Question

You are the financial analyst for the Glad It’s Finally Over Company. The director of capital budgeting has asked you to analyze a proposed capital investment. The project has a cost of $30,000 and the cost of capital is 10%. The project’s expected net cash flows are as follows:

Year                Expected Net Cash Flow

0                               ($30,000)

1 12,500

2 10,000

3 10,000

4 8,000

A) What is the project’s payback period?

B) What is the project’s discounted payback period?

C) What is the project’s net present value?

D) What is the project’s internal rate of return?

E) What is the project’s modified internal rate of return?

Answer 1

A & B

Project			Discount rate=	10%
Year	Cash flow stream	Cumulative cash flow	Discounting factor	Discounted cash flows project	Cumulative discounted CF
0	-30000	-30000	1	-30000	-30000.00
1	12500	-17500	1.1	11363.63636	-18636.36
2	10000	-7500	1.21	8264.46281	-10371.90
3	10000	2500	1.331	7513.148009	-2858.75
4	8000	10500	1.4641	5464.107643	2605.35

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-(-7500))/(2500-(-7500))

2.75 Years

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-(-2858.75))/(2605.35-(-2858.75))

3.52 Years

Where

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

Discounted Cashflow=Cash flow stream/discounting factor

C)

Discount rate	10.000%
Year	0	1	2	3	4
Cash flow stream	-30000	12500	10000	10000	8000
Discounting factor	1.000	1.100	1.210	1.331	1.464
Discounted cash flows project	-30000.000	11363.636	8264.463	7513.148	5464.108
NPV = Sum of discounted cash flows
NPV Project =	2605.35
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

D)

Project
IRR is the rate at which NPV =0
IRR	14.25%
Year	0	1	2	3	4
Cash flow stream	-30000.000	12500.000	10000.000	10000.000	8000.000
Discounting factor	1.000	1.143	1.305	1.492	1.704
Discounted cash flows project	-30000.000	10940.452	7660.384	6704.645	4694.519
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=	14.25%

E)

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 4 modified cash flow=(16637.5)+(12100)+(11000)+(8000)
=47737.5
Thus year 0 modified cash flow=-30000
=-30000

Discount rate	10.000%
Year	0	1	2	3	4
Cash flow stream	-30000.000	12500.000	10000.000	10000.000	8000.000
Discount factor	1.000	1.100	1.210	1.331	1.464
Compound factor	1.000	1.331	1.210	1.100	1.000
Discounted cash flows	-30000.000	0	0	0	0
Compounded cash flows	0.000	16637.5	12100	11000	8000
Modified cash flow	-30000.000	0	0	0	47737.500
Discounting factor (using MIRR)	1.000	1.123	1.261	1.417	1.591
Discounted cash flows	-30000.000	0.000	0.000	0.000	30000.000
NPV = Sum of discounted cash flows
NPV=	0.00
MIRR is the rate at which NPV = 0
MIRR=	12.31%
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