# Using the Payback Method, IRR, and NPV

Purpose of Assignment The purpose of this assignment is to allow the student to calculate the project cash flow using net present value (NPV), internal rate of return (IRR), and the payback methods. Assignment Steps Resources: Corporate FinanceSTEP 1 (SUBMIT AS A WORD DOCUMENT IN MEMO FORMAT)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.
Minimum required reference includes your textbook.STEP 2 (SUBMIT AS AN EXCEL SPREADSHEET)Calculate the following time value of money problems using Microsoft® Excel®: :
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%?
What is the future value if you plan to invest \$200,000 for 5 years and the interest rate is 5%?
What is the interest rate for an initial investment of \$100,000 to grow to \$300,000 in 10 years?
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?
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.
What is the project cash flow generated for Project A and Project B using the NPV method? Which would you choose and why? Assume a 10% discount rate.
What is the payback period for Project A and Project B using the payback method? Which would you choose and why?
Project A and Project B:
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#1 PV OF SINGLE LUMP SUM
PRESENT VALUE OF SINGLE LUMP SUM
If you want to accumulate \$5,000 in 10 years, how much do you need to deposit today that pays an
interest rate of 2%? This means ONE single lump sum invested at ONE time.
If they are asking you to find the value TODAY, this means they are asking you to find the
PRESENT VALUE. So, use your PV function in Excel as you are dealing with compounded interest.
Click formulas, insert function, financial, PV.
Variables are as follows:
Rate: .02 (this is your annual rate of interest)
Nper: 10 (this is the total number of compounding periods – in this case, you have been earning
interest on an annual basis for 10 years)
Pmt: 0 (not applicable as there are no payments)
FV: 5000 (this is your future value or value at the end of the period)
Click ok and you should get \$4101.74 as your PV (ignore the negative as the negative in a PV value
for Excel simply means money out or the initial investment “out” of your pocket).
#2 FV OF SINGLE LUMP SUM
FUTURE VALUE OF SINGLE LUMP SUM
What is the future value if you plan to invest \$1,000 for 7 years and the interest rate is 10%? This
means ONE single lump sum invested at ONE time.
Use your FV function in Excel. Click formula, insert function, financial, FV. Variables are as follows:
Rate: .10 (this is your annual rate of interest)
Nper: 7 (this is the total number of compounding periods – in this case, you have been earning
interest on an annual basis for seven years)
Pmt: 0 (not applicable as there are no payments)
PV: -1000 (this is the value at the beginning of the period – remember to enter as a negative in Excel
to indicate money out since this was your initial investment “out” of your pocket)
Click ok and you should get \$1948.72 as your FV.
#3 RATE OF INTEREST EARNED
RATE OF INTEREST EARNED
What is the interest rate for an initial investment of \$1050 to grow to \$1500 in 1 year?
Use your RATE function in Excel. Click formulas, insert function, financial, RATE.
Variables are as follows:
Nper: 1 (this is the total number of compounding periods – in this case, you have been earning
interest on an annual basis for one year only)
Pmt: 0 (not applicable to this problem)
PV: -1050 (this is the value at the beginning of the period – remember to enter as a negative in Excel
to indicate money “out”)
FV: 1500 (this is the future value or value at the end of the period)
Click ok and you should get .4286 or 42.86% as your rate.
#4 PV OF ANNUITY
PRESENT VALUE OF ANNUITY
If your company purchases an annuity that will pay \$1,000/year for 20 years at a 15% 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?
If they are asking you to find the value TODAY (in this case they say value on the purchase date
which is TODAY), this means they are asking you to find the PRESENT VALUE. So, use
your PV function in Excel as you are dealing with compounded interest. Note however, they are
asking you to find the PV of the series of payments and not the value in the future. Also, this
is VERY IMPORTANT, they say that the first payment is made on the date of purchase. So that
means that this payment is made IN ADVANCE as there wasn’t time for interest accrue. So, you will
need to note that under your Type variable. Click formulas, insert function, financial, PV.
Variables are as follows:
Rate: .15 (this is your annual rate of interest)
Nper: 20 (this is the total number of compounding periods – in this case, you have been earning
interest on an annual basis for 20 years)
Pmt: 1000 (this is the amount of each payment you will receive)
FV: 0 (this is your future value or value at the end of the period – in this case, there is no future value
as when the payments are done, the annuity is worth zero)
Type: 1 (this means that the first payment was made in advance or prior to interest accruing – read
the problems carefully as some payments are made in advance and some are made at the end of
the period which is the norm so in those cases you would simply ignore the type variable)
Click ok and you should get \$7198.23 as your PV (ignore the negative as the negative in a PV value
for Excel simply means money out or the initial investment “out” of your pocket).
#5 RATE OF RETURN
RATE OF RETURN
What is the rate of return required to accumulate \$3000 if you invest \$100 per year for 10 years.
Assume all payments are made at the end of the period. Note that payments are made at the end
of the period so we can ignore the type variable.
Use your RATE function in Excel. Click formulas, insert function, financial, RATE.
Variables are as follows:
Nper: 10 (this is the total number of compounding periods – in this case, you have been earning
interest on an annual basis for one year only)
Pmt: -100 (this is the amount of the payment you will make so it is money “out” of your pocket so it
needs to be noted with a negative)
PV: 0 (this is the value at the beginning of the period and there is no lump sum value today to worry
about as all you are doing is making series of payments)
FV: 3000 (this is the future value or value at the end of the period)
Click ok and you should get .2292 or 22.92% as your rate.
#6 NPV CALCULATION
NPV CALCULATION
What is the net present value of a project with an initial cost of 50000 and cash inflows of 10000,
15000 and 25000 with a discount rate of 10%.
For this problem, PIECE OUT THE CASH FLOWS. So your equation here is:
Net Present Value = Purchase Price + Present Value of Cash Flows or abbreviated as PP + PVCF
PP: -50000 (This is given and in your equation, this should be a negative to indicate money out as
this is an outflow.)
PVCF: Use Excel and the NPV function. Click formula, insert function, financial, NPV. Variables are
as follows:
Rate: .10 (This is your discount rate in DECIMAL form.)
Value 1: 10000 (first year cash flow)
Value 2: 15000 (second year cash flow)
Value 3: 25000 (third year cash flow)
Click ok and you should get 40270.47 as your PVCF value.
#7 PAYBACK PERIOD
PAYBACK CALCULATION
Danica, Inc has the following mutually exclusive projects:
Project
Project
Project A
Project B
A
B
Year
Cumulative
Cumulative
Cash
Cash
Inflows
Inflows
Flows
Flows
0 -20000
NA
-23000
NA
1 12000 12000 13000 13000
2 8500
20500
9500
22500
3 2900
23400
8500
31000
What is the payback? Which would you choose?
Payback is simply the amount of time it takes for the inflows to equal your original outflow (initial
investment). This does NOT take into account time value of money, so no Excel formulary is
necessary. Review the chart above. I added a couple of columns above to tally the Cumulative
Inflows for each project as I like to lay out my variables at the beginning and see how the totals pan
out.
For project A, you can see that payback is going to be before the end of Year 2 (this is the year you
would recoup your 20000), but what fractional part of Year 2?
So, you have ONE full year and a partial of the second year.
Payback Period = Number of Full Years + (Initial Investment – Full Year(s) Cumulative Inflow)/Cash
Flow in Year of Payback
Payback Period = 1 + (20000-12000)/8500
Payback Period = 1 + (8000/8500)
Payback Period = 1+.9411
Payback Period = 1.941 years
For project B, you can see that payback is going to be before the end of Year 3 (this is the year you
would recoup your 23000), but what fractional part of Year 3?
So you have TWO full years and a partial of the third.
Payback Period = Number of Full Years + (Initial Investment – Full Year(s) Cumulative Inflow)/Cash
Flow in Year of Payback
Payback Period = 2 + (23000-22500)/8500
Payback Period = 2 + (500/8500)
Payback Period = 2+.0588
Payback Period = 2.059 years
Since Project A has a shorter payback, that is your winner!
Now all you do is add your PP and PVCF values together (round to 2 decimals) and you should be
good to go.
NPV = PP + PVCF
NPV = -50000 + 40270.47
NPV = -9729.53
This project should actually be REJECTED as the NPV is negative. If you had a choice
between two mutually exclusive projects, you would choose the one with the higher NPV.

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