Calculating Payback and Profitability

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Complete a series of five problems in which you discount the cash flows of alternative capital investments, compare the expected values of alternative investments, and choose the investment that will provide maximum value for shareholders.

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Calculating Payback and Profitability Complete a series of five problems in which you discount the cash flows of alternative capital investments, compare the expected values of alternative investments, and choose the investment that will provide maximum value for shareholders. Note: The assessments in this course build upon each other, so you are strongly encouraged to complete them in sequence. Suggested Resources The resources provided here are optional. You may use other resources of your choice to prepare for this assessment; however, you will need to ensure that they are appropriate, credible, and valid. They provide helpful information about the topics in this unit. The MBA-FP6016 – Finance and Value Creation Library Guide can help direct your research. The Supplemental Resources and Research Resources, both linked from the left navigation menu in your courseroom, provide additional resources to help support you. The following resources will provide assistance to complete the assessment. • Assessment Problems – Helpful Tips [DOCX]. • Excel Examples [XLS]. The following texts are designed to assist learners to master core concepts, solve financial problems, and analyze results. • Boundless. (n.d.). Boundless finance. Retrieved from https://www.boundless.com/finance/textbooks/boundless-finance-textbook/ • Chapter 5, "Time Value Money". • Chapter 6, "Bond Valuation" • Chapter 7, "Stock Valuation". • Chapter 15, "Dividends". 1. Assessment Instructions • Demonstrate your understanding of financial concepts by completing the following problems. Where appropriate, show or explain your work. You may use Excel to work on the problems. Problem 1. Calculating net present value (NPV): Porter Incorporated has two exclusive projects, listed in the table below. Use the NPV rule to rank these two projects. If the appropriate discount rate is 13 percent, which project should be chosen? Problem 1. Calculating NPV Year Project A Project B 0 −$12,700 −$9,400 1 $7,000 $4,800 Year Project A Project B 2 $5,500 $3,750 3 $2,500 $3,400 Problem 2. Calculating payback period: An investment project provides cash inflows of $920 per year for eight years. Calculate the project's payback period if the initial cost is each of the following: • $4,500. • $5,500. • $7,000. Problem 3. Calculating internal rate of return (IRR) for cash flows: Calculate the internal rate of return for the cash flows of the two projects in the table below. Problem 3. Calculating IRR for Cash Flows Year Project A Project B 0 −$4,600 −$3,500 1 $1,400 $1,250 2 $2,200 $1,800 3 $2,700 $1,600 Problem 4. Calculating profitability index of a project: Jeff plans to open a small health club. The equipment will cost $225,000. Jeff expects that there will be after-tax cash inflows of $62,000 annually for seven years. The equipment will then be scrapped and the health club will close. At year-end of the first year, the first cash inflow occurs. The required return is 13 percent. What is the project's profitability index? Should it be accepted? Problem 5. Calculating project NPV: Jenny's Creamery is considering the purchase of a $27,000 ice cream maker. The ice cream maker has an economic life of eight years. Using the straightline method, it will be fully depreciated. The machine will produce 250,000 servings per year, with each costing $1.25 to make, and priced at $1.99. The discount rate is 12 percent. The tax rate is 35 percent. Should the company make the purchase? Provide a rationale using the calculations. Calculating Payback and Profitability Scoring Guide Criteria Calculate the payback period and net present value (NPV) of a Proficient Distinguished Calculates the payback period and Calculates the net present value (NPV) of a payback period Criteria project. Proficient project. Distinguished and net present value (NPV) of a project; arrives at accurate calculations to recommend whether to purchase or not. Calculate the internal rate of return Calculates the internal rate of (IRR) for the cash flows. return (IRR) for the cash flows. Calculates the internal rate of return (IRR) for the cash flows; uses appropriate methods to arrive at accurate calculations. Calculate the profitability index of a Calculates the profitability index project. of a project. Calculates the profitability index of a project; uses appropriate methods to calculate the profitability index. MBA-FP6016 Assessment Problems – Helpful Tips Assessment 2 – Financial Statements Use the inputs provided in the Excel spreadsheet to come up with formula inputs. Basic accounting equations and formulas: • 𝐴𝑠𝑠𝑒𝑡𝑠 − 𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠 = 𝐸𝑞𝑢𝑖𝑡𝑦. This formula can be manipulated with simple algebra to place any of the three inputs separately on one side of the equation. • The equity multiplier formula starts out as 𝑇𝑜𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠⁄𝑇𝑜𝑡𝑎𝑙 𝐸𝑞𝑢𝑖𝑡𝑦, but it is derived into the following formula: 1 + 𝐷𝑒𝑏𝑡 − 𝐸𝑞𝑢𝑖𝑡𝑦 𝑅𝑎𝑡𝑖𝑜. • The return on equity formula is 𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒⁄𝑇𝑜𝑡𝑎𝑙 𝐸𝑞𝑢𝑖𝑡𝑦, but it can be derived into the following formula: 𝑅𝑂𝐴 × 𝐸𝑞𝑢𝑖𝑡𝑦 𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟. Assessment 3 – Calculating Financial Values For all of the problems, be sure to use the correct built-in Excel formulas to derive your answers. Do not use algebra. Assessment 4 – Calculating Payback and Profitability Problem 1: When you calculate NPV using the built-in NPV formula in Excel, be sure to place the year 0 cash outflow outside of the parentheses in the formula because the payment occurs at the beginning of the first period. Problem 2: The payback period formula is the amount of time it takes to recover the cost of the project or investment. The formula to use is 𝐶𝑜𝑠𝑡 𝑜𝑓 𝑃𝑟𝑜𝑗𝑒𝑐𝑡⁄𝐴𝑛𝑛𝑢𝑛𝑎𝑙 𝐶𝑎𝑠ℎ 𝐼𝑛𝑓𝑙𝑜𝑤𝑠. Problem 4: When you find the NPV as the first step of calculating the profitability index, be sure to exclude using the year 0 cash outflow (initial cost), using the built-in NPV formula in Excel. When calculating the profitability index, make sure the year 0 initial cost is a positive number. Problem 5: When calculating the operating cash flow, use this formula: 𝑂𝐶𝐹 = (𝑆𝑎𝑙𝑒𝑠 − 𝐶𝑜𝑠𝑡𝑠) × (1 − 𝑇𝑎𝑥 𝑅𝑎𝑡𝑒) + 𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 × 𝑇𝑎𝑥 𝑅𝑎𝑡𝑒 First, you will have to multiply a few of the inputs given in the assessment to come up with some of the formula inputs. For the first part of the formula, you need to multiply the number of servings produced per year by the price of each ice cream serving to derive the sales, which are not given in their entirety in the problem. You need to find this in order to derive the costs and depreciation. Assessment 6 – Calculating Risks and Returns Problem 8: Under CAPM, the cost of equity (or expected return on equity) formula is: 𝑅𝑖𝑠𝑘 𝐹𝑟𝑒𝑒 𝑅𝑎𝑡𝑒 + 𝐵𝑒𝑡𝑎 × (𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑅𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑡ℎ𝑒 𝑀𝑎𝑟𝑘𝑒𝑡 − 𝑅𝑖𝑠𝑘 𝐹𝑟𝑒𝑒 𝑅𝑎𝑡𝑒) 1 MBA-FP6016 Assessment 7 – Dividends and Stocks Problem 2: If the stock split increases the number of shares, then the stock price has to be lower than it originally was. If it is a reverse stock split, where number of shares decrease, then the stock price must be higher than it originally was. Problem 3: For this problem, rearrange what is known as the Lintner formula. You want to isolate Div1 (the dividend one year from now) so the formula should look like the following: Div1 = Div0 + s*(t *EPS1 – Div0) (Note: The * indicates multiplying.) 𝐷𝑖𝑣1 = 𝐷𝑖𝑣0 + 𝐴𝑑𝑗𝑢𝑠𝑡𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒(𝑃𝑎𝑦𝑜𝑢𝑡 𝑅𝑎𝑡𝑖𝑜 × 𝐸𝑃𝑆1 − 𝐷𝑖𝑣0) Assessment 8 – Megaware Case Study Problem 5: Use what you know about the situation and the theory to come up with an answer that seems appropriate according to the theory. Do not focus on having all exact numbers to accomplish everything. The final number is not what is important. What does each factor stand for and what happens if one chooses one of the possibilities for each factor individually? 𝑃0 = 𝐸1(1 − 𝑏) 𝑅𝑠 = 𝑅𝑂𝐸 × 𝑏 What each variable stands for is known in problem 5: • b = retention ratio. • E1 = earnings next year. • ROE = return on equity. • Dividend-payout ratio = 1 minus b. • P0 = dividend next year; the earnings next year times 1 minus the retention ratio. • Rs = sustainable growth rate; the return on equity times the retention ratio. Eight years in from the start of the company, the profit is $42 million from the sale of a fixed asset. • What happens to P0 and ROE if all other factors remain steady and b goes up or down? • What effect does the one-time influx of $42 million have on the formula? Assessment 9 – Financing and Exchange Rates Problem 1: When calculating the cash for this problem, use the following given data to derive the answer: • Net worth. • Long-term debt. • Net working capital (excluding cash). • Fixed assets. Problem 2: • For the first calculation, just find the dollar value of the current shares outstanding and add that to the value for the rights offering using the given data. • For the second calculation, you will use the number of shares outstanding and number of new shares outstanding in the future (rights offering) to derive the answer. 2 MBA-FP6016 • • For the third calculation, you will use the new market value of the company, the number of shares outstanding, and the number of new shares outstanding in the future (rights offering) to derive the answer. For the last calculation, you will use the current stock price and ex-rights price to derive the answer. 3 Excel Examples EXAMPLE 1: Discount Rate Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 ANSWER: NPV EXAMPLE 2: Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 ANSWER EXAMPLE 3: Finance Rate Reinvestment Rate ANSWER Beginning in column A, there are 16 examples of how to calculate basic accounting and math equations in Excel. Column C includes annotations for some of the examples. NET PRESENT VALUE 12% -65 10 20 40 65 -20 $18.30 Don't include the year 0 cash flow of -$65 (cell B6) because the payments occur at the BEGINNING of the first period. INTERNAL RATE OF RETURN (IRR) -65 10 20 40 65 -20 22.41% MODIFIED INTERNAL RATE OF RETURN (MIRR) 12% 15% 18.12% EXAMPLE 4: Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 ANSWER PRESENT VALUE EXAMPLE 5: Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 ANSWER FUTURE VALUE 12% 5 100 Note: Use the yearly data from Example 2. Discount $100 back 5 years at a 12% discount rate. (Discount Rate) (# Periods or years being discounted) (FV) $56.74 12% 5 100 $176.23 Compound $100 up 5 years at a 12% discount rate. (Discount Rate) (# Periods or years being compounded) (PV) EXAMPLE 6: Present Value = Future Value = Discount Rate ANSWER FINDING N (NPER) NUMBER OF PERIODS (OR YEARS) $50 $100 12% 6.12 How long would it take to compound $50 up to $100 using a 12% discount rate? Or 6.12 years. Note that you have to make either the Future Value or Present Value input negative for the formula to work. How long would it take to discount $100 down to $25 using a 12% discount rate? Present Value = Future Value = Discount Rate $100 $25 12% ANSWER -12.23 EXAMPLE 7: Present Value = Future Value = N (Nper) ANSWER Payment (PMT) = Future Value = N (Nper) ANSWER EXAMPLE 8: Present Value = Future Value = N (Nper) Interest Rate ANSWER EXAMPLE 9: SUM AVERAGE VARIANCE STANDARD DEVIATION CORRELATION COVARIANCE FINDING I (INTEREST RATE) $100 $200 5 14.87% $100 $750 5 20.40% Or 12.23 years. Note that years cannot be negative. You have to make either the Future Value or Present Value input negative for the formula to work. If you start with $100 and end with $200 after 5 years, what was the annual interest rate earned? Or 14.87%. You must keep either the Present Value or Future Value input negative. If you receive payments of $100 each year for 5 years and end up with $750 after 5 years, what was the annual interest rate earned? Or 20.40%. Note that the Payment input or Future Value input must be negative for the formula to work. FINDING THE PAYMENT AMOUNT (PMT) OR ANNUITY AMOUNT $0 $100,000 20 12% $1,387.88 SUM, AVERAGE, VARIANCE, STANDARD DEVIATION, CORRELATION, COVARIANCE 0.12 0.15 0.08 0.06 0.08 0.4900 0.0980 0.0013 0.0363 0.3928 0.0012 What would have to be the annual payment amount (or annuity amount) to have $100,000 after 20 years with a 12% discount rate? Note: You want the Future Value input to be negative so your answer comes out positive. 0.09 0.11 0.15 0.03 -0.12 EXAMPLE 10: CALCULATING A BOND'S PRICE Suppose we have a bond with 22 years to maturity, a coupon rate of 8 percent, and a yield to maturity of 9 percent. If the bond makes semiannual payments, what is its price today? Settlement Maturity Rate YTM 1/1/00 1/1/22 0.08 0.09 Redemption 100 Frequency Basis Bond Price 2 0 90.49 Multiply by 10 904.91 Think of Settlement as the beginning of the duration of the bond. Think of Maturity as the end of the duration of the bond. (Coupon Rate) (Yield to Maturity or Required Rate of Return) (Bond's Face Value, Par Value, or Fair Price) Note that it is $100, not $1,000. You make the adjustments by multiplying the answer by 10. Coupon payments are semiannual, so you put in a 2. If they are annual, then you input a 1. Always leave it blank. The answer, but you need to multiply it by 10 to get the actual bond price. Note: Excel gives the bond price in 2 digits like in cell B109. You need to multiply it by 10 to get the actual bond price.) (ANSWER = 904.91) EXAMPLE 11: CALCULATING A BOND'S YIELD TO MATURITY Suppose we have a bond with 22 years to maturity, a coupon rate of 8 percent and a price of $960.17. If the bond makes semiannual payments, what is its yield to maturity? Settlement Maturity Rate Pr 1/1/00 1/1/22 0.08 96.017 Redemption 100 Frequency Basis Yield to Maturity 2 0 8.40% Think of Settlement as the beginning of the duration of the bond. Think of Maturity as the end of the duration of the bond. (Coupon Rate) The bond's price per $100 face value. (Bond's Face Value, Par Value, or Fair Price) Note that it is $100, not $1,000. Coupon payments are semiannual, so you put in a 2. If they are annual, then you input a 1. Always leave it blank. (ANSWER = 8.40%) EXAMPLE 12: CALCULATING THE EFFECTIVE ANNUAL INTEREST RATE Suppose you have a Nominal Interest Rate of 5.25% that is compounded quarterly (4 times) during the year. What is the Effective Annual Interest Rate? Nominal Interest Rate Npery Effective Annual Interest Rate 5.25% 4 5.3543% (Number of compounding periods per year) Note: The EAR is always higher than the Nominal Rate as long as there is more than 1 compounding period per year. If you increase the compounding periods per year, the Effective Annual Rate will increase, but at a decreasing rate. (ANSWER = 5.35%) EXAMPLE 13: CALCULATING THE ANNUAL NOMINAL INTEREST RATE Suppose you have an Effective Annual Interest Rate of 5.35% that is compounded quarterly (4 times) during the year. What is the Nominal Annual Interest Rate? Effective Annual Interest Rate Npery Nominal Annual Interest Rate 5.35% 4 5.2459% (Number of compounding periods per year) (ANSWER = 5.25%) CALCULATING THE INTEREST RATE PER PERIOD OF A LOAN OR AN INVESTMENT EXAMPLE 14: If you make monthly payments of $200 on an $8,000 loan over 4 years, what is the Annual Interest Rate of the loan? 4 -200 8000 Years of the Loan Monthly Payment Amount of the Loan Monthly Interest Rate of the Loan 0.77% Annual Interest Rate of the Loan 9.24% Note: Multiply the years of the loan by 12 months for the monthly rate. (ANSWER = .77%) Note: Multiply the Monthly Interest Rate by 12 to get the annual rate. (ANSWER = 9.24%) EXAMPLE 15: CALCULATING THE GEOMETRIC AVERAGE RETURN (OR MEAN) A stock has produced returns of 14.6 percent, 5.3 percent, 17.6 percent, and -4.7 percent over the past four years, respectively. What is the geometric average return? Year 1 Year 2 Year 3 1.146 1.053 1.176 0.953 7.84% EXAMPLE 16: Adding cell B163 to cell B164: Subtracting cell B163 from cell B164: Multiplying cell B163 by cell B164: Dividing cell B164 by cell B163: Using Parentheses: Multiplying cell B163 by (cell B164 + cell B165): Calculating cell B163 to the power of cell B164: Calculating the Square Root of cell B171: Calculating the Natural Logarithm of cell B171: End of worksheet SIMPLE MATH CALCULATIONS 2 2 5 4 0 4 1 14 4 2 1.3863 Add 1 to all positive returns. Add 1 to all positive returns. Add 1 to all positive returns. For negative returns, subtract it from 1. You have to do this to keep all data positive. Note: Place a minus 1 after the formula to get rid of the whole number. (ANSWER = 7.84%)
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Year
0
1
2
3
NPV

Project A
−$12,700
$7,000
$5,500
$2,500

Project B
−$9,400
$4,800
$3,750
$3,400

Discounte Discounte
dA
dB
−$12,700
6194.6903
$4,307.31
$1,732.63
12234.622

−$9,400
$4,247.79
$2,936.80
$2,356.37...


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