# Payback Method, IRR, and NPV

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### Question Description

Create a 350-word memo to management including the following:

• Describe the use of internal rate of return (IRR), net present value (NPV), and the payback method in evaluating project cash flows.

Calculate the following time value of money problems:

1. If you want to accumulate \$500,000 in 20 years, how much do you need to deposit today that pays an interest rate of 15%?
2. What is the future value if you plan to invest \$200,000 for 5 years and the interest rate is 5%?
3. What is the interest rate for an initial investment of \$100,000 to grow to \$300,000 in 10 years?
4. If your company purchases an annuity that will pay \$50,000/year for 10 years at a 11% discount rate, what is the value of the annuity on the purchase date if the first annuity payment is made on the date of purchase?
5. What is the rate of return required to accumulate \$400,000 if you invest \$10,000 per year for 20 years. Assume all payments are made at the end of the period.

Calculate the project cash flow generated for Project A and Project B using the NPV method.

• Which project would you select, and why?
• Which project would you select under the payback method? The discount rate is 10% for both projects.

Sample Template for Project A and Project B:

Kindly submit all word and excel sheets.

Submit the memo and all calculations. Strict APA, No plagiarism.. also attached is grading guide.

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ameliajamie
School: UC Berkeley

Hello, please review and advice if we can combine the two word document or i leave it as it is and also inform of any other part that requires clarification or editionLooking forward to here from you

Investment decision based on NPV
Project A
Year 0
Year 1
Year 2
Year 3

cash flows
\$
(10.000,00)
5.000,00
5.000,00
5.000,00

Project B
Year 0
Year 1
Year 2
Year 3

(55.000,00)
20.000,00
20.000,00
20.000,00

Investment decision based on payback
Project A
year 0
year 1
year 2
year 3

(10.000,00)
5.000,00
5.000,00
5.000,00

Project B
Year 0
Year 1
Year 2
Year 3

(55.000,00)
20.000,00
20.000,00
20.000,00

Based on NPV, project A should be chosen because it has a positive net present value
Based on the payback period, project A should be selected because it takes shorter period

PVIT=1/(1+r0^n
1,00
0,91
0,83
0,75
NPV

2.434,26

1,00
0,91
0,83
0,75
NPV

(55.000,00)
18.181,82
16.528,93
15.026,30
(5.262,96)

Recovery period

Cummulative amount
1
2

PB

5.000,00
10.000,00

2 Years

1
2
0,75

PB

PV
\$
(10.000,00)
4.545,45
4.132,23
3.756,57

20.000,00
40.000,00
15.000,00

2.75 years

because it takes shorter period to recover the initial capital

Time value of money-workings
1 Present value
FV=PV(1+r)^n
PV=FV/(1+r)^n
FV
n
r
PV

\$500.000
20 years
15%
30.550,14

2 Future value=PV(1+r)^n
Present value
n
r
FV

\$200.000
5 years
5%
255.256,31

3 FV=PV(1+r)^n
(1+r)^n=FV/PV
r=(FV/PV)^1/10-1
Present value
future value
n

r

\$100.000
\$300.000
10 years
3
0,12

4 Present value of an annuity due
PV=PMT/r[1-1/(1+r)^n]*(1+r)
PMT
r
n
PMT/r
1/1+r^10
1-(1/1+r^10)

\$50.000
11%
10 years
454.545,45
0,35
0,65

1+r

1,11

PV

326.852,38

5 Rate of return in an ordinary annuity
FV=PMT*(1+r)^n/r-1
FV
PMT
n
r

\$400.000
\$10.000
20 years
?

From the future value table for n=20
with future interest factor of 40
r

7%

Date:

March 30TH, 2017

To:

The Management.

From:

The Finance and Investment Division.

Subject: Uses of IRR, NPV and the Payback method of project evaluation

The Internal Rate of Return is the interest rate that makes the cash outflows spent on a project
equal the cash inflows that is generated after undertaking the investment. Companies will
compute the projected IRR when evaluating one or more projects to establish if the rate is more
or less than the cost of capital. If the IRR exceeds the company’s cost of capital, then it is
financially wise to invest in the project. In situations of multiple investments, the project with a
higher IRR will be preferable. When
The advantage of using the IRR is that it’s easy to understand and is based on the discounted
cash flow technique. Its drawback is that at times it can yield no answer when nonconventional
cash flow is used. In mutually exclusive projects IRR can lead to incorrect investment decisions.
The net present value looks at the projected present value of the dollar amount generated after
the initial invested has been recovered. It is used to measure the increase in a company’s value
which in term will increase the shareholders’ value thus help the management make decisions
that will maximize shareholders value. Projects that yield an NPV of greater than zero should be
accepted and those that are below zero should be rejected.
The net present value approach uses discounted cash flows valuation method; it also provides an
accurate amount of how much an investment will add to the worth of the firm. The disadvantage
of this technique is difficult to understand especially to the non-accountants. The method is not

beneficial for comparing more than one project of different scale since the magnitude of the net
present value produced is determined on most occasions by the size of the input.
The payback period emphasizes on the period a project takes to recover its initial investment.
This method is used to make decisions based on the project that has a shorter period to recover
the capital injected into the business.
The use of the payback period is simple to comprehend and compute and also a simple to
measure the liquidity of a project. This method does not factor in the time value of money and it
ignores the cash flow generated after the payback period and hence bias for projects that take a
long period.

Yours Sincerely,
Sign….
Name….

References:
Drake, P. P. Capital budgeting techniques. Online (datum poslední revize: 29.6. 2006): www. fau. edu/~
ppeter/fin3403/module6/capbudtech. pdf.

1
Time value of Money

Time value of Money
Name
Instructor
Institutional Affiliation
Date

2
Time value of Money

Time value of Money
1) Future value = \$500,000
n=20 years
r=15%
Present Value=FV/ (1+r) ^n
=\$500,000/1.15^20
=\$500,000/16.37
=\$30.550.14
2) Present value=\$200,000
n=5 years
r=5%
FV=PV (1+r) ^n
=\$200,000(1+0.05) ^5
=\$200,000*1.28
=\$255,256.31
3) Present value=\$100,000
Future value=\$300,000
n=10 years
FV=PV (1+r) ^n
\$300,000=\$100000(1+r) ^10
(1+r)^10=\$300,000/\$100,000
r= (\$300,000/\$100,000) ^1/10-1
r=3^0.1-1

3
Time value of Money

=0.12*100
=12%

4) Present value of an annuity due
PV=PMT/r[1-{1/(1+r)^n]*(1+r)
PMT=\$50,000
R=11%
N=10 years
PV=\$50, 0000/0.11[1-1/ (1.11^10)*1.11
=\$454545.50(1-0.35)*1.11
=\$326,852.38

5) Rate of return in an ordinary annuity

FV=PMT [(1+r) ^n-1]/r

FV=\$400,000
PMT=\$10,000
n=20 years
r=?
From the future value table of an ordinary annuity. The future value interest factor
of n=20 is 40.99549 at interest rate of 7%
Therefore r=7%

4
Time value of Money

References:
Brealey, R., Myers, S. C., & Marcus, A. J. (2007). FundamentalsofCorporate Finance. Mc Graw Hill, New
York.

Brigham, E. F., & Houston, J. F. (2012). Fundamentals of financial management. Cengage
Learning.

Drake, P. P. Capital budgeting techniques. Online (datum poslední revize: 29.6. 2006): www. fau. edu/~
ppeter/fin3403/module6/capbudtech. pdf.

TIME VALUE OF MONEY TABLES
Change figures in blue cells to obtain interest factors you might need for other n and i
------- ----------------- ----------------- ----------------- ----------------- ----------------- ----------------- ----------------- ----------------- ----------------- ----------------- ----------------- ----------------- ----------------- ----------------- ----------------- ----------------PRESENT VALUE OF \$1
n
1%
1,5%
2,0%
2,5...

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Anonymous
Top quality work from this guy! I'll be back!

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