Question

consider the following two project A AND B

year Cfa. Cfb

0 -1500 -1500

1 150 750

2 750 650

3. 950 350

if discount rate is 10%. calculate the following

project A project B

payback

discounted payback

NPV

IRR

PI

Crossover rate

Answer 1

1. Payback period is the time that it takes to retain the cost of investment.

Project A receives 900 in two years and receives remaining 600 (1500-900) in year3

In 3rd year=600/950=0.63

project A payback period=2.63 years

Project B receives 1400 in 2 years and receives remaining 100 (1500-1400) in year3

in 3rd year=100/350=0.29

project B payback period=2.29 years

2. The discounted cashflows for Project A and B look as below

	ProjectA	project B
	Cashflows	Present value factor@10%	Discounted cashflows	Cashflows	Present value factor@10%	Discounted cashflows
Year1	150	0.909090909	136.4	750	0.909090909	681.8
Year2	750	0.826446281	619.8	650	0.826446281	537.2
Year3	950	0.751314801	713.7	350	0.751314801	263.0

Project A receives only 1469.9 in three years and unable to retain the total investment

project A discounted payback period is more than 3 years

Project B receives only 1482 in three years and unable to retain the total investment

project B discounted payback period is more than 3 years

The other techniques are shown below

discount rate	10%
	project A	project B	Difference of Project A-B
Year0	-1500	-1500	0
Year1	150	750	-600
Year2	750	650	100
Year3	950	350	600
NPV	-30.05	-18.03
IRR	9.1%	9.2%
PI	0.98	0.99
Crossover rate		8.7%	IRR

=NPV(rate,Year1 to year3 cashflows)-Year0 cashflow

=IRR(Year0 to year3 cashflows)

PI==NPV(rate,Year1 to year3 cashflows)/Year0 cashflow

Cross over rate is the rate at which both the Projects NPV becomes equal.

First subtract the cashflows from one project to another

Then use IRR function, =IRR(Year0 to year1 differential cashflows)=8.7%