Question

A firm with a 14% WACC is evaluating two projects for this year's capital budget. After-tax cash flows, including depreciation, are as follows:

0

1

2

3

4

5

Project M	-$6,000	$2,000	$2,000	$2,000	$2,000	$2,000
Project N	-$18,000	$5,600	$5,600	$5,600	$5,600	$5,600

1. Calculate NPV for each project. Do not round intermediate calculations. Round your answers to the nearest cent.

   Project M:    $  

   Project N:    $  

   Calculate IRR for each project. Do not round intermediate calculations. Round your answers to two decimal places.

   Project M:     %

   Project N:     %

   Calculate MIRR for each project. Do not round intermediate calculations. Round your answers to two decimal places.

   Project M:     %

   Project N:     %

   Calculate payback for each project. Do not round intermediate calculations. Round your answers to two decimal places.

   Project M:     years

   Project N:     years

   Calculate discounted payback for each project. Do not round intermediate calculations. Round your answers to two decimal places.

   Project M:     years

   Project N:     years

2. Assuming the projects are independent, which one(s) would you recommend?

   1. Only Project M would be accepted because NPV(M) > NPV(N).

   2. Only Project N would be accepted because NPV(N) > NPV(M).

   3. Both projects would be accepted since both of their NPV's are positive.

   4. Only Project M would be accepted because IRR(M) > IRR(N).

   5. Both projects would be rejected since both of their NPV's are negative.

3. If the projects are mutually exclusive, which would you recommend?

   1. If the projects are mutually exclusive, the project with the highest positive NPV is chosen.

   2. Accept Project N.If the projects are mutually exclusive, the project with the highest positive IRR is chosen.

   3. Accept Project M.If the projects are mutually exclusive, the project with the highest positive MIRR is chosen.

   4. Accept Project M.If the projects are mutually exclusive, the project with the shortest Payback Period is chosen.

   5. Accept Project M.If the projects are mutually exclusive, the project with the highest positive IRR is chosen. Accept Project N.

4. Notice that the projects have the same cash flow timing pattern. Why is there a conflict between NPV and IRR?

   1. The conflict between NPV and IRR is due to the fact that the cash flows are in the form of an annuity.

   2. The conflict between NPV and IRR is due to the difference in the timing of the cash flows.

   3. There is no conflict between NPV and IRR.

   4. The conflict between NPV and IRR occurs due to the difference in the size of the projects.

   5. The conflict between NPV and IRR is due to the relatively high discount rate.

Answer 1

Project M
Discount rate	0.14
Year	0	1	2	3	4	5
Cash flow stream	-6000	2000	2000	2000	2000	2000
Discounting factor	1	1.14	1.2996	1.481544	1.6889602	1.925415
Discounted cash flows project	-6000	1754.386	1538.935	1349.943	1184.1606	1038.737
NPV = Sum of discounted cash flows
NPV Project M =	866.16
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
Project N
Discount rate	0.14
Year	0	1	2	3	4	5
Cash flow stream	-18000	5600	5600	5600	5600	5600
Discounting factor	1	1.14	1.2996	1.481544	1.6889602	1.925415
Discounted cash flows project	-18000	4912.281	4309.018	3779.84	3315.6496	2908.465
NPV = Sum of discounted cash flows
NPV Project N =	1225.25
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
Project M
IRR is the rate at which NPV =0
IRR	0.198577097
Year	0	1	2	3	4	5
Cash flow stream	-6000	2000	2000	2000	2000	2000
Discounting factor	1	1.198577	1.436587	1.72186	2.0637824	2.473602
Discounted cash flows project	-6000	1668.645	1392.189	1161.534	969.09443	808.5374
NPV = Sum of discounted cash flows
NPV Project M =	1.03923E-05
Where
Discounting factor =	(1 + IRR)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	19.86%
Project N
IRR is the rate at which NPV =0
IRR	0.167976214
Year	0	1	2	3	4	5
Cash flow stream	-18000	5600	5600	5600	5600	5600
Discounting factor	1	1.167976	1.364168	1.593316	1.8609555	2.173552
Discounted cash flows project	-18000	4794.618	4105.065	3514.682	3009.2068	2576.428
NPV = Sum of discounted cash flows
NPV Project N =	7.65978E-07
Where
Discounting factor =	(1 + IRR)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	16.80%
Project M
Combination approach
All negative cash flows are discounted back to the present and all positive cash flows are compounded out to the end of the project’s life
Thus year 5 modified cash flow=(3377.92)+(2963.09)+(2599.2)+(2280)+(2000)
=13220.21
Thus year 0 modified cash flow=-6000
=-6000
Discount rate	0.14
Year	0	1	2	3	4	5
Cash flow stream	-6000	2000	2000	2000	2000	2000
Discount factor	1	1.14	1.2996	1.481544	1.6889602	1.925415
Compound factor	1	1.68896	1.481544	1.2996	1.14	1
Discounted cash flows	-6000	0	0	0	0	0
Compounded cash flows	-0.000166667	3377.92	2963.09	2599.2	2280	2000
Modified cash flow	-6000	0	0	0	0	13220.21
Discounting factor (using MIRR)	1	1.171163	1.371623	1.606395	1.8813504	2.203368
Discounted cash flows	-6000	0	0	0	0	6000
NPV = Sum of discounted cash flows
NPV=	1.90647E-05
MIRR is the rate at which NPV = 0
MIRR=	17.12%
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
Compounding factor =	(1 + reinvestment rate)^(time of last CF-Corresponding period in years)
Compounded Cashflow=	Cash flow stream*compounding factor

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