Question

If you invest $250,000 today and receive $90,000, $85,000 and $83,000 over the next three years, and expect a 7.7% return, would you make this investment? FV = 90,000

Your great Uncle has left you $350,000 in his will. You believe he will die ten years from now, and you will receive it then. What if you need the money now, how much would you take as a discount from your Uncle that is equivalent to the $350,000 in ten years?

Answer 1

The present value of the $250,000 investment's future cash flows is $224,824.31, which is less than the initial investment, making it unattractive. The equivalent present value of $350,000 to be received in 10 years at a 7.7% discount rate is $167,197.73.

Step-by-step explanation:

To determine if the investment of $250,000 is worthwhile, we need to calculate the present value (PV) of the future cash flows discounted at the investor's required rate of return of 7.7%. Using the formula PV = FV / (1 + r)n, where FV is future value, r is the discount rate, and n is the number of periods, we calculate:

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• PV of $90,000 received in 1 year: $90,000 / (1 + 0.077)1 = $83,533.98
• 
  
• PV of $85,000 received in 2 years: $85,000 / (1 + 0.077)2 = $73,895.56
• 
  
• PV of $83,000 received in 3 years: $83,000 / (1 + 0.077)3 = $67,394.77

The total PV of the cash flows equals $83,533.98 + $73,895.56 + $67,394.77 = $224,824.31. Since the PV of the returns is less than the initial investment of $250,000, the investment does not meet the required return of 7.7%.

To compute the present discounted value of $350,000 received in 10 years, the formula is PV = FV / (1 + r)n. Assuming a discount rate of 7.7%, we have:

• 
  
• PV = $350,000 / (1 + 0.077)10 = $167,197.73

If the required rate is constant, you would be indifferent to receiving $167,197.73 now or $350,000 in 10 years.