Seminar 1 with solutions PDF

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Seminar 1 with solutions...

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CORPORATE FINANCE PRACTICE SESSION 1 1.

These are the 2009–2013 financial statements and share price data for Mydeco Corp.

a. What is Mydeco’s market capitalization at the end of each year? b. What is Mydeco’s market-to-book ratio at the end of each year? c. What is Mydeco’s enterprise value at the end of each year? d. By how much did Mydeco increase its debt from 2009 to 2013?

e.

What was Mydeco’s EBITDA/Interest coverage ratio in 2009 and 2013? Did its coverage ratio ever fall below 2? f. Overall, did Mydeco’s ability to meet its interest payments improve or decline over this period? g. What are Mydeco’s ROA and ROE for each year? h. What are Mydeco’s P/E ratios at the end of each year? i. Comment on the financial health of Mydeco by analyzing the information in the cash-flow statement.

a.

b.

c.

d.

Mydeco increased its debt from $500 million in 2009 to $600 million in 2013 (by $100 million).

e.

61.4 + 27.3 =2.6 33.7 2009 EBITDA/Interest coverage ratio . =

72.8 + 38.6 =2.8 39.4 2013 EBITDA/Interest coverage ratio . =

Mydeco’s coverage ratio fell below 2 in 2010, where it was 1.96. f.

Overall Mydeco’s ability to meet its interest payments improved over this period, although it experienced a slight dip in 2010.

g.

h.

i. Here the comments can be done by pointing at the data in the Statement of cash-flows. The key points to notice are: in principle, operations are generating a healthy (and relatively stable) inflow of cash, so the business of the company looks solid, though one would expect a bit more of growth of cash from operations, especially given the high investments in capital goods. Investment activities are quite high, so the business seems to be growing significantly in size: we would like to see, therefore, a higher increase in income. The financing of these investments can be covered by cash from operations, which is very good, except for the two years of abnormally high investment (2011 and 2012) when extra debt had to be issued to finance growth. If cash from operations does not grow in the future, it may not have been a good idea to take on so much extra debt to finance stable (but not growing) operations.

2. Your daughter is currently eight years old. You oi that she will be going to college in 10 years. You would like to have $100,000 in a savings account to fund her education at that time. If the account promises to pay a fixed interest rate of 3% per year, how much money do you need to put into the account today to ensure that you will have $100,000 in 10 years? 0

Timeline: 1

2

3

10

PV = ?

100,000 PV=

100, 000 10

= 74, 409.39

1.03 3.

Your grandfather put some money in an account for you on the day you were born. You are now 18 years old and are allowed to withdraw the money for the first time. The account currently has $3996 in it and pays an 8% interest rate. a.

How much money would be in the account if you left the money there until your 25th birthday?

b. What if you left the money until your 65th birthday? c.

How much money did your grandfather originally put in the account?

a.

Timeline:

18 0

19 1

20 2

21 3

25 7

3,996

FV = ? 7

FV = 3, 996(1.08) =6, 848.44 b. 18 0

Timeline: 19 20 1 2

21 3

65 47

3,996

FV = ? 47

=148, 779

3

4

FV =3, 996(1.08) 0

c. 1

Timeline: 2

PV=?

3,996 PV =

4.

18

3, 996 1.08 18

=1, 000

You have a loan outstanding. It requires making three annual payments at the end of the next three years of $1000 each. Your bank has offered to allow you to skip making the next two payments in lieu of making one large payment at the end of the loan’s term in three years. If the interest rate on the loan is 5%, what final payment will the bank require you to make so that it is indifferent between the two forms of payment?

Timeline: 0

1

2

3

1,000

1,000

1,000

First, calculate the present value of the cash flows: PV =

1, 000

+

1.05

1, 000 2

+

1.05

1, 000 1.053

= 952 + 907 + 864 = 2, 723

Once you know the present value of the cash flows, compute the future value (of this present value) at date 3. FV3 =2, 723 1.053 =3,152

5.

You work for a pharmaceutical company that has developed a new drug. The patent on the drug will last 17 years. You expect that the drug’s profits will be $2 million in its first year and that this amount will grow at a rate of 5% per year for the next 17 years. Once the patent expires, other pharmaceutical companies will be able to produce the same drug and competition will likely drive profits to zero. What is the present value of the new drug if the interest rate is 10% per year? 0

Timeline: 1

2

2

3

17

2(1.05)

2(1.05)2

2(1.05)16

This is a 17-year growing annuity. By the growing annuity formula we have 2, 000, 000 

17 1.05    PV =   = 21, 861, 455.80  1  0.1  0.05   1.1  

6.

Suppose you currently have $5000 in your savings account, and your bank pays interest at a rate of 0.5% per month. If you make no further deposits or withdrawals, how much will you have in the account in 5 years? We calculate the future value as FV = C × (1+r)n. The initial amount C = $5000 and the interest rate r = 0.5% per month. Because we have a monthly interest rate, we also need to express the number of periods, n, in months, so n = 5 × 12 = 60. Thus, FV = $5000 × 1.00560 = $6744.25 We will have $6744.25 in the account in 5 years time.

7.

You are thinking of purchasing a house. The house costs $350,000. You have $50,000 in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price. The bank is offering a 30-year mortgage that requires annual payments and has an interest rate of 7% per year. What will your annual payment be if you sign up for this mortgage? 0

Timeline: (From the perspective of the bank) 1 2 3

–300,000

C

C

C

30

C

C=

8.

300, 000 = $24,176 1  1  1   30  0.07  1.07 

You would like to buy the house and take the mortgage described in Problem 36. You can afford to pay only $23,500 per year. The bank agrees to allow you to pay this amount each year, yet still borrow $300,000. At the end of the mortgage (in 30 years), you must make a balloon payment; that is, you must repay the remaining balance on the mortgage. How much will this balloon payment be? 0

Timeline: (where X is the balloon payment.) 1 2 3

–300,000

23,500

23,500

23,500

30

23,500 + X

The present value of the loan payments must be equal to the amount borrowed: 300, 000 =

23, 500 

1  X . + 1 30  30 0.07  1.07   1.07 

Solving for X:

 

X = 300, 000  9.

23, 500  1  1 30 0.07  1.07

30    1.07  = $63, 848 

You have an investment opportunity that requires an initial investment of $5000 today and will pay $6000 in one year. What is the IRR of this opportunity? Timeline: 0

1

–5,000

6,000

IRR is the r that solves: 6, 000 I+ r 10.

=5, 000 =

6, 000

 1 = 20%.

5, 000

Suppose a security with a risk-free cash flow of $150 in one year trades for $140 today. If there are no arbitrage opportunities, what is the current risk-free interest rate? The PV of the security’s cash flow is ($150 in one year)/(1 + r), where r is the one-year risk-free interest rate. If there are no arbitrage opportunities, this PV equals the security’s price of $140 today. Therefore, $140 today =

 $150 in one year   1+ r 

Rearranging:

 $150 in one year  $140 today 11.

= 1 + r =$1.0714 in one year / $ today, so r =7.14%

Consider two securities that pay risk-free cash flows over the next two years and that have the current market prices shown here:

a.

What is the no-arbitrage price of a security that pays cash flows of $100 in one year and $100 in two years?

b. What is the no-arbitrage price of a security that pays cash flows of $100 in one year and $500 in two years? c.

Suppose a security with cash flows of $50 in one year and $100 in two years is trading for a price of $130. What arbitrage opportunity is available?

a.

This security has the same cash flows as a portfolio of one share of B1 and one share of B2. Therefore, its no-arbitrage price is 94 + 85 = $179.

b.

This security has the same cash flows as a portfolio of one share of B1 and five shares of B2. Therefore, its no-arbitrage price is 94 + 5 × 85 = $519

c.

There is an arbitrage opportunity because the no-arbitrage price should be $132 (94 / 2 + 85). One should buy two shares of the security at $130/share and sell one share of B1 and two shares of B2. Total profit would be $4 (94 + 85 × 2 – 130 × 2)....