10. Uneven cash flows

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	$20,000	$180,000	$300,000	$350,000	$725,000

The CFO of the company believes that an appropriate annual interest rate on this investment is 9%. What is the present value of this uneven cash flow stream, rounded to the nearest whole dollar?

$600,000

$1,395,097

$1,775,000

$1,975,000

Identify whether the situations described in the following table are examples of uneven cash flows or annuity payments:

Description	Uneven Cash Flows	Annuity Payments
Debbie has been donating 10% of her salary at the end of every year to charity for the last three years. Her salary increased by 15% every year in the last three years.
You deposit a certain equal amount of money every year into your pension fund.
Amit receives quarterly dividends from his investment in a high-dividend yield, index exchangetraded fund.
Aakash borrowed some money from his friend to start a new business. He promises to pay his friend $2,650 every year for the next five years to pay off his loan along with interest.

11. Nonannual compounding period

The number of compounding periods in one year is called compounding frequency. The compounding frequency affects both the present and future values of cash flows.

An investor can invest money with a particular bank and earn a stated interest rate of 6.60%; however, interest will be compounded quarterly. What are the nominal, periodic, and effective interest rates for this investment opportunity?

Interest Rates
Nominal rate
Periodic rate
Effective annual rate

Rahul needs a loan and is speaking to several lending agencies about the interest rates they would charge and the terms they offer. He particularly likes his local bank because he is being offered a nominal rate of 6%. But the bank is compounding monthly. What is the effective interest rate that Rahul would pay for the loan?

6.074%

6.253%

6.046%

6.168%

Another bank is also offering favorable terms, so Rahul decides to take a loan of $18,000 from this bank. He signs the loan contract at 10% compounded daily for three months. Based on a 365-day year, what is the total amount that Rahul owes the bank at the end of the loan's term? (Hint: To calculate the number of days, divide the number of months by 12 and multiply by 365.)

$18,086.74

$18,271.30

$18,824.98

$18,455.86

12. More on the time value of money

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 $650 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 isnt a good deal if you only remain a member for a couple of years, but if you remain a member for 40 years, its a great deal. Suppose that the appropriate annual interest rate is 5.9%. 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 $650 in annual membership dues? (Note: Round your answer up to the nearest year.)

19 years

21 years

16 years

13 years

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 5.75% annual interest rate, what is its value as of 2018 (392 years later)?

$79,089,467,621.87

$104,398,097,260.87

$67,226,047,478.59

$90,952,887,765.15