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: Project M Project N -$18,000 $6,000 $6,000 $6,000 $6,000 $6,000 -$54,000 $16,800 $16,800 $16,800 $16,800 $16,800 a. 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

Answer 1

a
Project M
Discount rate	0.14
Year	0	1	2	3	4	5
Cash flow stream	-18000	6000	6000	6000	6000	6000
Discounting factor	1	1.14	1.2996	1.481544	1.6889602	1.925415
Discounted cash flows project	-18000	5263.158	4616.805	4049.829	3552.4817	3116.212
NPV = Sum of discounted cash flows
NPV Project M =	2598.49
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	-54000	16800	16800	16800	16800	16800
Discounting factor	1	1.14	1.2996	1.481544	1.6889602	1.925415
Discounted cash flows project	-54000	14736.84	12927.05	11339.52	9946.9487	8725.394
NPV = Sum of discounted cash flows
NPV Project N =	3675.76
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
b
Project M
IRR is the rate at which NPV =0
IRR	0.198577097
Year	0	1	2	3	4	5
Cash flow stream	-18000	6000	6000	6000	6000	6000
Discounting factor	1	1.198577	1.436587	1.72186	2.0637824	2.473602
Discounted cash flows project	-18000	5005.936	4176.566	3484.603	2907.2833	2425.612
NPV = Sum of discounted cash flows
NPV Project M =	3.1177E-05
Where
Discounting factor =	(1 + IRR)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	20%
Project N
IRR is the rate at which NPV =0
IRR	0.167976214
Year	0	1	2	3	4	5
Cash flow stream	-54000	16800	16800	16800	16800	16800
Discounting factor	1	1.167976	1.364168	1.593316	1.8609555	2.173552
Discounted cash flows project	-54000	14383.85	12315.19	10544.05	9027.6204	7729.284
NPV = Sum of discounted cash flows
NPV Project N =	2.29795E-06
Where
Discounting factor =	(1 + IRR)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	17%
c
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=(10133.76)+(8889.26)+(7797.6)+(6840)+(6000)
=39660.62
Thus year 0 modified cash flow=-18000
=-18000
Discount rate	0.14
Year	0	1	2	3	4	5
Cash flow stream	-18000	6000	6000	6000	6000	6000
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	-18000	0	0	0	0	0
Compounded cash flows	0	10133.76	8889.26	7797.6	6840	6000
Modified cash flow	-18000	0	0	0	0	39660.62
Discounting factor (using MIRR)	1	1.171163	1.371623	1.606394	1.88135	2.203368
Discounted cash flows	-18000	0	0	0	0	18000
NPV = Sum of discounted cash flows
NPV=	5.71936E-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

Project N 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=128374.53)+(24889.94)+(21833.28)+(19152)+(16800) =111049.75 Thus year o modified cash flow=-54000 =-54000 Discount rate 0.14 Year 4 5 Cash flow strea -54000 16800 16800 16800 16800 16800 Discount factor 1.14 1.2996 1.481544 1.6889602 1.925415 Compound fact 1 1.68896 1.481544 1.2996 1.14 1 Discounted cas! -54000 0 0 0 0 Compounded c 028374.53 24889.94 21833.28 19152 16800 Modified cash f -54000 0 0 0 6 111049.8 Discounting fac 1 1.155114 1.334288 1.541254 1.7803241 2.056477 Discounted cas! -54000 0 0 54000 NPV = Sum of discounted cash flows NPV= 2.40137E-05 MIRR is the rate at which NPV = 0 MIRR= 15.51% Where Discounting fac(1 + discount rate)^(Corresponding period in years) Discounted Cas Cash flow stream/discounting factor Compounding f(1+reinvestment rate)^(time of last CF-Corresponding period in years) Compounded Cash flow stream*compounding factor

Project M Year Cash flow stre: Cumulative cash flow -18000 18000 6000 - 12000 6000 -6000 6000 0 6000 6000 6000 12000 Payback period is the time by which undiscounted cashflow cover the intial investment outlay this is happening at the end of year 3 therefore payback period is: 3 Years Project N Year Cash flow stre: Cumulative cash flow -54000 54000 16800 -37200 16800 -20400 16800 -3600 16800 13200 16800 30000 Payback period is the time by which undiscounted cashflow cover the intial investment outlay this is happening between year 3 and 4 therefore by interpolation payback period = 3 + (0-(-3600))/(13200-(-3600)) 3.21 Years

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