Answer:
future worth:
project A 11,615.26
project B 12,139.18
It should choose project B as their future value is greater
IRR of project A: 13.54%
We should remember that the IRR is the rate at which the net value is zero thus, equals the inflow with the cash outlay
It is calculate with excel or financial calculator due to the complex of the formula.
Explanation:
Project A
We calculate the future value of the cash flow per year and cost as we are asked for future value. The salvage value is already at the end of the project life so we don't adjust it.
Revenues future value
[tex]C \times \frac{(1+r)^{time} -1}{rate} = FV\\[/tex]
C 15,000
time 8
rate 0.12
[tex]15000 \times \frac{(1+0.12)^{8} -1}{0.12} = FV\\[/tex]
FV $184,495.3970
Expenses future value
[tex]C \times \frac{(1+r)^{time} -1}{rate} = FV\\[/tex]
C 3,000
time 10
rate 0.12
[tex]3000 \times \frac{(1+0.12)^{10} -1}{0.12} = FV\\[/tex]
FV $52,646.2052
Cost future value
[tex]Principal \: (1+ r)^{time} = Amount[/tex]
Principal 40,000.00
time 10.00
rate 0.12000
[tex]40000 \: (1+ 0.12)^{10} = Amount[/tex]
Amount 124,233.93
Net future worth:
-124,233.93 cost - 52,646.21 expenses + 184,495.40 revenues + 4,000 salvage value
future worth 11,615.26
Project B
cost:
[tex]Principal \: (1+ r)^{time} = Amount[/tex]
Principal 60,000.00
time 10.00
rate 0.12000
[tex]60000 \: (1+ 0.12)^{10} = Amount[/tex]
Amount 186,350.89
expenses 52,646.21 (same as previous)
revenues
[tex]C \times \frac{(1+r)^{time} }{rate} = FV\\[/tex]
C 24,000
time 7
rate 0.12
[tex]24000 \times \frac{(1+0.12)^{7} -1}{0.12} = FV\\[/tex]
FV $242,136.2815
TOTAL
242,136.28 + 9,000 - 52,646.21 - 186,350.89 = 12,139.18
Internal rate of return of project A
we write the time and cash flow for each period.
Time Cash flow
0 -40,000
1 -3,000
2 -3,000
3 12,000
4 12,000
5 12,000
6 12,000
7 12,000
8 12,000
9 12,000
10 16,000
IRR 13.54%
Then we write on excel the function =IRR(select the cashflow)
and we got the IRR of the project
