV = 20000/(1 + 0.075)5 = $13,931.17

Corrected Answer: n =50

PV = 20000/(1 + 0.075)50 = $537.78

QUESTION 2

We will use the same time value of money function that we used in previous question. Here, we need to calculate FV, when PV = $1,500, r = 3.5%/12 = 0.292%, n = 5 * 12 = 60 months

FV = 1,500 * (1 + 0.292%)60

FV = 1,786.414

QUESTION 3

We need to calculate PV of an ordinary annuity, where PV of an annuity is represented mathematically as:

PV = $20,351.59

QUESTION 4

Cost of Shares Purchased = $8 * 100 = $800

Value of Shares Held = $12 * 9600 = $115,200

n = 25 years. We need to calculate the rate of annual growth

We will use the TVM function in question 1 and 2

115,200 = 800 * (1 + r)25

r = 21.99%

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