CORP FIN 51: Using the Payback Method, IRR, and NPV

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Questions 1-5

Week 3
Using the Payback Method, IRR, and NPV
All solutions are performed using a financial calculator (i.e. HP 10BII) and/or Microsoft Excel.
Set up each of these in the following format, showing what you know and what you don't know.
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%?
FV = 500,000
N = 20 This is a Present Value problem. Use the PV formula for excel or an HP.
I = 15% Excel formula on page 99
PMT = 0
PV=? PV=?
2.     What is the future value if you plan to invest $200,000 for 5 years and the interest rate is 5%?
FV=?
N = This is a Future Value problem. Use the FV formula for excel or an HP.
I = X% Excel formula on page 99
PMT = 0
PV = FV=?
3.     What is the interest rate for an initial investment of $100,000 to grow to $300,000 in 10 years?
FV=
N = In this problem, you are solving for the interest rate. Use the Discount Rate formula for excel or an HP.
I =? Excel formula on page 99
PMT = 0
PV = I=?
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?
N =
I = PV=?
PMT = This is a Present Value problem. Use the PV formula for excel or an HP.
PV = ? Excel formula on page 99
* Make sure to set your calculator in "BEGIN" mode to solve this problem
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.
N =
I = ? i=?
PMT = In this problem, you are solving for the interest rate. Use the Discount Rate formula for excel or an HP.
FV = Excel formula on page 99
* Make sure to set your calculator in "END" mode to solve this problem

Project Cash Flow

Use the Spreadsheet Application on page 137 for help. Set up the problem like the example for Question 12 on page 164.
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. Use Microsoft Excel to prepare your answer. Note that a similar problem is in the textbook in Section 5.1.
Chapter 5
Question 12
Set up the problem similar to the way Problem 12 is solved.
Annual cash flows: I II
Year 0 $ (35,000) $ (16,000)
Year 1 $ 19,800 $ 9,400
Year 2 $ 19,800 $ 9,400
Year 3 $ 19,800 $ 9,400
Required return 10%
Output area:
Profitability index (I) 1.407
Profitability index (II) 1.461
The profitability index implies accept Project II
NPV (I) $ 14,239.67
NPV (II) $ 7,376.41
NPV decision rule implies accept Project I
Using the profitability index to compare mutually exclusive
projects can be ambiguous when the magnitude of the cash
flows for the two projects are of different scale.
The following problem will help solve for the payback part of the question.
Chapter 5
Question 1
Input area:
Year Cash Flow (A) Cash Flow (B)
0 $ (20,000) $ (24,000)
1 13,200 14,100
2 8,300 9,800
3 3,200 7,600
Required payback 2
Discount rate 15%
Output area:
a) Project A Payback 1.819
Project A Accept
Project B Payback 2.013
Project B Reject
b) Project A NPV $ (141.69)
Project A Reject
Project B NPV $ 668.20
Project B Accept
Accept Project B because it has a greater NPV.