# Calculating Payback Period & Comparing Investment Criteria

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Question 1

Payback (PB) calculation will give us an idea on how long it will take

for a project to recover the initial investment.

Then if:

Y = the year before full recovery of investment I;

U = Unrecovered cost at the start of last year;

CFi = CF of the year Y+1;

PB = Y + U/CFi

-Project A:

CFi = $18,000

I = $38,000

After the year 2 we will have recovered only $35,000 and we will

finish to recover the investment during the year 3, then:

Y = 2

and

U = $38,000 - $35,000 = $3,000

PB = 2 + 3,000/18,000 = 2.16 years

-Project B:

CFi = $250,000

I = $70,000

After the year 3 we will have recovered only $45,000 and we will

finish to recover the investment during the year 4, then:

Y = 3

and

U = $70,000 - $45,000 = $25,000

PB = 3 + 25,000/250,000 = 3.1 years

Definition of Payback Criterion:

-Accept a project if its payback period is less than maximum

acceptable payback period.

-Reject a project if its payback period is longer than maximum

acceptable payback period.

The payback cutoff is 3 years. Since project A has a payback period of 2.16 years, it should be selected.

Question 2

a. If you apply the payback criterion, which investment will you choose? Why?

Payback (PB) calculation will give us an idea on how long it will take

for a project to recover the initial investment.

Then if:

Y = the year before full recovery of investment I;

U = Unrecovered cost at the start of last year;

CFi = CF of the year Y+1;

PB = Y + U/CFi

-Project A:

CFi = $425,000

I = $210,000

After the year 3 we will have recovered only $77,000 ...

#### Solution Summary

The solution explains how to calculate the payback period and decide between mutually exclusive projects,

Comparing Investment Criteria

Comparing Investment Criteria

Consider the following two mutually exclusive projects:

Year Cash Flow A Cash Flow B

0 -$257,851 -$31,827

1 25,500 11,483

2 57,000 12,954

3 51,000 11,412

4 405,000 9,674

Whichever project you choose, if any, you require a 15 percent return on your investment.

Required:

(a) The payback period for Projects A and B is and years, respectively. (Round your answers to 2 decimal places, e.g. 32.16.)

(b) The discounted payback period for Projects A and B is and years, respectively. (Round your answers to 2 decimal places, e.g. 32.16.)

(c) The NPV for Projects A and B is $ and $ , respectively. (Round your answers to 2 decimal places, e.g. 32.16.)

(d) The IRR for Projects A and B is percent and percent, respectively. (Do not include the percent sign (%). Round your answers to 2 decimal places, e.g. 32.16.)

(e) The profitability index for Projects A and B is and , respectively. (Round your answers to 3 decimal places, e.g. 32.161.)

(f) Based on your answers in (a) through (e), you will finally choose Project

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