A property costs $100,000. A borrower can obtain an 80% loan with an 8% interest rate and monthly payments. The loan is to be fully amortized over 25 years. Alternatively he could obtain a 90% loan at an 8.5% interest rate with the same loan term. (annualize percentages)

A. The borrower plans to own the property for the entire loan term. What is the incremental cost of borrowing the additional funds?

B. How would your answer change if two points were charged on the 90% loan?

C. How would your answer to (b) change if the borrower planned to own the property for only five years?

You have purchased 30 shares of Games Inc. for $ 15 and 120 shares of Thrones Co for 721. Over the following three quarters, the companies earned the returns below Quarter 1 Quarter 2 Quarter 3 Games Inc. 20% 46% 44% Thrones Co. -20% -39% -12% What was the buy-and-hold return on your portfolio? Provide your answer in percent, rounded to two decimals, omitting the % sign.

Assume a property can be purchased for $105,000. The existing mortgage has a balance of only $50,000, 15 years remaining and payments are $507.13. You want to assume the mortgage, but need to finance $70,000 total so you must take out a second mortgage for $20,000 for 15 years at 14%. Alternatively you could purchase an equivalent property for $100,000 by obtaining a loan for $70,000 for 15 years at the market rate of 11%.

a.       What is the effective return (or cost) of assuming the loan and taking out a 2^ndmortgage?

b.       Is it better to assume the loan and take out a second mortgage, or should you buy the alternative property and finance the purchase with a new loan at the market rate (answer should be "assume" or "new"?

Advanced Time Value of Money Problems

(Try to work this question WITHOUT using Excel, get calculation in detail)

Question (Retirement planning)

You have just graduated Hofstra University at age 22. You hard work has paid off as you already have a job as an investment banker at Goldman Sachs waiting for you. You plan to work continuously until age 65 and retire exactly on that day. You expect to live until exactly 90 and enjoy your golden years and leave you heirs NOTHING. Assume your investments earn 8% per year.

You plan to contribute $10,000 to your retirement fund every year on your birthday starting at age 23. Your last deposit will be at exactly age 65 and your first withdrawal will be at age 66. Your last withdrawal will be at the moment you die at age 90.

Ignore all tax considerations for this problem.
(i) How much you will be able to spend each year in retirement?

(ii)

FV (deposits) = PV (withdrawals)
NOTE: This could be at any time period but t=65 is particularly convenient

How much will you be able to spend each year in retirement if you begin deposits at age 30?

(iii) How much larger do your deposits have to be if deposits start at age 30 to equal your answer in part (i)?

Now let’s consider the effect of inflation.
The values calculated above are nominal values. However, what is more important is real, i.e. inflation-adjusted, values.
Assume inflation averages 4% per year.

4. (iv) Re-calculate parts (i), (ii) and (iii) above.

5. (v) Comment on above.

The following chart provides price (P) and number of shares outstanding (Q) data for stocks A, B, and C at the end of year 0 and at the end of year1.

P0 Q0 P1 Q1

A 45 100 50 100

B 60 150 50 150

C 28 200 35 200

What are the equal-, price-, and value-weighted returns on an index comprised of A, B and C?

Equal weighted return Price weighted return Value weighted return A. 2.09% B. 1.5% C. 6.48%

Advanced Time Value of Money Problems

(Try to work this question WITHOUT using Excel, get calculation in detail)

Question (College planning)

Your child was just born and you are planning for his/her college education. Based on your wonderful experience in Financial Economics you decide to send your child to Hofstra University as well. You anticipate the annual tuition to be $60,000 per year for the four years of college. You plan on making equal deposits on your child’s birthday every year starting today, the day of your child’s birth. No deposits will be made after starting college. The first tuition payment is due in exactly 18 years from today (the day your child turns 18 – no deposit required, i.e. last deposit is on 17th birthday). Assume the annual expected return on your investments is 10% over this period.

1. (i) Calculate the annual deposit.

2. (ii) Calculate the amount needed if only equal annual deposits are made on birthday’s 5-10 inclusive.

3. (iii) Calculate the amount needed if two equal annual deposits are made on birthday’s 5 and 13.

4. (iv) Answer part (i), now assume tuition rises 10% per year.

5. (v) Answer part (i) assuming first deposit will be made on your child’s 1st birthday. All other information is the same. What is the annual tuition payment? How does it compare to part (i)? Is your answer surprising?

An engineer wishes to buy a house but can only afford monthly payments of $1500. 30-

year loans are available at 5.75% interest compounded monthly. If the engineer can make

a $20,000 down payment, what is the price of the most expensive house that the engineer

can afford to purchase?

Question ( mortgage problem) (Try to work this question WITHOUT using Excel, get calculation in detail)

You are considering the purchase of a $500,000 home. You plan to take a 30-year fixed mortgage after making a 20% downpayment to avoid PMI. Payments are to be made monthly (at the end of the month) and the APR is 8%.

1. What is the monthly payment?

2. During what month does the principal portion first exceed the interest portion? Are you surprised by your answer?

3. How long does it take to pay off your mortgage if you pay an additional $300 towards principal each payment?

4. How long does it take to pay off your mortgage if you pay an additional amount each month equal to the current month’s principal?

8. Suppose that you are now 30 and that you would like $2 million at age 65 to fund your retirement. You would like to save each year an amount that grows by 5% each year (that is, if you save $1 this year, you will save $1.05 next year). Assume that the discount rate is 8%. How much should you start saving at the end of this year? (Hint: first calculate the present value of the $2 million, then use the growing annuity formula to calculate the amount you must save at the end of this year).

9. You’ve decided to buy a new computer that costs $1,500. But Best Buy will let you take the computer home without making paying the full price immediately. Rather, Best Buy will let you pay $500 now, and $500 at the end of each of the next two years.

Your bank offers you a savings account that earns 2% annually, and a two-year certificate of deposit (CD) that earns 5% annually. Note that to earn the 5% on the CD, you have to leave your money there for the full two years.

How much money do you need today to make sure you can make all the payments to Best Buy?

Cute Camel Woodcraft Company’s income statement reports data for its first year of operation. The firm’s CEO would like sales to increase by 25% next year.

Complete the Year 2 income statement data for Cute Camel, then answer the questions that follow. Be sure to round each dollar value to the nearest whole dollar.

Given the results of the previous income statement calculations, complete the following statements:

Does a correlation exist between volume and performance level? Explain.

If you borrow $40,000 today and agree to repay the loan in 24 annual payments, how much do you owe every year? Assume this is an amortized loan with 10% interest rate, compounded annually?

I have 8 million at 9% per annum payable over next five years . The tax rate is 28%. How do I determine the value of the tax shield?

I am doing corporate finance/Finance for decision makers