# Time Value of Money Calculations

STEP 1 – Time Value of Money Calculations

As the manager of the pension fund, considering different investment options will help you make better decisions for your company and your clients. Please respond to the following questions, providing supporting data and showing your calculations.

Question 1: If the pension plan invests $95 million today in 10-year US Treasury bonds (riskless investment with guaranteed return) at an interest rate of 3.5 percent a year, how much will it have by the end of year 10?

Question 2: If the pension plan needs to accumulate $14 million in 13 years, how much must it invest today in an asset that pays an annual interest rate of 4 percent?

Question 3: How many years will it take for $197 million to grow to be $554 million if it is invested in an account with a quoted annual interest rate of 5 percent with monthly compounding of interest?

Question 4: The pension plan also invests in physical assets. It is considering the purchase of an office building today with the expectation that the price will rise to $20 million at the end of 10 years. Given the risk of this investment, there should be a yield of 10 percent annually on this investment. The asking price for the lot is $12 million. What is the annual yield (internal rate of return) of the investment if the purchase price is $12 million today and the sale price 10 years later is $20 million? Should the pension plan buy the office building given its required rate of return?

Question 5a: The pension plan is also considering investing $70 million of its cash today at a 3.5 percent annual interest for five years with a commercial bank. How much will the $70 million grow to at the end of 5 years?

Question 5b: Now take the amount of your answer in Ques 5a, and assume this money is invested in an annuity due with the first payment made at the beginning of the 6th year. The annuity due makes a total of 15 yearly (equal) payments. How much will the annual payments be from years 6 to 20, if the rate at which these payments are discounted is also 3.5 percent?

Question 6: The pension plan is about to take out a 10-year fixed-rate loan for the purchase of an information management system for its operations. The terms of the loan specify an initial principal balance (the amount borrowed) of $4 million and an APR of 3.75 percent. Payments will be made monthly. What will be the monthly payment? How much of the first payment will be interest, and how much will be principal? Use the Excel PMT function to provide the answers to these questions.

Be sure to show all your calculations in Excel and provide a narrative analysis in Excel. Your narrative analysis should summarize the results of your analysis and make recommendations for the benefit of the company.

Before you submit your assignment, review the competencies below, which your instructor will use to evaluate your work. A good practice would be to use each competency as a self-check to confirm you have incorporated all of them in your work.

3.1 Identify numerical or mathematical information that is relevant in a problem or situation.

3.2 Employ mathematical or statistical operations and data analysis techniques to arrive at a correct or optimal solution.

Before you submit your assignment, review the competencies below, which your instructor will use to evaluate your work. A good practice would be to use each competency as a self-check to confirm you have incorporated all of them in your work.

3.1 Identify numerical or mathematical information that is relevant in a problem or situation.

3.2 Employ mathematical or statistical operations and data analysis techniques to arrive at a correct or optimal solution.

3.3 Analyze mathematical or statistical information, or the results of quantitative inquiry and manipulation of data.

3.4 Employ software applications and analytic tools to analyze, visualize, and present data to inform decision-making.

10.3 Determine optimal financial decisions in pursuit of an organization's goals.

10.4 Make strategic managerial decisions for obtaining capital required for achieving organizational goals.

Additional Guidance on Project 4

Ques 7. Payback period --- how long will it take to recoup the initial investment. If $X invested today, given expected cash inflow over time --- the question becomes, how long will it take to recoup the initial investment $X. Be sure calculate the precise period of time, which often times is a mixed number like 2 1/2 years.

Ques 8. Run the NPV in Excel for each option and determine which option is better. Use = NPV(.........) and Excel will display the requirements. Note that Year 0 is already in present value format so do not include Year 0 in your PV cash flow range. However, you will need to deduct the initial investment from the PV of future cash flows, like = NPV(CF1....CFN) - Initial Investment.

Ques 9. For IRR calculation, use =IRR(CF0...CFN), include the entire cash flow stream.

3.3 Analyze mathematical or statistical information, or the results of quantitative inquiry and manipulation of data.

3.4 Employ software applications and analytic tools to analyze, visualize, and present data to inform decision-making.

10.3 Determine optimal financial decisions in pursuit of an organization's goals.

10.4 Make strategic managerial decisions for obtaining capital required for achieving organizational goals.

Additional Guidance on Project 4

For Ques 1 to 6, note that these are time value problems. Use the framework I shared with you to help you derive the answers.

Here's the framework:

NPER = years * compounding period

INT(RATE) = interest rate / compounding period

PMT = payment (use as annuity payments - regular periodic payments (daily, monthly, etc)

PV = present value

FV = future value

Typically, the question will provide you with 4 out of the 5 factors, and you solve for the missing item. Use the Excel functions to help you solve these problems. For example, for a present value problem, in Excel, enter =PV(rate, nper, pmt, (fv), type), Excel will then display the requirements needed to derive present value. Also, remember that if the problem asks for a value today --- this implies present value, whereas a value in the future, implies future value. How much should one pay each month for the next 5 years to pay off a car loan ... equal monthly payment over time implies annuity payments or PMT, etc.

STEP 3 – Capital Budgeting-Decide Which Projects to Complete

Another one of your responsibilities as CFO is to determine the suitability of new and current products. Your CEO has asked you to evaluate Android01. That task will require you to combine data from your production analysis from Project 2 with data from a consultant's study that was done last year. Information provided by the consultant is as follows:

initial investment: $120 million composed of $50 million for the plant and $70 million net working capital (NWC)

yearly expenses from year 1 to year 3: $30 million

yearly revenues from year 1 to year 3: $0

yearly expenses from year 4 to year 10: $55 million

yearly expected revenues from year 4 to year 10: $95 million

yearly expenses from year 11 to year 15: $60 million

yearly expected revenues from year 11 to year 15: $105 million

You are to calculate NPV using the “expected values”. The actual cash flow may be variable (risky) and that is the reason why the discount rate is greater than the riskless rate.

This concludes the information provided by the consultant.

You also have the following information:

Assume that both expenses and revenues for a year occur at the end of the year. NWC pays the bills during the year, but has to be replenished at the end of the year.

Android01 is expected to cannibalize the sales of Processor01 while also reducing the variable costs for the production of Processor01. From years 4 to 10, revenues are expected to fall by $5M, whereas variable costs will go down by $1 million. Processor01 is to be phased out at the end of the 10th year.

At the end of the 15th year, the plant will be scrapped for a salvage value of $10 million. NWC will be recovered.

Question 10: Calculate the expected cash flows from the Android01 project based on the information provided.

Question 11: Calculate the NPV for a required rate of return of 6.5 percent. Also calculate the IRR and the Payback Period.

Be sure to show your calculations in Excel and provide a narrative analysis in Excel. Your narrative analysis should summarize the results of your analysis and make recommendations for the benefit of the company.

Before you submit your assignment, review the competencies below, which your instructor will use to evaluate your work. A good practice would be to use each competency as a self-check to confirm you have incorporated all of them in your work.

3.1 Identify numerical or mathematical information that is relevant in a problem or situation.

3.2 Employ mathematical or statistical operations and data analysis techniques to arrive at a correct or optimal solution.

3.3 Analyze mathematical or statistical information, or the results of quantitative inquiry and manipulation of data.

3.4 Employ software applications and analytic tools to analyze, visualize, and present data to inform decision-making.

10.3 Determine optimal financial decisions in pursuit of an organization's goals.

10.4 Make strategic managerial decisions for obtaining capital required for achieving organizational goals.

Additional Guidance on Project 4

For Q10, set up your problem in an income statement format, much like the following and establish a 15-year time line.

Year 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Revenue

Expense

Item 1

Item 2

Item 3

Total Expense

Cash Flows (Rev - Exp)

Carefully, read the instruction and input the data in the respective cell for Revenue items and Expense items

Ques 11. Calculate NPV for Cash Flows over the 15-year period; calculate IRR and payback

STEP 4 – Cost of Capital

The firm decides to raise $30 million by selling equity and debt. The investment bankers hired by your firm contact potential investors and come back with the following numbers:

Debt that pays $1 million coupons a year and $18 million maturity value after 10 years will sell for $20 million.

Equity that pays expected dividends of $1.2 million starting next year and growing at a rate of 3 percent per year thereafter sells for $10 million.

Question 12: Calculate the cost of debt, equity, and the WACC.

Be sure to show all your calculations in Excel and provide a narrative analysis in Excel. Your narrative analysis should summarize the results of your analysis and make recommendations for the benefit of company.

Before you submit your assignment, review the competencies below, which your instructor will use to evaluate your work. A good practice would be to use each competency as a self-check to confirm you have incorporated all of them in your work.

3.1 Identify numerical or mathematical information that is relevant in a problem or situation.

3.2 Employ mathematical or statistical operations and data analysis techniques to arrive at a correct or optimal solution.

3.3 Analyze mathematical or statistical information, or the results of quantitative inquiry and manipulation of data.

3.4 Employ software applications and analytic tools to analyze, visualize, and present data to inform decision-making.

10.3 Determine optimal financial decisions in pursuit of an organization's goals.

10.4 Make strategic managerial decisions for obtaining capital required for achieving organizational goals.

Additional Guidance on Project 4

Q12. Calculate the cost of debt, which is similar to the interest rate. Therefore, calculate the interest rate.

Use the perpetuity to derive the cost of equity. Make r = rate, the subject of the equation.

WACC then is computed as ---- proportion of capital structure * cost of debt + proportion of capital structure * cost of equity

STEP 5 – Financing Options

Your firm has decided to spin off Android01 and Processor01 as a separate firm. The owners of the new firm will be equity holders and debt holders. After speaking with potential investors, investment banks have identified two possible capital structures (structure of equity and debt ownership):

Prepare a Capital Budgeting and Cost of Capital report that answers the following Question 13.

Question 13: Which particular capital structure should be chosen for the spin-off?

Before you submit your assignment, review the competencies below, which your instructor will use to evaluate your work. A good practice would be to use each competency as a self-check to confirm you have incorporated all of them in your work.

3.1 Identify numerical or mathematical information that is relevant in a problem or situation.

3.2 Employ mathematical or statistical operations and data analysis techniques to arrive at a correct or optimal solution.

3.3 Analyze mathematical or statistical information, or the results of quantitative inquiry and manipulation of data.

3.4 Employ software applications and analytic tools to analyze, visualize, and present data to inform decision-making.

10.3 Determine optimal financial decisions in pursuit of an organization's goals.

10.4 Make strategic managerial decisions for obtaining capital required for achieving organizational goals.

Additional Guidance on Project 4

Ques 13. Note that this question asks for the price of debt (not the cost of debt) -- similar calculation, except this approach suggest that debt instruments are being sold to raise capital. Select the price of financing that produces the larger sum of money.

As the manager of the pension fund, considering different investment options will help you make better decisions for your company and your clients. Please respond to the following questions, providing supporting data and showing your calculations.

Question 1: If the pension plan invests $95 million today in 10-year US Treasury bonds (riskless investment with guaranteed return) at an interest rate of 3.5 percent a year, how much will it have by the end of year 10?

Question 2: If the pension plan needs to accumulate $14 million in 13 years, how much must it invest today in an asset that pays an annual interest rate of 4 percent?

Question 3: How many years will it take for $197 million to grow to be $554 million if it is invested in an account with a quoted annual interest rate of 5 percent with monthly compounding of interest?

Question 4: The pension plan also invests in physical assets. It is considering the purchase of an office building today with the expectation that the price will rise to $20 million at the end of 10 years. Given the risk of this investment, there should be a yield of 10 percent annually on this investment. The asking price for the lot is $12 million. What is the annual yield (internal rate of return) of the investment if the purchase price is $12 million today and the sale price 10 years later is $20 million? Should the pension plan buy the office building given its required rate of return?

Question 5a: The pension plan is also considering investing $70 million of its cash today at a 3.5 percent annual interest for five years with a commercial bank. How much will the $70 million grow to at the end of 5 years?

Question 5b: Now take the amount of your answer in Ques 5a, and assume this money is invested in an annuity due with the first payment made at the beginning of the 6th year. The annuity due makes a total of 15 yearly (equal) payments. How much will the annual payments be from years 6 to 20, if the rate at which these payments are discounted is also 3.5 percent?

Question 6: The pension plan is about to take out a 10-year fixed-rate loan for the purchase of an information management system for its operations. The terms of the loan specify an initial principal balance (the amount borrowed) of $4 million and an APR of 3.75 percent. Payments will be made monthly. What will be the monthly payment? How much of the first payment will be interest, and how much will be principal? Use the Excel PMT function to provide the answers to these questions.

Be sure to show all your calculations in Excel and provide a narrative analysis in Excel. Your narrative analysis should summarize the results of your analysis and make recommendations for the benefit of the company.

Before you submit your assignment, review the competencies below, which your instructor will use to evaluate your work. A good practice would be to use each competency as a self-check to confirm you have incorporated all of them in your work.

3.1 Identify numerical or mathematical information that is relevant in a problem or situation.

3.2 Employ mathematical or statistical operations and data analysis techniques to arrive at a correct or optimal solution.

Before you submit your assignment, review the competencies below, which your instructor will use to evaluate your work. A good practice would be to use each competency as a self-check to confirm you have incorporated all of them in your work.

3.1 Identify numerical or mathematical information that is relevant in a problem or situation.

3.2 Employ mathematical or statistical operations and data analysis techniques to arrive at a correct or optimal solution.

3.3 Analyze mathematical or statistical information, or the results of quantitative inquiry and manipulation of data.

3.4 Employ software applications and analytic tools to analyze, visualize, and present data to inform decision-making.

10.3 Determine optimal financial decisions in pursuit of an organization's goals.

10.4 Make strategic managerial decisions for obtaining capital required for achieving organizational goals.

Additional Guidance on Project 4

Ques 7. Payback period --- how long will it take to recoup the initial investment. If $X invested today, given expected cash inflow over time --- the question becomes, how long will it take to recoup the initial investment $X. Be sure calculate the precise period of time, which often times is a mixed number like 2 1/2 years.

Ques 8. Run the NPV in Excel for each option and determine which option is better. Use = NPV(.........) and Excel will display the requirements. Note that Year 0 is already in present value format so do not include Year 0 in your PV cash flow range. However, you will need to deduct the initial investment from the PV of future cash flows, like = NPV(CF1....CFN) - Initial Investment.

Ques 9. For IRR calculation, use =IRR(CF0...CFN), include the entire cash flow stream.

3.3 Analyze mathematical or statistical information, or the results of quantitative inquiry and manipulation of data.

3.4 Employ software applications and analytic tools to analyze, visualize, and present data to inform decision-making.

10.3 Determine optimal financial decisions in pursuit of an organization's goals.

10.4 Make strategic managerial decisions for obtaining capital required for achieving organizational goals.

Additional Guidance on Project 4

For Ques 1 to 6, note that these are time value problems. Use the framework I shared with you to help you derive the answers.

Here's the framework:

NPER = years * compounding period

INT(RATE) = interest rate / compounding period

PMT = payment (use as annuity payments - regular periodic payments (daily, monthly, etc)

PV = present value

FV = future value

Typically, the question will provide you with 4 out of the 5 factors, and you solve for the missing item. Use the Excel functions to help you solve these problems. For example, for a present value problem, in Excel, enter =PV(rate, nper, pmt, (fv), type), Excel will then display the requirements needed to derive present value. Also, remember that if the problem asks for a value today --- this implies present value, whereas a value in the future, implies future value. How much should one pay each month for the next 5 years to pay off a car loan ... equal monthly payment over time implies annuity payments or PMT, etc.

STEP 3 – Capital Budgeting-Decide Which Projects to Complete

Another one of your responsibilities as CFO is to determine the suitability of new and current products. Your CEO has asked you to evaluate Android01. That task will require you to combine data from your production analysis from Project 2 with data from a consultant's study that was done last year. Information provided by the consultant is as follows:

initial investment: $120 million composed of $50 million for the plant and $70 million net working capital (NWC)

yearly expenses from year 1 to year 3: $30 million

yearly revenues from year 1 to year 3: $0

yearly expenses from year 4 to year 10: $55 million

yearly expected revenues from year 4 to year 10: $95 million

yearly expenses from year 11 to year 15: $60 million

yearly expected revenues from year 11 to year 15: $105 million

You are to calculate NPV using the “expected values”. The actual cash flow may be variable (risky) and that is the reason why the discount rate is greater than the riskless rate.

This concludes the information provided by the consultant.

You also have the following information:

Assume that both expenses and revenues for a year occur at the end of the year. NWC pays the bills during the year, but has to be replenished at the end of the year.

Android01 is expected to cannibalize the sales of Processor01 while also reducing the variable costs for the production of Processor01. From years 4 to 10, revenues are expected to fall by $5M, whereas variable costs will go down by $1 million. Processor01 is to be phased out at the end of the 10th year.

At the end of the 15th year, the plant will be scrapped for a salvage value of $10 million. NWC will be recovered.

Question 10: Calculate the expected cash flows from the Android01 project based on the information provided.

Question 11: Calculate the NPV for a required rate of return of 6.5 percent. Also calculate the IRR and the Payback Period.

Be sure to show your calculations in Excel and provide a narrative analysis in Excel. Your narrative analysis should summarize the results of your analysis and make recommendations for the benefit of the company.

Before you submit your assignment, review the competencies below, which your instructor will use to evaluate your work. A good practice would be to use each competency as a self-check to confirm you have incorporated all of them in your work.

3.1 Identify numerical or mathematical information that is relevant in a problem or situation.

3.2 Employ mathematical or statistical operations and data analysis techniques to arrive at a correct or optimal solution.

3.3 Analyze mathematical or statistical information, or the results of quantitative inquiry and manipulation of data.

3.4 Employ software applications and analytic tools to analyze, visualize, and present data to inform decision-making.

10.3 Determine optimal financial decisions in pursuit of an organization's goals.

10.4 Make strategic managerial decisions for obtaining capital required for achieving organizational goals.

Additional Guidance on Project 4

For Q10, set up your problem in an income statement format, much like the following and establish a 15-year time line.

Year 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Revenue

Expense

Item 1

Item 2

Item 3

Total Expense

Cash Flows (Rev - Exp)

Carefully, read the instruction and input the data in the respective cell for Revenue items and Expense items

Ques 11. Calculate NPV for Cash Flows over the 15-year period; calculate IRR and payback

STEP 4 – Cost of Capital

The firm decides to raise $30 million by selling equity and debt. The investment bankers hired by your firm contact potential investors and come back with the following numbers:

Debt that pays $1 million coupons a year and $18 million maturity value after 10 years will sell for $20 million.

Equity that pays expected dividends of $1.2 million starting next year and growing at a rate of 3 percent per year thereafter sells for $10 million.

Question 12: Calculate the cost of debt, equity, and the WACC.

Be sure to show all your calculations in Excel and provide a narrative analysis in Excel. Your narrative analysis should summarize the results of your analysis and make recommendations for the benefit of company.

Before you submit your assignment, review the competencies below, which your instructor will use to evaluate your work. A good practice would be to use each competency as a self-check to confirm you have incorporated all of them in your work.

3.1 Identify numerical or mathematical information that is relevant in a problem or situation.

3.2 Employ mathematical or statistical operations and data analysis techniques to arrive at a correct or optimal solution.

3.3 Analyze mathematical or statistical information, or the results of quantitative inquiry and manipulation of data.

3.4 Employ software applications and analytic tools to analyze, visualize, and present data to inform decision-making.

10.3 Determine optimal financial decisions in pursuit of an organization's goals.

10.4 Make strategic managerial decisions for obtaining capital required for achieving organizational goals.

Additional Guidance on Project 4

Q12. Calculate the cost of debt, which is similar to the interest rate. Therefore, calculate the interest rate.

Use the perpetuity to derive the cost of equity. Make r = rate, the subject of the equation.

WACC then is computed as ---- proportion of capital structure * cost of debt + proportion of capital structure * cost of equity

STEP 5 – Financing Options

Your firm has decided to spin off Android01 and Processor01 as a separate firm. The owners of the new firm will be equity holders and debt holders. After speaking with potential investors, investment banks have identified two possible capital structures (structure of equity and debt ownership):

Prepare a Capital Budgeting and Cost of Capital report that answers the following Question 13.

Question 13: Which particular capital structure should be chosen for the spin-off?

Before you submit your assignment, review the competencies below, which your instructor will use to evaluate your work. A good practice would be to use each competency as a self-check to confirm you have incorporated all of them in your work.

3.1 Identify numerical or mathematical information that is relevant in a problem or situation.

3.2 Employ mathematical or statistical operations and data analysis techniques to arrive at a correct or optimal solution.

3.3 Analyze mathematical or statistical information, or the results of quantitative inquiry and manipulation of data.

3.4 Employ software applications and analytic tools to analyze, visualize, and present data to inform decision-making.

10.3 Determine optimal financial decisions in pursuit of an organization's goals.

10.4 Make strategic managerial decisions for obtaining capital required for achieving organizational goals.

Additional Guidance on Project 4

Ques 13. Note that this question asks for the price of debt (not the cost of debt) -- similar calculation, except this approach suggest that debt instruments are being sold to raise capital. Select the price of financing that produces the larger sum of money.

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