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 $480,000 $450,000 $550,000 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? $1,307,822 $767,500 $1,625,000 $2,142,500

Answer 1

Present value of cash flows should be $1,307,822

Step-by-step explanation:

We cannot use annuity formula for this problem because the amount of cash flows occurring in each year is different and we would need to find the present value of each cash flow separately

The present value of the cash flow can be computed using the following formula

PV = FV/(1+i)^n

The rate at which the cash flows are to be discounted is 9 percent

For the first year the cash flow is $250,000 and we can compute the pressent value of the cash flow as under

250,000/(1+0.09) = 250,000/1.09 = $229,357.80

Foe the second year the cash flow is $37,500

37,500/(1+0.09)^2= 37,500/1.1881 = $31,563

The present value of the cash flows for the subsequent years are provided as under

480,000/(1+0.09)^3 = 480,000/1.295 = $370,648.07

450,000/(1+0.09)^4 = 450,000/1.4116 = $318,791.34

550,000/(1+0.09)^5 = 550,000/1.5386 = $357,462.26

Adding up all the present values computed above, gives us the present value of cash flows

229,357.8 + 31,563 + 370,648.07 + 318,791.34 + 357,462.26 = $1,307,822 approx

Answer 2

PV of the cash flow: $1,307,822

Step-by-step explanation:

We will calculate the present value of a lump sum for each cash flow:

`(cashflow)/((1 + rate)^(time) ) = PV`

cashflow 250,000.00

time 1.00

rate 0.09

`(250000)/((1 + 0.09)^(1) ) = PV`

PV 229,357.80

cashflow 37,500.00

time 2.00

`(37500)/((1 + 0.09)^(2) ) = PV`

PV 31,563.00

cashflow 480,000.00

time 3.00

rate 0.09

`(480000)/((1 + 0.09)^(3) ) = PV`

PV 370,648.07

cashflow 450,000.00

time 4.00

rate 0.09

`(450000)/((1 + 0.09)^(4) ) = PV`

PV 318,791.34

cashflow 550,000.00

time 5.00

rate 0.09

`(550000)/((1 + 0.09)^(5) ) = PV`

PV 357,462.26

Then, we will add each present value:

year 1: 229,357.7982

year 2: 31,562.99975

year 3: 370,648.0704

year 4: 318,791.345

year 5: 357,462.2625

total PV 1,307,822.476