Question

Roshek Company is considering a capital investment proposal. Estimates regarding the project are provided below: I

nitial Investment: $85,000

Annual Net income: $5,750

Estimated Useful Life: 5 years

Salvage Value: $10,000

The Company requires a 9% rate of return on all new investments.

a. The Payback Period (rounded) for this proposal is?

b. The Net Present Value (rounded) for this proposal is?

c. The Annual Rate of Return (rounded) for this proposal is?

Answer 1

Cash flows for the year 1- 4 as net income +(initial investment-salvage value)/ life )

=5750 +(85000-10000)/5 =20750

and for the last year

5750 +(85000-10000)/5 + 10000 =30750

a

Year	Cash flow stream	Cumulative cash flow
0	-85000	-85000
1	20750	-64250
2	20750	-43500
3	20750	-22750
4	20750	-2000
5	30750	28750

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

this is happening between year 4 and 5

therefore by interpolation payback period = 4 + (0-(-2000))/(28750-(-2000))

4.07 Years

b

Project
Discount rate	9.000%
Year	0	1	2	3	4	5
Cash flow stream	-85000	20750	20750	20750	20750	30750
Discounting factor	1.000	1.090	1.188	1.295	1.412	1.539
Discounted cash flows project	-85000.000	19036.697	17464.860	16022.807	14699.823	19985.390
NPV = Sum of discounted cash flows
NPV Project =	2209.58
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

c

IRR is the rate at which NPV =0
IRR	9.94%
Year	0	1	2	3	4	5
Cash flow stream	-85000.000	20750.000	20750.000	20750.000	20750.000	30750.000
Discounting factor	1.000	1.099	1.209	1.329	1.461	1.606
Discounted cash flows project	-85000.000	18873.504	17166.706	15614.260	14202.207	19143.322
NPV = Sum of discounted cash flows
NPV Project =	0.000
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	9.94%