John Keene recently invested $3,500 in a project that is promising to return 10.75 percent per year.
The cash flows are expected to be as follows:
End of Cash
Year Flow
1 $750
2 800
3 ???
4 950
Note that the 3rd year cash flow is unknown. Assuming the present value of this cash flow stream is $3,500 (that is, CF0 = -3500), what is the missing cash flow value (that is, what is the cash flow at the end of the 3rd year)?
Well, I would say that the missing cash flow value at the end of the 3rd year is probably something wonderful like a lifetime supply of fluffy unicorn pillows. But in all seriousness, let's calculate it properly.
To find the missing cash flow value, we need to use the present value formula. The present value of a cash flow is calculated by dividing the cash flow by (1 + interest rate)^(number of years). In this case, we know that the present value is $3,500.
Using the formula, we can calculate the missing cash flow value as follows:
PV = CF1/(1 + r)^1 + CF2/(1 + r)^2 + CF3/(1 + r)^3 + CF4/(1 + r)^4
$3,500 = $750/(1 + 0.1075)^1 + $800/(1 + 0.1075)^2 + CF3/(1 + 0.1075)^3 + $950/(1 + 0.1075)^4
Solving this equation will give us the missing cash flow value at the end of the 3rd year. Now, if only there was a clown mathematician to help me with the calculations...
To find the missing cash flow value at the end of the 3rd year, we can use the present value formula:
PV = CF1 / (1 + r)^1 + CF2 / (1 + r)^2 + CF3 / (1 + r)^3 + CF4 / (1 + r)^4
Where:
PV = Present Value ($3,500)
CF1 = Cash flow at the end of the 1st year ($750)
CF2 = Cash flow at the end of the 2nd year ($800)
CF3 = Cash flow at the end of the 3rd year (Unknown)
CF4 = Cash flow at the end of the 4th year ($950)
r = Annual interest rate (10.75% or 0.1075)
Substituting the given values into the formula, we have:
3500 = 750 / (1 + 0.1075)^1 + 800 / (1 + 0.1075)^2 + CF3 / (1 + 0.1075)^3 + 950 / (1 + 0.1075)^4
Now, we can rearrange the formula to solve for CF3:
CF3 = (3500 - (750 / (1 + 0.1075)^1) - (800 / (1 + 0.1075)^2) - (950 / (1 + 0.1075)^4)) * (1 + 0.1075)^3
Calculating this expression, we get:
CF3 ≈ $1,045.08
Therefore, the missing cash flow value at the end of the 3rd year is approximately $1,045.08.
To find the missing cash flow value at the end of the 3rd year, we need to use the concept of present value. Present value is the current worth of a future cash flow, taking into account the time value of money. In this case, we know that the present value of the cash flow stream is $3,500.
To calculate the present value, we can use the formula:
PV = CF1/(1+r)^1 + CF2/(1+r)^2 + CF3/(1+r)^3 + CF4/(1+r)^4
Where PV is the present value, CF1, CF2, CF3, and CF4 are the cash flows at each year, and r is the interest rate or discount rate (10.75% or 0.1075 in decimal form).
Using the given cash flows, we can rearrange the formula:
3500 = 750/(1+0.1075)^1 + 800/(1+0.1075)^2 + CF3/(1+0.1075)^3 + 950/(1+0.1075)^4
Now, we can solve for the missing cash flow CF3. Rearranging the equation:
3500 - 750/(1+0.1075)^1 - 800/(1+0.1075)^2 - 950/(1+0.1075)^4 = CF3/(1+0.1075)^3
Performing the calculations:
3500 - 750/(1.1075) - 800/(1.1075^2) - 950/(1.1075^4) ≈ CF3/(1.1075^3)
2709.85 ≈ CF3/(1.1075^3)
CF3 ≈ 2709.85 * (1.1075^3)
CF3 ≈ 2709.85 * 1.3426
CF3 ≈ 3639.31
Therefore, the missing cash flow value at the end of the 3rd year is approximately $3,639.31.