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!
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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