Consider the following case:The Purple Lion Beverage Company expects the following cash flows from its manufacturing plant in Palau over the next four years:Annual Cash FlowsYear 1Year 2Year 3Year 4$250,000$37,500$180,000$300,000The 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?
Present value is the sum of discounted cash flows.
present value can be calculated using a financial calculator
Cash flow in year 1 = $250,000
Cash flow in year 2 = $37,500
Cash flow in year 3 = $180,000
Cash flow in year 4 = $300,000
Cash flow in year 5 = $550,000
I = 6.5%
Present value = $1,051,448
To find the PV using a financial calculator:
1. Input the cash flow values by pressing the CF button. After inputting the value, press enter and the arrow facing a downward direction.
2. after inputting all the cash flows, press the NPV button, input the value for I, press enter and the arrow facing a downward direction.
3. Press compute
1 Purple Lion Beverage Company
Year Cash flows($) 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.
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
The sum of the present values of the stream of cash flows is $1,011,772.58
We need to compute the present value of the cash flows separately for each amount
The first cash flow is occurring at the end of the first year
We use the formula PV = FV/(1+i)^n
Where PV = Present Value, FV = Future value, i = Interest rate, which is the rate at which the cash flows are to be discounted and n = the year in which the cash flow occurs
Plugging the values in the formula, we get the present value for the first year
PV = 250,000/(1+0.065)^1 = 250,000/1.065 = 93,896.71= $93,896.71
The present values for the successive years are provided as under
PV = 20,000/(1+0.065)^2 = 20,000/(1.065)2 = 17,633.1857= $17,633.1857
PV = 180,000/(1+0.065)^3 =180,000/(1.065)3 = 149,012.8365= $149,013.8365
PV = 450,000/(1+0.065)^4 =450,000/(1.065)4 = 349,795.3909= $349,795.3909
PV = 550,000/(1+0.065)^5 =550,000/(1.065)5 = 401,434.4601= $401,434.4601
Adding up the present values for each of the years, we obtain the present value of the cash flow stream
93,896.71+17,633.1857+149,013.8365+349,795.3909+401,434.4601 = $1,011,773,.58 approximately (only the final answer is rounded off to two decimal points)
The solution in word format is also attached here