Question

16. 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 five years:

Annual Cash Flows
Year 1	Year 2	Year 3	Year 4	Year 5
$250,000	$37,500	$180,000	$300,000	$550,000

The CFO of the company believes that an appropriate annual interest rate on this investment is 6.5%. What is the present value of this uneven cash flow stream, rounded to the nearest whole dollar? (Note: Do not round your intermediate calculations.)

$467,500

$1,051,448

$1,475,000

$1,692,500

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

Description	Uneven Cash Flows	Annuity Payments
You recently moved to a new apartment and signed a contract to pay monthly rent to your landlord for a year.
SOE Corp. hires an average of 10 people every year and matches the contribution of each employee toward his or her retirement fund.
Franklinia Venture Capital (FVC) invested in a budding entrepreneur’s restaurant. The restaurant owner promises to pay FVC 10% of the profit each month for the next 10 years.
You have committed to deposit $600 in a fixed interest–bearing account every quarter for four years.

Answer 1

Calculate present value of uneven cash flow stream
Year	Annual cash flow	Discount factor @ 6.5%		Present value
1	$250,000	0.93897	1/(1.065^1)	$234,742
2	$37,500	0.88166	1/(1.065^2)	$33,062
3	$180,000	0.82785	1/(1.065^3)	$149,013
4	$300,000	0.77732	1/(1.065^4)	$233,197
5	$550,000	0.72988	1/(1.065^5)	$401,434
Total				$1,051,448
Thus, present value of uneven cash flow stream is $1,051,448
In case of annuity payment the amount of cash flow for each period is fixed while in case of uneven cash flow the amount of cash flow for each period varies
Monthly rent paid is fixed and thus is annuity payment
The contribution amount differs for each employee and for each period as salaries for employees differ and thus is uneven cash flow
The profit for each period would differ and thus the payment of 10% of profit would also differ and thus is uneven cash flow
The commitment deposit $600 every quarter is fixed amount and thus is annuity payment