Question

A project has an initial cost of $40,000, expected net cash inflows of $9,000 per year for 7 years, and a cost of capital of 11%. What is the project’s NPV? (Hint: Begin by constructing a time line.)

Financial Calculator: CFo=-40000, CF1=9000, F1=7, NPV I=11, CPT NPV=2409.7664

NPV = $2,409.77

What is the project’s IRR?

Financial Calculator: CFo=-40000, CF1=9000, F1=7, NPV I=11, CPT NPV=2409.7664, CPT IRR=12.842

IRR = 12.84%

What is the project’s MIRR?

What is the project’s PI?

What is the project’s payback period?

What is the project’s discounted payback period?

Answer 1

Project
Discount rate	11.000%
Year	0	1	2	3	4	5	6	7
Cash flow stream	-40000	9000	9000	9000	9000	9000	9000	9000
Discounting factor	1.000	1.110	1.232	1.368	1.518	1.685	1.870	2.076
Discounted cash flows project	-40000.000	8108.108	7304.602	6580.722	5928.579	5341.062	4811.768	4334.926
NPV = Sum of discounted cash flows
NPV Project =	2409.77
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Project
IRR is the rate at which NPV =0
IRR	12.84%
Year	0	1	2	3	4	5	6	7
Cash flow stream	-40000.000	9000.000	9000.000	9000.000	9000.000	9000.000	9000.000	9000.000
Discounting factor	1.000	1.128	1.273	1.437	1.621	1.830	2.065	2.330
Discounted cash flows project	-40000.000	7975.753	7068.071	6263.688	5550.848	4919.132	4359.310	3863.197
NPV = Sum of discounted cash flows
NPV Project =	-0.001
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	12.84%

Reinvestment Approach
All cash flows except the first are compounded to the last time period and IRR is calculated
Thus year 7 modified cash flow=(16833.73)+(15165.52)+(13662.63)+(12308.68)+(11088.9)+(9990)+(9000)
=88049.46
Discount rate	11.000%
Year	0	1	2	3	4	5	6	7
Cash flow stream	-40000.000	9000.000	9000.000	9000.000	9000.000	9000.000	9000.000	9000.000
Compound factor	1.000	1.870	1.685	1.518	1.368	1.232	1.110	1.000
Compounded cash flows	-40000.000	16833.73	15165.52	13662.63	12308.68	11088.9	9990	9000
Modified cash flow	-40000.000	0	0	0	0	0	0	88049.460
Discounting factor (using MIRR)	1.000	1.119	1.253	1.402	1.570	1.757	1.967	2.201
Discounted cash flows	-40000.000	0.000	0.000	0.000	0.000	0.000	0.000	40000.000
NPV = Sum of discounted cash flows
NPV Discount rate =	0.00
MIRR is the rate at which NPV = 0
MIRR=	11.93%
Where
Compounding factor =	(1 + reinvestment rate)^(time of last CF-Corresponding period in years)
compounded Cashflow=	Cash flow stream*compounding factor

PI= (NPV+initial inv.)/initial inv.

=(2409.77+40000)/40000

1.06

Project			Discount rate=	11.00%
Year	Cash flow stream	Cumulative cash flow	Discounting factor	Discounted cash flows project	Cumulative discounted CF
0	-40000	-40000	1	-40000	-40000.00
1	9000	-31000	1.11	8108.108108	-31891.89
2	9000	-22000	1.2321	7304.601899	-24587.29
3	9000	-13000	1.367631	6580.722432	-18006.57
4	9000	-4000	1.51807041	5928.578767	-12077.99
5	9000	5000	1.685058155	5341.061953	-6736.93
6	9000	14000	1.870414552	4811.767525	-1925.16
7	9000	23000	2.076160153	4334.925698	2409.77

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-(-4000))/(5000-(-4000))

4.44 Years

Discounted payback period is the time by which discounted cashflow cover the intial investment outlay

this is happening between year 6 and 7

therefore by interpolation payback period = 6 + (0-(-1925.16))/(2409.77-(-1925.16))

6.44 Years

Where

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

Discounted Cashflow=Cash flow stream/discounting factor