Please show steps The KJL Company is contemplating five independent projects, wi
ID: 2792337 • Letter: P
Question
Please show steps
The KJL Company is contemplating five independent projects, with cash flows as in Table 9-16. The MARR is 12% and the budget constraint is $200000. (a) Compute the rate of return for each project. (b) What is the optimum portfolio, if the minimum desired payback period (Section 8.3) is two years? Ans. (a) i = ii-i8-i= i-15%. (b) PBPa = PBPa = PBPc= 2.28 years, PBPD=2.055 years PBPE = 2.0 years; the only acceptable choice is project E. 9.34 Table 9-16 End of Year Project Project Project Project Project $60 00095000 50 000 45 000 26 609 -$100 000$50 000$75 000 43 798 43 798 43 79821899 21 899 21 899 38 848.50 38 848.50 38 848.50 30 000 29 000 18 228 How would the result of Problem 9.34(b) change if (a) the minimum desired payback period is 2.2 years? (b) the minimum desired payback period is 2.2 years and the budget constraint is $150 000? Ans. (a) D, or E, or D and E; (b) D or E 9.35Explanation / Answer
Note: There is a printing error in the problem. The Cash Flow for Project C should be 32,848.5 and not 38,848.5 as in the problem. I am going ahead with solving the problem after making this correction.
9.34 Part (a)
Rate of Return for each project would be the Internal rate of Return (IRR) and should be the rate at which the present value of future cash flows is equal to the outflow at point zero. Hence, each project rate of return would be calculated as:
Step 1: Outflow at Point zero = {Cash Flow at year1/(1+r)} + {Cash Flow at year 2/(1+r)2} + {cash Flow at year 3/(1+r)3}
Step 2: By trial and error method, put a value for r and solve. Remember, the r would be the rate at which the PV of future Cash Flows would be equal to outflow at point zero.
Showing the calculation of rate of return for project A as an example:
1,00,000 = {43,798/(1+r)} + {43,798/(1+r)2} + {43,798/(1+r)3}
By trial and error, take r = 14, the result of the right hand side of the quation would be = 1,01,683. This value is slightly more than 1,00,000, hence we need to take a rate that is greater than 14% to bring the Present value down to 1,00,000.
Again, by trial and error take r=15, the result of the right hand side of the equation would be = 1,00,000 approx. Hence, this is the rate of return on Project A.
Similarly, repeat this exercise for rest of the projects and you will find that the rate of return for all the projects would come to approx 15%.
9.34 Part (b)
The payback period for Project A, B and C can be simply calculated as :
Net Investment/Net annual cash inflow
Project A = 1,00,000/43,798 = 2.28 years
Project B = 50,000/21,899 = 2.28 years
Project C = 75,000/32,848.5 = 2.28 years.
For project D and E, since the monthly payments are not same, we have to make a cumulative discounted table like below :
Example for project D:
initial investment = 60,000
Year Cash Flow Cum. Cash Flow
1 30,000 30,000
2 29,000 59,000
3 18,228 77,228
payback period = 2 + 1,000/18,228
= 2.055 years
Project E
Initial Investment = 95,000
Year Cash Flow Cum. Cash Flow
1 50,000 50,000
2 45,000 95,000
3 26,609 . 121,609
Payback period = 2 years
Since, the minimum payback period is 2 years and except project E, all the other projects have got a payback period of more than 2 years, only acceptable choice is project E. Since there is a budget of 2,00,000 and this project requires 95,000, we will still have 1,05,000 as left over money to be utilised.
9.35 part (a)
if the minimum desired payback period is 2.2 years, even project D with a payback period of 2.055 years would be eligible for investment. Hence the optimum portfolio would be consisting of Project D and/or E with total investment of (60,000 + 95,000 = 1,55,000) which is still under the budget of 2,00,000.
9.35 part (b)
In case there is a budget contraint of 1,50,0000 which means we cannot both invest in Project D and E. Hence we would be only able to invest in Project D or E. We should select the project with the highest NPV at the required rate of return.