Cost Management: A Strategic Emphasis 5th Edition by David Stout, Edward Blocher, Gary Cokins

Exercise 39

Future and Present Values, Spreadsheet Application

a. It is said (S. Branch Walker) that the Indian who sold Manhattan for $24 was a sharp salesman. If he had put his $24 away at 6 percent compounded semiannually, it would now be worth over $9 billion, and he could buy most of the now-improved land back! Assume that this seller invested on January 1, 1701, the $24 he received.

Required

1. Use Excel to determine the balance (in billions) of the investment as of December 31, 2009, assuming a 6 percent interest rate compounded semiannually. (Hint: Use the FV function in Excel.)

2. Carry out the same calculation using an 8 percent annual interest rate, compounded semiannually.

3. What would be the balances for requirements 1 and 2 if interest is compounded quarterly?

4. Assume that the account consisting of this investment had a balance of $9.5 billion as of December 31, 2009. How much would the total amount be on December 31, 2015, if the annual interest rate is 8 percent, compounded semiannually?

b. In 2000, Alex Rodriguez signed a 10-year, $252 million dollar contract with the Texas Rangers. Assume that equal payments would have been made each year to Alex and that the owner’s cost of capital (discount rate) was 12 percent at the time the contract was signed. What is the present value cost of the contract to the owners as of January 1, 2000, the date the contract was signed, in each of the following independent situations?

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Required

1. Alex received the first payment on December 31, 2000.

2. Alex received the first payment on January 1, 2000, the date the contract was signed.

3. Assuming the owner is in the 45 percent income tax bracket, calculate your answer for requirement 1.

Step 1 of 8

A.?To calculate future values, use the following Excel function: ?????                      FV(rate,nper,pmt, pv,type)

??1. Between January 1, 1701 and December 31, 2009 there are 618 six-month periods (nper). Thus, at the end of year 2009, at an annual interest rate of 6% compounded semiannually, the $24.00 will have grown to $2,058,809,244, as follows:

?     ??FV(0.06/2,618,0,-24,0)