Question

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

a$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.)

a.$1,692,500

b.$467,500

c.$1,475,000

d.$1,051,448

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

Answer:

1                      Purple Lion Beverage Company

Year          Cash flows($)                        Dfc (6.5%)                  Present Value($)

 1                   250,000                             0.9389                         234,741.78

2                     37,500                              0.8817                           33,062.22

3                    180,000                            0.8278                           149,012.84

4                    300,000                            0.7773                         233,196.93

5                    550,000                           0.7299                         401,434.46

Total Present value =                                                                 1,051,448.23 (D)

2) Annuity Payment - You recently moved to a new apartment and signed a contract to pay monthly rent to your landlord for a year.

Uneven Cash flow - SOE Corp. hires an average of 10 people every year and matches the contribution of each employee toward his or her retirement fund.

Uneven Cash flow - 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.

Annuity Payment - You have committed to deposit $600 in a fixed interest–bearing account every quarter for four years.

Explanation:

1) Dfc i.e. discount factor is calculated by - 1 / (1 + r)ⁿ

where r is the rate at 6.5%

and n is the time period - 1,2,3,4,5

for year 1 = 1 / (1 + 0.065)¹ = 1/1.065 = 0.9389

for year 2 = 1 / (1 + 0.065)² = 1/1.1342 = 0.8817

for year 3 = 1 / (1 + 0.065)³ = 1/1.2079 = 0.8278

for year 4 = 1 / (1 + 0.065)⁴ = 1/1.2865 = 0.7773

for year 5 = 1 / (1 + 0.065)⁵ = 1/1.3701 = 0.7299

while Present value is gotten by multiplying annual cash flow by the discount factor

2) a) Monthly rental payment is normally for the same amount i.e it is an annuity payment

b) The contribution of each employee would vary and not always be the same and as such it would be an uneven cash flow

c) The profit from the restaurant would not always be the same for every month and as such the payment of 10% on profit would also vary per month

d) The deposit of $600 is for a fixed amount and such is an annuity payment

Note: an annuity is a fixed payment made at equal intervals while uneven cash flows as cash flows that vary with amount paid