Question

1. Given the following four projects and their cash flows, calculate the discounted payback period with a 5% discount rate discount rate.

Cash Flow	A	B	C	D
Cost	$     10,000	$    25,000	$   45,000	$        100,000
Cash flow year 1	$      4,000	$      2,000	$   10,000	$          40,000
Cash flow year 2	$      4,000	$      8,000	$   15,000	$          30,000
Cash flow year 3	$      4,000	$    14,000	$   20,000	$          20,000
Cash flow year 4	$      4,000	$    20,000	$   20,000	$          10,000
Cash flow year 5	$      4,000	$    26,000	$   15,000	$                  -
Cash flow year 6	$      4,000	$    32,000	$   10,000	$                   -

PLEASE SHOW ME ALL THE STEPS, I'M TRYING TO LEARN THE BASICS OF IT. THANK YOU!

Answer 1

A			Discount rate=	0.05
Year	Cash flow stream	Cumulative cash flow	Discounting factor	Discounted CF	Cumulative cash flow	Cumulative discounted CF
0	-10000	-10000	1	-10000	-10000	-10000
1	4000	-6000	1.05	3809.524	-6000	-6190.48
2	4000	-2000	1.1025	3628.118	-2000	-2562.36
3	4000	2000	1.157625	3455.35	2000	892.9921
4	4000	6000	1.215506	3290.81	6000	4183.802
5	4000	10000	1.276282	3134.105	10000	7317.907
6	4000	14000	1.340096	2984.862	14000	10302.77
Discounted payback period is the time by which discounted cashflow cover the intial investment outlay
this is happening between year 2 and 3
therefore by interpolation payback period = 2 + (0-(-2562.36))/(892.99-(-2562.36))
2.74 Years
Where
Discounting factor =(1 + discount rate)^(corresponding year)
Discounted Cashflow=Cash flow stream/discounting factor
B			Discount rate=	0.05
Year	Cash flow stream	Cumulative cash flow	Discounting factor	Discounted CF	Cumulative cash flow	Cumulative discounted CF
0	-25000	-25000	1	-25000	-25000	-25000
1	2000	-23000	1.05	1904.762	-23000	-23095.2
2	8000	-15000	1.1025	7256.236	-15000	-15839
3	14000	-1000	1.157625	12093.73	-1000	-3745.28
4	20000	19000	1.215506	16454.05	19000	12708.77
5	26000	45000	1.276282	20371.68	45000	33080.45
6	32000	77000	1.340096	23878.89	77000	56959.35
Discounted payback period is the time by which discounted cashflow cover the intial investment outlay
this is happening between year 3 and 4
therefore by interpolation payback period = 3 + (0-(-3745.28))/(12708.77-(-3745.28))
3.23 Years
Where
Discounting factor =(1 + discount rate)^(corresponding year)
Discounted Cashflow=Cash flow stream/discounting factor
C			Discount rate=	0.05
Year	Cash flow stream	Cumulative cash flow	Discounting factor	Discounted CF	Cumulative cash flow	Cumulative discounted CF
0	-45000	-45000	1	-45000	-45000	-45000
1	10000	-35000	1.05	9523.81	-35000	-35476.2
2	15000	-20000	1.1025	13605.44	-20000	-21870.7
3	20000	0	1.157625	17276.75	0	-4594
4	20000	20000	1.215506	16454.05	20000	11860.05
5	15000	35000	1.276282	11752.89	35000	23612.95
6	10000	45000	1.340096	7462.154	45000	31075.1
Discounted payback period is the time by which discounted cashflow cover the intial investment outlay
this is happening between year 3 and 4
therefore by interpolation payback period = 3 + (0-(-4594))/(11860.05-(-4594))
3.28 Years
Where
Discounting factor =(1 + discount rate)^(corresponding year)
Discounted Cashflow=Cash flow stream/discounting factor

A			Discount rate=	0.05
Year	Cash flow stream	Cumulative cash flow	Discounting factor	Discounted CF	Cumulative cash flow	Cumulative discounted CF
0	-100000	-100000	1	-100000	-100000	-100000
1	40000	-60000	1.05	38095.24	-60000	-61904.8
2	30000	-30000	1.1025	27210.88	-30000	-34693.9
3	20000	-10000	1.157625	17276.75	-10000	-17417.1
4	10000	0	1.215506	8227.025	0	-9190.1
Discounted payback period is the time by which discounted cashflow cover the intial investment outlay
This is not happening during project life hence it cannot be calculated
Where
Discounting factor =(1 + discount rate)^(corresponding year)
Discounted Cashflow=Cash flow stream/discounting factor