Question

Consider the following uneven cash flow stream: Year Cash Flow 0 $0 1 $250 2 $400 3 $500 4 $600 5 $600 What is the present (Year 0) value if the opportunity cost (discount) rate is 10 percent? A Spreadsheet solution: $1,815.87 B Spreadsheet solution: $1,715.87 C Spreadsheet solution: $1,915.87 D Spreadsheet solution: $1,615.87

Answer 1

The present value of an uneven cash flow stream can be calculated by discounting each cash flow back to Year 0 using the opportunity cost (discount) rate. The present values of the cash flows are then added up to get the present value of the cash flow stream.

Step-by-step explanation:

To calculate the present value of the uneven cash flow stream, we need to discount each cash flow back to Year 0 using the opportunity cost (discount) rate of 10%. Here is how the calculation is done:

1. Year 1 cash flow: $250 divided by (1 + 0.10) to the power of 1 = $227.27
2. Year 2 cash flow: $400 divided by (1 + 0.10) to the power of 2 = $330.58
3. Year 3 cash flow: $500 divided by (1 + 0.10) to the power of 3 = $375.13
4. Year 4 cash flow: $600 divided by (1 + 0.10) to the power of 4 = $428.31
5. Year 5 cash flow: $600 divided by (1 + 0.10) to the power of 5 = $424.37

Add up the present values of each cash flow to get the present value of the cash flow stream:

Year 0 cash flow: $0

Present value of Year 1 cash flow: $227.27

Present value of Year 2 cash flow: $330.58

Present value of Year 3 cash flow: $375.13

Present value of Year 4 cash flow: $428.31

Present value of Year 5 cash flow: $424.37

Summing these values gives a present value of $1,785.66. Therefore, the closest option is B: Spreadsheet solution: $1,715.87.

Answer 2

The correct answer is: $1715,87

Step-by-step explanation:

To calculate the present value you need to use the Net Present Value. The NPV is the difference between the present value of cash inflows and the present value of cash outflows over a period of time.

The formula is:

n

NPV= ∑ [Rt/(1+i)^t] - I0

t-1

where:

R t​ =Net cash inflow-outflows during a single period t

i=Discount rate of return that could be earned in alternative investments

t=Number of timer periods

In this exercise:

NPV= 0+ 250/1,10^1 + 400/1,10^2 + 500/1,10^3 + 600/1,10^4 + 600/1,10^5

NPV= $1715,87