Payback, NPV, and MIRR Your division is considering two investment projects, eac
ID: 2786712 • Letter: P
Question
Payback, NPV, and MIRR
Your division is considering two investment projects, each of which requires an up-front expenditure of $26 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):
A.) What is the regular payback period for each of the projects? Round your answers to two decimal places.
Project A ______years
Project B ______years
B.) What is the discounted payback period for each of the projects? Round your answers to two decimal places.
Project A ______years
Project B ______years
C.) If the two projects are independent and the cost of capital is 10%, which project or projects should the firm undertake?
Answer: Both Porjects (verified correct)
D.) If the two projects are mutually exclusive and the cost of capital is 5%, which project should the firm undertake?
Answer: Project A (verified correct)
E.) If the two projects are mutually exclusive and the cost of capital is 15%, which project should the firm undertake?
Answer: Project B (verified correct)
F.) What is the crossover rate? Round your answer to two decimal places.
_______%
G.) If the cost of capital is 10%, what is the modified IRR (MIRR) of each project? Round your answers to two decimal places.
Project A _______%
Project B _______%
Explanation / Answer
Pay back period A
Payback period is the time it takes for a project to return the initial capital, Payback period is different than discounted payback in which cash flows are discounted first with required rate of return/discount rate, in payback period method cash flows are not discounted.
Year
Cash Inflow
Cumulative cash flow
1
5000000
5000000
2
10000000
15000000
3
15000000
30000000
4
20000000
50000000
Payback period will fall between year 2 and 3
Payback period will be,
= 2+ (26000000 - 15000000)/15000000
= 2+ (11000000)/ 15000000
= 2+ 0.73
= 2.73 years
Payback period B
Year
Cash Inflow
Cumulative cash flow
1
20000000
20000000
2
10000000
30000000
3
8000000
38000000
4
6000000
44000000
Payback period will fall between year 1 and 2
Payback period will be,
= 1+ (26000000 - 20000000)/10000000
= 1+ (6000000)/ 10000000
= 1+ 0.6
= 1.6 years
Discounted Payback A
While calculating payback Cash flow from asset/project first discounted using required rate of return then payback period is calculated. Discounted payback is the time it takes for a project to return the initial cost.
If the required rate of return is 0.1
Payback period will be,
Year
Cash Inflow
Present value factor
Present value of cash flow
Cumulative cash flow
1
5000000
0.90909
4545454.545
4545454.545
2
10000000
0.82645
8264462.81
12809917.36
3
15000000
0.75131
11269722.01
24079639.37
4
20000000
0.68301
13660269.11
37739908.48
Payback period will fall between year 3 and 4
Payback period will be calculated following way,
= 3+ (26000000 - 24079639.3688956)/ 13660269.1073014
= 3+ (1920360.63110444)/ 13660269.1073014
= 3+ 0.140580000000001
= 3.14 years
Discounted payback B
Year
Cash Inflow
Present value factor @ 10%
Present value of cash flow
Cumulative cash flow
1
20000000
0.90909
18181818.18
18181818.18
2
10000000
0.82645
8264462.81
26446280.99
3
8000000
0.75131
6010518.407
32456799.4
4
6000000
0.68301
4098080.732
36554880.13
Payback period will fall between year 1 and 2
Payback period will be calculated following way,
= 1+ (26000000 - 18181818.1818182)/ 8264462.80991735
= 1+ (7818181.81818182)/ 8264462.80991735
= 1+ 0.946
= 1.95 years.
The project with shortest payback and discounted payback should be selected.
Year
Cash Inflow
Cumulative cash flow
1
5000000
5000000
2
10000000
15000000
3
15000000
30000000
4
20000000
50000000
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