Question
In: Finance
Internal rate of return and modified internal rate of return. Lepton Industries has three potential projects,...
Internal rate of return and modified internal rate of return. Lepton Industries has three potential projects, all with an initial cost of $1,700,000. Given the discount rate and the future cash flows of each project, what are the IRRs and MIRRs of the three projects for Lepton Industries?
|
Cash Flow |
Project Q |
Project R |
Project S |
||||
|
Year 1 |
$400,000 |
$600,000 |
$900,000 |
||||
|
Year 2 |
$400,000 |
$600,000 |
$700,000 |
||||
|
Year 3 |
$400,000 |
$600,000 |
$500,000 |
||||
|
Year 4 |
$400,000 |
$600,000 |
$300,000 |
||||
|
Year 5 |
$400,000 |
$600,000 |
$100,000 |
||||
|
Discount rate |
9% |
14% |
18% |
||||
What is the IRR for project Q?_________%(Round to two decimal places.)
What is the MIRR for project Q?________%(Round to two decimal places.)
What is the IRR for project R?________%(Round to two decimal places.)
What is the MIRR for project R?________%(Round to two decimal places.)
What is the IRR for project S?_________%(Round to two decimal places.)
What is the MIRR for project S?________% (Round to two decimal places.)
Solutions
Expert Solution
| Answer 1 | ||||||
| Calculation of IRR of project Q | ||||||
| Year | Cash flow | |||||
| 0 | -$1,700,000.00 | |||||
| 1 | $400,000.00 | |||||
| 2 | $400,000.00 | |||||
| 3 | $400,000.00 | |||||
| 4 | $400,000.00 | |||||
| 5 | $400,000.00 | |||||
| IRR of Project Q = | =IRR(B5:B10) | |||||
| IRR of Project Q = | 5.67% | |||||
| Calculation of Modified Internal rate of return (MIRR) of Project Q | ||||||
| MIRR = (Future value of cash inflows / Present value of cash outflows)^(1/n) - 1 | ||||||
| Future value of cash inflows | ||||||
| Year | Cash inflows | Future value factor @ 9% | Future value | |||
| 0 | $0.00 | 1.538623955 | $0.00 | |||
| 1 | $400,000.00 | 1.41158161 | $564,632.64 | |||
| 2 | $400,000.00 | 1.295029 | $518,011.60 | |||
| 3 | $400,000.00 | 1.1881 | $475,240.00 | |||
| 4 | $400,000.00 | 1.09 | $436,000.00 | |||
| 5 | $400,000.00 | 1 | $400,000.00 | |||
| Future value of cash inflows | $2,393,884.24 | |||||
| MIRR = ($2393884.24 / $1700000)^(1/5) - 1 | ||||||
| MIRR = 1.0709 - 1 | ||||||
| MIRR = 0.0709 | ||||||
| Modified Internal rate of return (MIRR) of project Q = 7.09% | ||||||
| Answer 2 | ||||||
| Calculation of IRR of project R | ||||||
| Year | Cash flow | |||||
| 0 | -$1,700,000.00 | |||||
| 1 | $600,000.00 | |||||
| 2 | $600,000.00 | |||||
| 3 | $600,000.00 | |||||
| 4 | $600,000.00 | |||||
| 5 | $600,000.00 | |||||
| IRR of Project R = | =IRR(B35:B40) | |||||
| IRR of Project R = | 22.50% | |||||
| Calculation of Modified Internal rate of return (MIRR) of Project R | ||||||
| MIRR = (Future value of cash inflows / Present value of cash outflows)^(1/n) - 1 | ||||||
| Future value of cash inflows | ||||||
| Year | Cash inflows | Future value factor @ 14% | Future value | |||
| 0 | $0.00 | 1.925414582 | $0.00 | |||
| 1 | $600,000.00 | 1.68896016 | $1,013,376.10 | |||
| 2 | $600,000.00 | 1.481544 | $888,926.40 | |||
| 3 | $600,000.00 | 1.2996 | $779,760.00 | |||
| 4 | $600,000.00 | 1.14 | $684,000.00 | |||
| 5 | $600,000.00 | 1 | $600,000.00 | |||
| Future value of cash inflows | $3,966,062.50 | |||||
| MIRR = ($3966062.50 / $1700000)^(1/5) - 1 | ||||||
| MIRR = 1.1846 - 1 | ||||||
| MIRR = 0.1846 | ||||||
| Modified Internal rate of return (MIRR) of Project R = 18.46% | ||||||
| Answer 3 | ||||||
| Calculation of IRR of project S | ||||||
| Year | Cash flow | |||||
| 0 | -$1,700,000.00 | |||||
| 1 | $900,000.00 | |||||
| 2 | $700,000.00 | |||||
| 3 | $500,000.00 | |||||
| 4 | $300,000.00 | |||||
| 5 | $100,000.00 | |||||
| IRR of Project S = | =IRR(B65:B70) | |||||
| IRR of Project S = | 20.37% | |||||
| Calculation of Modified Internal rate of return (MIRR) of Project S | ||||||
| MIRR = (Future value of cash inflows / Present value of cash outflows)^(1/n) - 1 | ||||||
| Future value of cash inflows | ||||||
| Year | Cash inflows | Future value factor @ 18% | Future value | |||
| 0 | $0.00 | 2.287757757 | $0.00 | |||
| 1 | $900,000.00 | 1.93877776 | $1,744,899.98 | |||
| 2 | $700,000.00 | 1.643032 | $1,150,122.40 | |||
| 3 | $500,000.00 | 1.3924 | $696,200.00 | |||
| 4 | $300,000.00 | 1.18 | $354,000.00 | |||
| 5 | $100,000.00 | 1 | $100,000.00 | |||
| Future value of cash inflows | $4,045,222.38 | |||||
| MIRR = ($4045222.38 / $1700000)^(1/5) - 1 | ||||||
| MIRR = 1.1893 - 1 | ||||||
| MIRR = 0.1893 | ||||||
| Modified Internal rate of return (MIRR) of Project S = 18.93% | ||||||
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