In: Finance
1)
A series of cash flows may not always necessarily be an annuity. Cash flows can also be uneven and variable in amount, but the concept of the time value of money will continue to apply.
Consider the following case:
The Purple Lion Beverage Company expects the following cash flows from its manufacturing plant in Palau over the next six years:
Annual Cash Flows | |||||
---|---|---|---|---|---|
Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 |
$400,000 | $37,500 | $480,000 | $450,000 | $550,000 | $375,000 |
The CFO of the company believes that an appropriate annual interest rate on this investment is 4%. What is the present value of this uneven cash flow stream, rounded to the nearest whole dollar?
$1,979,094
$1,775,000
$917,500
$2,292,500
2)
Lloyd is a divorce attorney who practices law in Florida. He wants to join the American Divorce Lawyers Association (ADLA), a professional organization for divorce attorneys. The membership dues for the ADLA are $750 per year and must be paid at the beginning of each year. For instance, membership dues for the first year are paid today, and dues for the second year are payable one year from today. However, the ADLA also has an option for members to buy a lifetime membership today for $7,000 and never have to pay annual membership dues.
Obviously, the lifetime membership isn’t a good deal if you only remain a member for a couple of years, but if you remain a member for 40 years, it’s a great deal. Suppose that the appropriate annual interest rate is 8.9%. What is the minimum number of years that Lloyd must remain a member of the ADLA so that the lifetime membership is cheaper (on a present value basis) than paying $750 in annual membership dues? (Note: Round your answer up to the nearest year.)
13 years
17 years
18 years
20 years
3)
In 1626, Dutchman Peter Minuit purchased Manhattan Island from a local Native American tribe. Historians estimate that the price he paid for the island was about $24 worth of goods, including beads, trinkets, cloth, kettles, and axe heads. Many people find it laughable that Manhattan Island would be sold for $24, but you need to consider the future value (FV) of that price in more current times. If the $24 purchase price could have been invested at a 4.5% annual interest rate, what is its value as of 2012 (386 years later)?
$488,110,646.00
$758,007,120.84
$660,384,991.64
$574,247,818.82
ANSWER
1.
A)1979094
CASH FLOWS | PV FACTOR @4% | PV OF CASH FLOWS | |
YEAR 0 | 0.00 | 0 | |
YEAR 1 | 400000.00 | 0.962 | 384615.38 |
YEAR 2 | 37500.00 | 0.925 | 34670.86 |
YEAR 3 | 480000.00 | 0.889 | 426718.25 |
YEAR 4 | 450000.00 | 0.855 | 384661.89 |
YEAR 5 | 550000.00 | 0.822 | 452059.91 |
YEAR 6 | 375000.00 | 0.790 | 296367.95 |
ROR | 4.00% | NPV = | 1979094.24 |
2.
D) 20 years
We must determine the net present value of the annual payments in a similar way to calculating the present value of annuities. We can use an excel spreadsheet and the present value formula with a 8.9% interest rate and then subtract the lifetime fee ($7,000):
Present value 13 years = $5,645 - $7,000 = -$1,355
Present value 17 years = $6,449 - $7,000 = -$551
Present value 18 years = $6,610 - $7,000 = $390
Present value 20 years = $6,895 - $7,000 = $105
3.
D)$574,247,818.82
Future value (FV) of amount invested today (P) at interest rate of r after n periods is given by following equation: | |||||||||||
4 | FV = P*(1+r)n | ||||||||||
5 | |||||||||||
6 | Amount Invested (P) | $24 | |||||||||
7 | Interest rate (r) | 4.50% | |||||||||
8 | Number of years (n) | 386 | |||||||||
9 | |||||||||||
10 | Future value as of 2012 | = P*(1+r)n | |||||||||
11 | =$24*(1+4.5%)386 | ||||||||||
12 | $574,247,818.82 | =D6*((1+D7)^D8) | |||||||||
13 | |||||||||||
14 | Hence the Future value as of 2012 | $574,247,818.82 | |||||||||
15 | Thus the fourth option is correct. |