Question

Compute the future worth of each project at the end of six years with variable MARRs as follows: 11% for n = 0 to n = 3 and 16% for n = 4 to n = 6.

Project A worth at the end of six years will be $764.15. (Round to the nearest cent.)

More Info
Project Cash Flows B $140 $50 $50 $50 $25 $25
n 0 1 2 3 4 5 6
A -$250 $70 $70 $70 $125 $500 $500
c $105 $35 $35 $35

Answer 1

To calculate the future worth of Project B, we compound the cash flows over two periods with different MARRs, 11% for the first three years and 16% for the last three. We first calculate the future value of later cash flows at 16%, and then compound the total cash flows for the first three years at 11%. The sum of these values, rounded to the nearest cent, gives us the future worth at the end of six years.

Step-by-step explanation:

To compute the future worth of Project B at the end of six years with variable Minimum Acceptable Rate of Return (MARR), we need to apply compound interest calculations over the two different MARR periods. For the first three years, we use 11% as the interest rate and for the last three years, we use 16%.

Firstly, calculate the future value (FV) for the cash flows from year 3 to year 6 at 16%:

• FV at n=6 for $50 at n=3: $50 × (1 + 0.16)^3
• FV at n=6 for $25 at n=4: $25 × (1 + 0.16)^2
• FV at n=6 for $25 at n=5: $25 × (1 + 0.16)^1

Then calculate the future value of the entire cash flow at n=3, using the MARR of 11% for the first three years:

1. Sum the future values obtained for the cash flows from n=3 to n=6.
2. Add the initial cash flow of $140 at n=0 (which remains unchanged) and the cash flows of $50 at n=1, and $50 at n=2 each compounded for three years at 11% respectively.
3. The final sum gives us the project B's future worth at the end of six years.

To add precision to the answer, round the final computed future worth to the nearest cent.