Use the cash flows from the following two projects to answer the questions 1 thr
ID: 2742274 • Letter: U
Question
Use the cash flows from the following two projects to answer the questions 1 through 7 below. The firms required rate of return is 11%. Make sure to show all your computations.
Year
Project A
Project B
0
-$200,000
-$200,000
1
$80,000
$100,000
2
$80,000
$100,000
3
$80,000
$100,000
4
$80,000
If your firm’s cutoff recovery period criterion is 2.40 years, which of these two projects would you accept:
using the payback period criterion?
using the discounted payback period criterion?
Would your investment decisions change if you used:
Net Present Value as your investment criterion?
Profitability Index (in times invested funds recovered) as your investment criterion?
Profitability Index (as percentage of invested funds) as your investment criterion?
Internal Rate of Return as your investment criterion?
Assume you are told that your firm only has $200,000 available to invest, which project of the two above would you chose if you used:
the Profitability Index (as percentage of invested funds) as your capital rationing criterion?
the Internal Rate of Return as your capital rationing criterion?
If the two criteria in a) and b) above differ in their recommended course of action, why do you think that is?
Which one of these two capital rationing criteria would you follow and why?
Using the replacement chain method to evaluate mutually exclusive projects of equal size, but unequal lifespans, which project out of the two above would you choose?
Year
Project A
Project B
0
-$200,000
-$200,000
1
$80,000
$100,000
2
$80,000
$100,000
3
$80,000
$100,000
4
$80,000
Explanation / Answer
The payback period for A is when whole investment 200,000 is recovered.After 2 years 160000 is recovered so rest of 40000 is recovered after 40000/80,000=0.5 years so that the entire 200,000 is recovered after 2.5 years.
The payback period for B is when whole investment 200,000 is recovered.After 2 years 200000 is recovered so rest of so that the entire 200,000 is recovered after 2 years.
Since the firm’s cutoff recovery period criterion is 2.40 years therefore choose the project with the payback period<2.40 years therefore choose project B with payback period of 2 years.
Discounted payback is when the total investment is recovered from the present values of the cash flows,thus after 3 years the present value of cash flows=72072.07+64929.79+58495.31=195497.17 the rest is recovered during the 4th year in (200000-195497.17)/200000=0.0225 thus in total of 3.0225 years the investment is recovered thus the discounted payback period is 3.0225 years.
Discounted payback is when the total investment is recovered from the present values of the cash flows,thus after 2 years the present value of cash flows=90090.09+81162.24=171252.33 the rest is recovered during the 3th year in (200000-171252.33 )/200000=0.1437 thus in total of 2.1437 years the investment is recovered thus the discounted payback period is 2.1437 years.
Since the firm’s cutoff recovery period criterion is 2.40 years therefore choose the project with the payback period<2.40 years therefore choose project B with payback period of 2.1437 years.
NPV of A=sum of the present values of all the cash flows =-200000+72072.07+64929.79+58495.31+52698.48=48195.65
NPV of B=sum of the present values of all the cash flows =-200000+90090.09+81162.24+73119.14=44371.47
Thus choose A as NPV of A>NPV of B.
Profitability Index A=1+48195.65/200000=1.240
Profitability Index B=1+44371.47/200000=1.22
Project A:
200000=80,000/(1+IRR)+80,000/(1+IRR)2+80,000/(1+IRR)3+80,000/(1+IRR)4
2.5=1/(1+IRR)+1/(1+IRR)2+1/(1+IRR)3+1/(1+IRR)4
IRR=12%,RHS=1/(1+.12)+1/(1+.12)2+1/(1+.12)3+1/(1+.12)4=3.04
IRR=13%,RHS=1/(1+.13)+1/(1+.13)2+1/(1+.13)3+1/(1+.13)4=2.97
IRR=14%,RHS=1/(1+.14)+1/(1+.14)2+1/(1+.14)3+1/(1+.14)4=2.91
IRR=17%,RHS=1/(1+.17)+1/(1+.17)2+1/(1+.17)3+1/(1+.17)4=2.74
IRR=20%,RHS=1/(1+.2)+1/(1+.2)2+1/(1+.2)3+1/(1+.2)4=2.59
IRR=22%,RHS=1/(1+.22)+1/(1+.22)2+1/(1+.22)3+1/(1+.22)4=2.49
Thus IRR is 22%.
Project B:
200000=100,000/(1+IRR)+100,000/(1+IRR)2+100,000/(1+IRR)3
2=1/(1+IRR)+1/(1+IRR)2+1/(1+IRR)3
IRR=22%,RHS=1/(1+.22)+1/(1+.22)2+1/(1+.22)3=2.04
IRR=23%,RHS=1/(1+.23)+1/(1+.23)2+1/(1+.23)3=2.01
Thus IRR~23%
Choose B as IRR of B>IRR of A
CF=Cash Flow Present value t CF(A) (=CF(A)/(1+r)^t 0 -200000 -200000 (=-200000/1.11^0) 1 80,000 72072.07 (=80000/1.11^1) 2 80,000 64929.79 (=80000/1.11^2) 3 80,000 58495.31 (=80000/1.11^3) 4 80,000 52698.48 (=80000/1.11^4)Related Questions
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