Question

Reynolds Enterprises is attempting to evaluate the feasibility of investing $85,000, CF₀, in a machine having a 5-year life. The firm has estimated the cash inflows associated with the proposal as shown below. The firm has a 12 percent cost of capital.

End of Year (t)	Cash Inflows (CFt)
1	$18,000
2	$22,500
3	$27,000
4	$31,500
5	$36,000

a.   Calculate the payback period for the proposed investment.

b.   Calculate the NPV for the proposed investment.

c.   Calculate the IRR for the proposed investment.

d.   Evaluate the acceptability of the proposed investment using NPV and IRR. What recommendation would you make relative to implementation of the project? Why?

Answer 1

a
Project
Year	Cash flow stream	Cumulative cash flow
0	-85000	-85000
1	18000	-67000
2	22500	-44500
3	27000	-17500
4	31500	14000
5	36000	50000
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-(-17500))/(14000-(-17500))
3.56 Years
b
Project
Discount rate	0.12
Year	0	1	2	3	4	5
Cash flow stream	-85000	18000	22500	27000	31500	36000
Discounting factor	1	1.12	1.2544	1.404928	1.5735194	1.762342
Discounted cash flows project	-85000	16071.43	17936.86	19218.07	20018.819	20427.37
NPV = Sum of discounted cash flows
NPV Project =	8672.54
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
c
Project
IRR is the rate at which NPV =0
IRR	0.155838927
Year	0	1	2	3	4	5
Cash flow stream	-8500000.00%	18000	22500	27000	31500	36000
Discounting factor	1	1.155839	1.335964	1.544159	1.7847988	2.06294
Discounted cash flows project	-85000	15573.1	16841.78	17485.25	17649.048	17450.82
NPV = Sum of discounted cash flows
NPV Project =	9.83164E-07
Where
Discounting factor =	(1 + IRR)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	15.58%

d

Accept the project as NPV is positive and IRR is more than discount rate