Question

Consider the following projects:

Cash Flows ($)
Project	C0	C1	C2	C3	C4	C5
A	−2,800	2,800	0	0	0	0
B	−5,600	2,800	2,800	5,800	2,800	2,800
C	−7,000	2,800	2,500	0	2,800	2,800

1. If the opportunity cost of capital is 12%, which project(s) have a positive NPV?

   Positive NPV Projects

2. Calculate the payback period for each project.

   Project A	years
   Project B	years
   Project C	years

3. Which project(s) would a firm using the payback rule accept if the cutoff period is three years?

   Project accepted

4. Calculate the discounted payback period for each project.

   Project A	years
   Project B	years
   Project C	years

5. Which project(s) would a firm using the discounted payback rule accept if the cutoff period is three years?

   Project accepted

Answer 1

a) Calculation of NPV

- Project A

Year	Cashflow	PVF@12%	Cashflow*PVF
0	(2,800)	1	-2800.00
1	2,800	0.8929	2500.00

NPV = PV of Inflows - PV of OUtflows

= 2500-2800

= -300

- Project B

Year	Cashflow	PVF@12%	Cashflow*PVF
0	(5,600)	1	-5600.00
1	2,800	0.8929	2500.00
2	2,800	0.7972	2232.14
3	5,800	0.7118	4128.33
4	2,800	0.6355	1779.45
5	2,800	0.5674	1588.80

NPV = PV of Inflows - PV of OUtflows

= (2500+2232.14+4128.33+1779.45+1588.80)-5600

= 12228.71-5600

= 6628.71

- Project C

Year	Cashflow	PVF@12%	Cashflow*PVF
0	(7,000)	1	-7000.00
1	2,800	0.8929	2500.00
2	2,500	0.7972	1992.98
3	-	0.7118	0.00
4	2,800	0.6355	1779.45
5	2,800	0.5674	1588.80

NPV = PV of Inflows - PV of OUtflows

= (2500+1992.98+0+1779.45+1588.8)-7000

= 7861.23-7000

=  861.23

So both B and C has positive NPV

b) Calculate the payback period & Discounted Payback Period for each project.

- Project A

Year	0	1
Cashflow(in $)	(2,800)	2,800
Cumulative Cashflow(in $)	(2,800)	-

Payback Period = A + (B/C)

where

A -  last time period where the cumulative cash flow was negative = 0

B - absolute value of the CCF at the end of that period A = 2800

C - value of the CF in the next period after A = 2800

Payback Period = 0+2800/2800

= 1 year

Year	0	1
Cashflow(in $)	(2,800)	2,800
PVF @12%	1	0.893
Discounted Cashflow (Cash flow * PVF)	(2,800)	2,500
Cumulative Cashflow(in $)	(2,800)	(300)

Discounted Payback Period = not ascertainable

- Project B

Year	0	1	2	3	4	5
Cashflow(in $)	(5,600)	2,800	2,800	5,800	2,800	2,800
Cumulative Cashflow(in $)	(5,600)	(2,800)	-	5,800	8,600	11,400

Payback Period = 1+2800/2800

= 2 years

Year	0	1	2	3	4	5
Cashflow(in $)	(5,600)	2,800	2,800	5,800	2,800	2,800
PVF @12%	1	0.893	0.797	0.712	0.636	0.567
Discounted Cashflow (Cash flow * PVF)	(5,600)	2,500	2,232	4,128	1,779	1,589
Cumulative Cashflow(in $)	(5,600)	(3,100)	(868)	3,260	5,040	6,629

Discounted Payback Period = 2+868/4128

= 2.21 years

- Project C

Year	0	1	2	3	4	5
Cashflow(in $)	(7,000)	2,800	2,500	-	2,800	2,800
Cumulative Cashflow(in $)	(7,000)	(4,200)	(1,700)	(1,700)	1,100	3,900

Payback Period = 3+1700/2800

= 3.61 years

Year	0	1	2	3	4	5
Cashflow(in $)	(7,000)	2,800	2,500	-	2,800	2,800
PVF @12%	1	0.893	0.797	0.712	0.636	0.567
Discounted Cashflow (Cash flow * PVF)	(7,000)	2,500	1,993	-	1,779	1,589
Cumulative Cashflow(in $)	(7,000)	(4,500)	(2,507)	(2,507)	(728)	861

Discounted Payback Period = 4+728/1589

= 4.46 years

Based on payback period, except C can be accepted and based on discounted payback B can be accepted.