Question

 You are considering a project with an initial cash outlay of ​$75,000 and expected cash flows of ​$21,750 at the end of each year for six years. The discount rate for this project is 9.7 percent. a.  What are the​ project's payback and discounted payback​ periods?

b.  What is the​ project's NPV?
c.  What is the​ project's PI?

d.  What is the​ project's IRR?

Answer 1

a. I have provided both cashflows and discounted cashflows in the below table

First find the discount factor like Year1=1/(1+9.7%), Year2=1/(1+9.7%)^2, Year3=1/(1+9,7%)^3 and so on.... Then multiply these discount factors with cashflows to find discounted cashflows

discount rate	9.70%
	Cashflows	Discount factor	Discounted cashflows
Year0	-75000
Year1	21750	0.9116	19826.80
Year2	21750	0.8310	18073.66
Year3	21750	0.7575	16475.53
Year4	21750	0.6905	15018.71
Year5	21750	0.6295	13690.71
Year6	21750	0.5738	12480.14

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

In 3 years, they receives 65,250 and remaining 9750 (75000-65250) in 4th year.

In 4th year=9750/21750=0.45

Payback period=3.45 years

For discounted Payback period, we should consider discounted cashflows.

In 4 years, they receives 69394.7 and remaining 5605.3 (75000-69394.7) in 5th year

in 5th Year=5605.3/13690.71=0.41

Discounted payback period=4.41 years

b. Use NPV function in EXCEL to calculate NPV

=NPV(rate,Year1 to Year6 cashflows)-Year0 cashflow

=NPV(9.7%,Year1 to Year6 cashflows)-75000

NPV=$20,565.56

To calculate PI, use same function

PI=NPV(rate,Year1 to Year6 cashflows)/Year0 cashflow

PI =NPV(9.7%,Year1 to Year6 cashflows)/75000

PI=1.27

Use IRR function

=IRR(Year0 to Year6 cashflows)

IRR=18.56%

discount rate	9.70%
	Cashflows
Year0	-75000
Year1	21750
Year2	21750
Year3	21750
Year4	21750
Year5	21750
Year6	21750
NPV	20565.56
PI	1.27
IRR	18.56%