Question

A. X-treme Vitamin Company is considering two investments, both of which cost $20,000. The firm’s cost of capital is 15 percent. The cash flows are as follows:

Year	Project A	Project B
1	12000	10000
2	8000	6000
3	6000	16000

(a) What is the payback period for each project? Which project would you accept based on the payback period?
(b) What is the discounted payback for each project? Which project would you accept based on the discounted payback criterion?
(c) Calculate the NPV of each project? Which project would you choose based on the NPV criterion?
(d) Based on the IRR criteria which project would you choose if they were mutually exclusive? Show all the workings.

Answer 1

a

Project A
Year	Cash flow stream	Cumulative cash flow
0	-20000	-20000
1	12000	-8000
2	8000	0
3	6000	6000

Payback period is the time by which undiscounted cashflow cover the intial investment outlay

this is happening at the end of year 2

therefore payback period is:

2 Years

Project B
Year	Cash flow stream	Cumulative cash flow
0	-20000	-20000
1	10000	-10000
2	6000	-4000
3	16000	12000

Payback period is the time by which undiscounted cashflow cover the intial investment outlay

this is happening between year 2 and 3

therefore by interpolation payback period = 2 + (0-(-4000))/(12000-(-4000))

2.25 Years

Select Project A as it has smaller payback period

b

Project A			Discount rate=	15.00%
Year	Cash flow stream	Cumulative cash flow	Discounting factor	Discounted cash flows project	Cumulative discounted CF
0	-20000	-20000	1	-20000	-20000.00
1	12000	-8000	1.15	10434.78261	-9565.22
2	8000	0	1.3225	6049.149338	-3516.07
3	6000	6000	1.520875	3945.097395	429.03

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-(-3516.07))/(429.03-(-3516.07))

2.89 Years

Where

Discounting factor =(1 + discount rate)^(corresponding year)

Discounted Cashflow=Cash flow stream/discounting factor

Project B			Discount rate=	15.00%
Year	Cash flow stream	Cumulative cash flow	Discounting factor	Discounted cash flows project	Cumulative discounted CF
0	-20000	-20000	1	-20000	-20000.00
1	10000	-10000	1.15	8695.652174	-11304.35
2	6000	-4000	1.3225	4536.862004	-6767.49
3	16000	12000	1.520875	10520.25972	3752.77

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-(-6767.49))/(3752.77-(-6767.49))

2.64 Years

Where

Discounting factor =(1 + discount rate)^(corresponding year)

Discounted Cashflow=Cash flow stream/discounting factor

Select project B as it has lower discounted payback

c

Project A
Discount rate	15.000%
Year	0	1	2	3
Cash flow stream	-20000	12000	8000	6000
Discounting factor	1.000	1.150	1.323	1.521
Discounted cash flows project	-20000.000	10434.783	6049.149	3945.097
NPV = Sum of discounted cash flows
NPV Project A =	429.03
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Project B
Discount rate	15.000%
Year	0	1	2	3
Cash flow stream	-20000	10000	6000	16000
Discounting factor	1.000	1.150	1.323	1.521
Discounted cash flows project	-20000.000	8695.652	4536.862	10520.260
NPV = Sum of discounted cash flows
NPV Project B =	3752.77
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Select project B as it has higher NPV

d

Project A
IRR is the rate at which NPV =0
IRR	16.46%
Year	0	1	2	3
Cash flow stream	-20000.000	12000.000	8000.000	6000.000
Discounting factor	1.000	1.165	1.356	1.580
Discounted cash flows project	-20000.000	10303.667	5898.087	3798.245
NPV = Sum of discounted cash flows
NPV Project A =	0.000
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Project B
IRR is the rate at which NPV =0
IRR	25.10%
Year	0	1	2	3
Cash flow stream	-20000.000	10000.000	6000.000	16000.000
Discounting factor	1.000	1.251	1.565	1.958
Discounted cash flows project	-20000.000	7993.637	3833.894	8172.469
NPV = Sum of discounted cash flows
NPV Project B =	0.000
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Select project B as it has higher IRR