Time Value of Money Exercises

TimeValueofMoneyExercises-Fall2020Asynchronous.docx

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Finance for Marketing Decisions

1. Which of the following investments would have the highest future value at the end of 10 years? Which has the highest present value today? Rank the choices below from highest to lowest present value. Assume that the effective annual interest rate for all investments is the same and is greater than zero.

a. Investment A pays $250,000 at the beginning of every year for the next 10 years (a total of 10 payments).

b. Investment B pays $125,000 at the end of every 6-month period for the next 10 years (a total of 20 payments).

c. Investment C pays $125,000 at the beginning of every 6-month period for the next 10 years (a total of 20 payments).

d. Investment D pays $2.5 million at the end of 10 years (just one payment).

e. Investment E pays $250,000 at the end of every year for the next 10 years (a total of 10 payments).

2. Given the uneven streams of cash flows shown in the following table, answer parts A and B:

Cash Flow Stream

End of Year A B

1 $50,000 $10,000

2 40,000 20,000

3 30,000 30,000

4 20,000 40,000

5 10,000 50,000

Total $150,000 $150,000

A. Find the present value of each series of cash flows, using a 12% discount rate.

B. Discuss how, and why, the two different present values are different given that the sum total of each series of cash flow is the same.

3. Calculate the present value of the following uneven stream of cash flows. Assume an 8 percent discount rate.

End of Year Cash Flow

1 $10,000

2 10,000

3 10,000

4 12,000

5 12,000

6 12,000

7 12,000

8 15,000

9 15,000

10 15,000

4. Assume that you just won the state lottery. Your prize can be taken either in the form of $40,000 at the end of each of the next 25 years or as a single payment of $500,000 paid immediately.

A. If you expect to be able to earn 5 percent annually on your investments over the next 25 years (i.e. 5 percent is the appropriate discount rate), ignoring taxes and other considerations, which alternative should you take? Assume that your only decision criteria is selecting the option with the highest present value.

B. Would your decision in part (a) be altered if you could earn 7 percent rather than 5 percent on your investments over the next 25 years?

5. You’re in your final semester at NYU. You’ve just received two job offers.

Offer 1

YouTube Marketing Analyst

San Bruno, CA

Signing bonus: $10,000 (received upfront)

Starting Salary: $100,000

Expected Salary Growth per Year: 10%

Offer 2

Social Media Manager, Glossier

New York, NY

Signing bonus: $20,000 (received upfront)

Starting Salary: $85,000

Expected Salary Growth per Year: 20%

Interest Rates on Spanish government bonds

2 yr - 2%

3 yr - 3%

5 yr - 4%

10 yr - 6%

30 yr - 9%

Interest Rates on U.S. government bonds

2 yr - 3%

3 yr - 4%

5 yr - 5%

10 yr - 7%

30 yr - 10%

Assume all cash flows occur at the end of the year.

A. Assuming your interest in the two jobs, and the costs associated with each of them (moving costs, living costs, taxes etc.), are identical, which job should you choose? Assume that your decision will be to choose the job with the higher NPV of compensation. You plan on being in whichever job you pick for 5 years.

B. What is the present value of your compensation for each of these jobs through year 3?

C. Would your decision change if you plan on quitting and going back to graduate school in 2 years?

D. What possible information would make you reverse your decision in part A?

6. Assume TikTok has recently filed to go public in the United States. They’ve filed their S-1, a document that includes all of their historical financial information, with the Securities & Exchange Commission for prospective investors to analyze. Assume all cash flows occur at the end of the year.

Assume that the S-1 shows TikTok’s cash flows to be the following:

2017 - ($430,000,000)

2018 - ($890,000,000)

2019 - ($1,600,000,000)

2020 - ($1,800,000,000)

You’ve projected that TikTok’s cash flows through the year 2024 to be the following:

2021 - ($1,400,000,000)

2022 - ($1,000,000,000)

2023 - ($500,000,000)

2024 - $0

2025 - $750,000,000

You’ve also projected that the value in 2025 of TikTok’s future cash flows beyond that date to be $10 billion. You’ve also estimated TikTok’s cost of capital (aka discount rate) to be 12%. Assume all cash flows occur at the end of the year.

Assuming TikTok goes public at the end of 2020, what should the value of the company be?

7. You are a social media marketing analyst for Zara. Your manager asks you two analyze two different influencer-marketing programs for a new campaign that will run throughout Europe.

Option 1

Hire a large group of micro-influencers (<10k followers) to promote your new line on instagram. You will pay your micro-influencers an average of €1000 each in a given year. You expect each micro influencers to generate €2,000 in cash flow from sales. The number of micro-influencers in your program will be as follows:

· Year 1 - 120 micro influencers

· Year 2 - Increase to 175 micro influencers total

· Year 3 - Increase to 275 micro influencers total

Option 2

Hire a select group of mega influencers (>100k followers) to promote the new line on instagram. You will pay each mega-influencers an average of €7,500 each in a given year. You expect each mega-influencer to generate €20,000 in cash flow from sales. The number of mega-influencers in your program is as follows:

· Year 1 - 10 mega-influencers

· Year 2 - Increase to 15 mega influencers total

· Year 3 - Increase to 25 mega influencers total

For both options, assume all cash flows occur at the end of the year