Question

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 $450,000 $350,000 

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? 

• $1,425,000 

• $467,500 

• $1,642,500 

• $1,022,070 

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

• Uneven Annuity Payments Description Cash Flows 

• 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

Present Value of the uneven cash flow stream

Present Value = CF1/(1 + r)¹ + CF2/(1 + r)² + CF3/(1 + r)³ + CF4/(1 + r)⁴ + CF4/(1 + r)⁵

= $250,000/(1 + 0.065)¹ + $37,500/(1 + 0.065)² + $180,000/(1 + 0.065)³ + $450,000/(1 + 0.065)⁴ + $350,000/(1 + 0.065)⁵

= [$250,000 / 1.065] + [$37,500 / 1.13423] + [$180,000 / 1.20795] + [$450,000 / 1.28647] + [$350,000 / 1.37009]

= $2,34,742 + $33,062 + $1,49,013 + $3,49,795 + $2,55,458

= $10,22,070

“Therefore, the Present Value of the uneven cash flow stream = $10,22,070”

Description	Type of cash flow
You recently moved to a new apartment and signed a contract to pay monthly rent to your landlord for a year	Annuity Payments
SOE Corp, hires an average of 10 peoples every year and matches the contribution of each employee towards his or her retirement fund	Uneven cash flows
Frankinia venture capital invested in a bussing entrepreneurs restaurant. The restaurant owner promises to pay FVC 10% of profit each month for the next 10 years	Uneven cash flows
You have committed to deposit $600 in a fixed interest bearing account every quarter for four years	Annuity Payments

Answer 2

Answer:

Part A)

Option D:1022070

PV=Cashflow/(1+r)^n

Where r= Rate of Interest

n= year in which cashflow occur

Sample Calculation:

For first year

Cashflow=$250000

r=6.5%

n=1

So PV=250000/(1+6.5%)^1=$234741.78

Year	Cash flow	PV of cash flow
1	250000	234741.78
2	37500	33062.22
3	180000	149012.84
4	450000	349795.39
5	350000	255458.29
Total	1267500	1022070.53

Part B)

1) Annuity Payment: Because each month you will pay the same amount to Landlord.

2) Uneven Cashflow: Because each year you are hiring different number of people. Since average is given so number of people can be greater than average or less than average or equal to average. So each year employee contribution will be different so do company's contribution.

3) Uneven Cashflow: Because each month Profit will be different and 10% of profit each month will also be different.

4) Annuity Payment: Because each month you are depositing same amount in Bank.