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ECN 134 Winter 2024

Homework #1

Due by Friday January 26 by 11:59 PM in Canvas

Assignment must be uploaded to Canvas as a pdf file or MS Word.

It is ok to scan a hand-written document, but scan to pdf only (no jpeg or camera photo, etc.)

Also, scan must be a single file (no multiple documents or files).

1)         Suppose a partnership and a C corporation both generate $250,000 each for their owners before taxes. Assume each business distributes all income to owners.

a)         If the corporate tax rate is 20% and the individual tax rate is 30%, what is the amount of after tax income the partnership owner receives and the corporation owner receives?

b)        Using the information from part a), what is the average or effective tax rate on the

income generated by the partnership and the corporation respectively on the entire stream of income?

c)         Individuals usually pay income tax based on a progressive schedule where the first X

dollars get taxed at a particular % then the dollars between X and Y get taxed and a different rate, etc. Suppose the corporate tax rate is still 20% but the individual tax rate is now the following progressive schedule.

Progressive Tax Schedule

What is the amount of after tax income the partnership owner and the corporation owner receives now?

d)        The marginal tax rate is the tax rate that would be applied on the next dollar of income earned. Using the information from part c), what is the marginal tax rate for one more  dollar of income the partnership owner receives? How does this compare to the partnership’s effective tax rate? Briefly explain.

2)        For each of the following state whether it is an operating cash flow, investment cash flow, or financial cash flow for the business.

a)        A bakery purchases kneading machine for its bread dough

b)        A bakery owner sells 20% of the bakery to a family friend in exchange for cash.

c)        A bakery increases its purchase of yeast for this month to make more loaves of bread.

d)        A bakery sells 50 loaves of bread to a local sandwich shop.

e)         A bakery receives a loan from a bank. It plans to remodel its storefront but hasn’t done so yet.

3)        A client has given you the following financial information for their company Small Tech Corporation) for Year 1 and Year 2. Assume the tax rate is 20%

a)         Calculate Net Working Capital for Year 1 and Year 2 for Small Tech Corporation.

b)        Calculate the Operating Cash Flow for Year 2 for Small Tech Corporation.

c)         Calculate the Free Cash Flow for Year 2 for Small Tech Corporation.

d)        Calculate the Free Cash Flow to Creditors and the Free Cash Flow to Shareholders for for Year 2 Small Tech Corporation.

e)         Above we have $0 of interest expense for Small Tech Corporation. All else the same, if interest expense was greater than $0, how would that affect, if at all, Small Tech Corporation’s Free Cash Flow to Shareholders we calculated? Briefly explain.

4)

a)         Calculate the future value in 6 years of $1000 today with annual compounding and a 6% semi-annual interest rate.

b)         Suppose someone saves $10000 today and will have $11000 one year from today. If compounding is quarterly, what must be the interest rate on this account?

c)         Suppose there is a current cash flow of $8 that is expected to grow by 16% each year. If the annual interest rate is 20%, what is the present value of this stream of future cash flows?

d)        Using the information from part c), what would be the future value of that same stream of cash 2 and a half years from now if compounding is annual and 20% annual interest?

e)         Suppose the present value of a growing perpetuity is $1050. If the annual interest rate is 10%, and the current cash flow is $50, what must be the growth rate of this perpetuity?

5)

a)         Jocelyn is going to begin saving for a new car in 5 years. She plans to set aside $400  every month starting at the end of the first month. If compounding is monthly and the annual interest rate is 9%, what will be the maximum price she can pay for the car?

b)         Suppose Jocelyn could start saving $400 right now at the beginning of the month. All else the same aspart a), what will be the maximum price she can pay for the car?

6)        Janelle is considering buying a 4-unit apartment building for $1,500,000. Assume the relevant interest rate is 4%.

a)         The 4-units are currently being rented for $2200, $2400, $2600, and $2800 per month

respectively. Rent is paid at the start of the month, which is today. Assuming no changes in rental amounts what would be present value the rents Janelle would earn over the next 15-years.

b)        To buy the apartment building Janelle is going to borrow $1,200,000 over 15-years.

Assuming the first mortgage payment is the next month and every month thereafter, what will be Janelle’s monthly mortgage payment?

7)        Jump Tech is considering two possible projects. They expect Project Hop to generate  $100,000 every quarter for the next 5-years with a discount rate of 5%. Project Skip is expected to generate $120,000 for the next 5-year with a discount rate of 12%. Each project can be started today but the first cash flow won’t be realized until next quarter.

a)         Which project should they do? Show calculations to support your answer.

b)        Suppose Jump Tech is worried that both projects may prematurely end 6 months earlier than expected. Would that change your answer to a)? Show calculations to support your answer.

You do not need to complete this question for the homework. However, this question is relevant for the exam and an answer will be provided on the answer key. It covers Bond valuation, our last topic before the exam.

8)        Jessica is considering two different standard corporate bonds. Each has a coupon rate of 5% and annual yield to maturity of 8% and face value of $1000 with semi-annual compounding. The only difference is one is a 5-year bond and one is a 10-year bond.

a)         Without calculation will these bonds be selling at a discount or premium and how do you know?

b)        What is the fair value or price of these bonds? Provide a calculation.

c)        After 1-year if nothing else changes but time passing, will the price of each bond rise, fall, stay the same, or do we not know? No calculation needed just briefly explain.