Problem 10-21 Payback NPV and MIRR Your Division is considering two investment p
ID: 2715122 • Letter: P
Question
Problem 10-21 Payback NPV and MIRR
Your Division is considering two investment projects each of which requires an up front expenditure of $25 million. You estimate that the cost of capital is 10% and that the investments will produce the following after tax cash flows (in millions of dollars)
Year Project A Project B
1 5 20
2 10 10
3 15 8
4 20 6
What is the regular payback period for each of the projects
What is the discounted payback period for each of the projects
If the two projects are independent and the cost of capital is 105 which project or projects should the firm undertake
If the two projects are mutually exclusive and the cost of capital is 5% which project should the firm undertake
If the two projects are mutually exclusive and the cost of capital is 15% which project should the firm undertake
What is the crossover rate
If the cost of capital is 10% what is the modified IRR (MIRR) of each project
Answers are as follows:
A= 2.67 years
B = 1.5 years
A = 3.07 years
B = 1.825 years
NPVa = $12,739,908; IRRa = 27.27%
NPVb = $11,554,880; IRRb = 36.15%
Choose Both
NPVa = $18, 243, 813
NPVb = $14,964,829
Choose A
NPVa = $8,207,071; NPVb = $8, 643, 390
Choose B
13.53%
MIRRa = 21.93%
MIRRb = 2.96%a
SHOW ALL WORK AND FORMULAS TO SUPPORT ANSWERS!!!
Explanation / Answer
Project A Project B At discount rate 10% At discount rate 10% $ in Millions $ in Millions Year Cahflows Discount factor Discounted cash flows Year Cahflows Discount factor Discounted cash flows 0 -25 1 -25 0 -25 1 -25 1 5 0.909 4.545 1 20 0.91 18.18 2 10 0.826 8.264 2 10 0.83 8.26 3 15 0.751 11.270 3 8 0.75 6.01 4 20 0.683 13.660 4 6 0.68 4.10 NPV 12.740 NPV 11.55 IRR 27.27% IRR 36.15% A Regular payback period A Regular payback period Year Amount received Cumulative Balance to be received Year Amount received Cumulative Balance to be received 1 5 5 20 1 20 20 5 2 10 15 10 2 10 30 -5 3 15 30 -5 Regular payback period =2 years+10*1/15 Regular payback period =1 years+5*1/10 Regular payback period =2.6667 years Regular payback period =1.5 years B Discounted payback period B Discounted payback period Year Amount received Cumulative Balance to be received Year Amount received Cumulative Balance to be received 1 4.55 4.55 20.45 1 18.18 18.18 6.82 2 8.26 12.81 12.19 2 8.26 26.45 -1.45 3 11.27 24.08 0.92 4 13.66 37.74 -12.74 Regular payback period =3 years+0.920360631/13.660291 Regular payback period =1 year+6.818181/8.26446281 Regular payback period =3.067375 Years Regular payback period =1.825 Years At discount rate 10.5% At discount rate 10.5% $ in Millions $ in Millions Year Cahflows Discount factor Discounted cash flows Year Cahflows Discount factor Discounted cash flows 0 -25 1 -25 0 -25 1 -25 1 5 0.90 4.52 1 20 0.90 18.10 2 10 0.82 8.19 2 10 0.82 8.19 3 15 0.74 11.12 3 8 0.74 5.93 4 20 0.67 13.41 4 6 0.67 4.02 NPV 12.24685542 NPV 11.24309355 IRR 27.27% IRR 36.15% C NPV of project A 12.24685542 NPV of project B 11.24309355 NPV of the Project A and B are Positive. Therefore Both the projects can be chosen At discount rate 5% At discount rate 5% $ in Millions $ in Millions Year Cahflows Discount factor Discounted cash flows Year Cahflows Discount factor Discounted cash flows 0 ($25.00) 1 ($25.00) 0 -25 1 -25 1 $5.00 0.95 $4.76 1 20 0.95 19.05 2 $10.00 0.91 $9.07 2 10 0.91 9.07 3 $15.00 0.86 $12.96 3 8 0.86 6.91 4 $20.00 0.82 $16.45 4 6 0.82 4.94 NPV $18.24 NPV 14.96 IRR 27.27% IRR 36.15% D NPV of project A $18.24 NPV of project B $14.96 NPV of the Project A and B are Positive. Therefore Both the projects can be chosen At discount rate 15% At discount rate 15% $ in Millions $ in Millions Year Cahflows Discount factor Discounted cash flows Year Cahflows Discount factor Discounted cash flows 0 -25 1 -25 0 -25 1 -25 1 5 0.870 $4.35 1 20 0.870 $17.39 2 10 0.756 $7.56 2 10 0.756 $7.56 3 15 0.658 $9.86 3 8 0.658 $5.26 4 20 0.572 $11.44 4 6 0.572 $3.43 NPV $8.21 NPV $8.64 IRR 27.27% E NPV of project A $8.21 NPV of project B $8.64 NPV of the Project A and B are Positive. Therefore Both the projects can be chosen
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