Mr. Danial has an opportunity of receiving #1000, 41500, $800, 41100 and $400 respectively at the end of each of the next five years. Required:
Answer (2)
Define the cash flows for each year: C F 1 = 1000 , C F 2 = 1500 , C F 3 = 800 , C F 4 = 1100 , C F 5 = 400 .
Assume an interest rate of 5% per year: r = 0.05 .
Calculate the present value of each cash flow: P V i = ( 1 + r ) i C F i .
Calculate the total present value: P V t o t a l = P V 1 + P V 2 + P V 3 + P V 4 + P V 5 ≈ 4222.42 . The present value of the income stream is 4222.42 .
Explanation
Understanding the Problem Mr. Danial will receive the following amounts at the end of each of the next five years: Year 1: $1000, Year 2: $1500, Year 3: $800, Year 4: $1100, Year 5: $400. The question is incomplete as it does not specify what is required. I will assume that the question requires us to calculate the present value of these future cash flows. To do this, we need an interest rate. Since the interest rate is not provided, I will assume an interest rate of 5% per year.
Defining Cash Flows and Interest Rate Let's define the cash flows for each year as C F 1 = 1000 , C F 2 = 1500 , C F 3 = 800 , C F 4 = 1100 , and C F 5 = 400 . Let's assume an interest rate of r = 0.05 per year.
Calculating Present Values Now, we calculate the present value of each cash flow using the formula P V i = ( 1 + r ) i C F i for i = 1 , 2 , 3 , 4 , 5 .
Calculating Individual Present Values P V 1 = ( 1 + 0.05 ) 1 1000 = 1.05 1000 ≈ 952.38 P V 2 = ( 1 + 0.05 ) 2 1500 = 1.1025 1500 ≈ 1360.54 P V 3 = ( 1 + 0.05 ) 3 800 = 1.157625 800 ≈ 690.95 P V 4 = ( 1 + 0.05 ) 4 1100 = 1.21550625 1100 ≈ 905.07 P V 5 = ( 1 + 0.05 ) 5 400 = 1.2762815625 400 ≈ 313.48
Calculating Total Present Value The total present value is the sum of the present values of each cash flow: P V t o t a l = P V 1 + P V 2 + P V 3 + P V 4 + P V 5 ≈ 952.38 + 1360.54 + 690.95 + 905.07 + 313.48 ≈ 4222.42
Final Answer Therefore, the present value of the income stream, assuming a 5% interest rate, is approximately $4222.42.
Examples
Understanding the present value of future income is crucial in many financial decisions. For example, when considering an investment, you need to compare the present value of the expected future returns with the initial investment cost. If the present value of the future returns is higher than the initial investment, the investment is likely worthwhile. Similarly, when evaluating a loan, calculating the present value of the future loan payments helps you understand the true cost of borrowing. This concept is also used in retirement planning, where you estimate the present value of your future retirement income to ensure you have enough savings to cover your expenses.
To find the present value of the cash flows Mr. Danial will receive over five years, we calculated each cash flow's present value using a 5% interest rate. The total present value of these cash flows amounts to approximately $4222.42. This calculation helps determine the value of future income in today's terms.
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