Answer :
Answer: $ FV_{total} = FV_{1} + FV_{2} + FV_{3} + FV_{4} $
Step-by-step explanation:
To calculate the future value of Sheridan, Inc.'s cash flows at the end of year 4 using a 7 percent discount rate, we'll use the future value formula for each cash flow and then sum them up. The formula for future value is:
$ FV = PV \times (1 + r)^n $
Where:
• ( FV ) is the future value,
• ( PV ) is the present value (or initial cash flow),
• ( r ) is the discount rate (7% or 0.07 in decimal),
• ( n ) is the number of periods until maturity.
Let's calculate the future value for each cash flow:
1.
Year 1 cash flow of $12,300 at the end of year 4:
$ FV_{1} = $12,300 \times (1 + 0.07)^{4-1} $
2.
Year 2 cash flow of $16,400 at the end of year 4:
$ FV_{2} = $16,400 \times (1 + 0.07)^{4-2} $
3.
Year 3 cash flow of $17,900 at the end of year 4:
$ FV_{3} = $17,900 \times (1 + 0.07)^{4-3} $
4.
Year 4 cash flow of $19,200 at the end of year 4:
$ FV_{4} = $19,200 \times (1 + 0.07)^{4-4} $
Now, let's compute the values:
1.
( FV_{1} = $12,300 \times (1.225) )
2.
( FV_{2} = $16,400 \times (1.1449) )
3.
( FV_{3} = $17,900 \times (1.07) )
4.
( FV_{4} = $19,200 \times (1) ) (since it's already at the end of year 4)
Adding these up:
$ FV_{total} = FV_{1} + FV_{2} + FV_{3} + FV_{4} $
