Decision #1:   Which set of Cash Flows is worth more now?

Assume that your grandmother wants to give you generous gift. She wants you to choose which one of the following sets of cash flows you would like to receive:

Option A: Receive a one-time gift of $ 10,000 today.   

Option B: Receive a $1500 gift each year for the next 10 years. The first $1500 would be

     received 1 year from today.             

Option C: Receive a one-time gift of $18,000 10 years from today.

Compute the Present Value of each of these options if you expect the interest rate to be 3% annually for the next 10 years.    Which of these options does financial theory suggest you should choose?

       Option A would be worth $__________ today.

      Option B would be worth $__________ today.

       Option C would be worth $__________ today.

       Financial theory supports choosing Option _______

Compute the Present Value of each of these options if you expect the interest rate to be 6% annually for the next 10 years. Which of these options does financial theory suggest you should choose?

       Option A would be worth $__________ today.

       Option B would be worth $__________ today.

       Option C would be worth $__________ today.

      Financial theory supports choosing Option _______

Compute the Present Value of each of these options if you expect to be able to earn 9% annually for the next 10 years. Which of these options does financial theory suggest you should choose?

       Option A would be worth $__________ today.

       Option B would be worth $__________ today.

       Option C would be worth $__________ today.

       Financial theory supports choosing Option _______

You are planning your retirement in 15 years.  You plan to retire with $3,000,000 and your retirement account earns 4.8% compounded monthly. After you retire, you plan on withdrawing $15,000 per month from your account until you have nothing left. How many years can you live off your retirement account after you retire?

1) CF1=-$2,000, CF2=$3,000, CF3=$4,000, CF4=$6,000, CF5=$8,000

Set I =12

Solve for NPV =

2)CF1=$10,000, CF2=$5,000,CF3=$5,000, CF4= $5,000, CF5= $5,000, CF6=$7,000

Set I =12

Solve for NPV =$

3)CF1=$10,000, CF2=$10,000, CF3= $10,000, CF4= $10,000, CF5= $10,000, CF6= $8,000, CF7= $8,000, CF8= $8,000, CF9= $8,000, CF10= $8,000

Set I =12

Solve for NPV =$

Decision #2: Planning for Retirement

Erich and Mallory are 22, newly married, and ready to embark on the journey of life.   They both plan to retire 45 years from today. Because their budget seems tight right now, they had been thinking that they would wait at least 10 years and then start investing $3000 per year to prepare for retirement. Mallory just told Erich, though, that she had heard that they would actually have more money the day they retire if they put $3000 per year away for the next 10 years - and then simply let that money sit for the next 35 years without any additional payments – then they would have MORE when they retired than if they waited 10 years to start investing for retirement and then made yearly payments for 35 years (as they originally planned to do).   Please help Erich and Mallory make an informed decision:   

Assume that all payments are made at the END a year (or month), and that the rate of return on all yearly investments will be 7.2% annually.  

(Please do NOT ROUND when entering “Rates” for any of the questions below)

1. How much money will Erich and Mallory have in 45 years if they do nothing for the next 10 years, then put $3000 per year away for the remaining 35 years?

2. How much money will Erich and Mallory have in 10 years if they put $3000 per year away for the next 10 years?

b2) How much will the amount you just computed grow to if it remains invested for the remaining

35 years, but without any additional yearly deposits being made?

3. How much money will Erich and Mallory have in 45 years if they put $3000 per year away for each of the next 45 years?

How much money will Erich and Mallory have in 45 years if they put away $250

4. per MONTH at the end of each month for the next 45 years? (Remember to adjust 7.2% annual rate to a Rate per month!)

5. If Erich and Mallory wait 25 years (after the kids are raised!) before they put anything away for retirement, how much will they have to put away at the end of each year for 20 years in order to have $1,000,000 saved up on the first day of their retirement 45 years from today?

1) Your parents spent $7,800 to buy 200 shares of stock in a new company 12 years ago. The stock has appreciated 14.6 percent per year on average. What is the current value of those 200 shares?

2)   Today, Georgia is investing $24,000 at 5.5 percent, compounded annually, for 6 years. How much additional income could she earn if she had invested this amount at 6.5 percent, compounded annually?

3)   You have $2,000 today in your savings account. How long must you wait for your savings to be worth $4,500 if you are earning 1.25 percent interest, compounded annually?

Suppose the gold spot price is $300/oz., the 1-year forward price is $310.686, and the continuously compounded risk-free rate is 5%. In class, we neglect the convenience yield for gold. In reality gold can may be lent and borrowed. Some entities operating in the wholesale gold market do lend gold and earn interest on such transactions. To sum up, there is a convenience yield for gold and it takes the name of “lease rate”.

(a) What is the lease rate?

(b) What is the return on a cash-and-carry if you cannot loan out the gold (i.e. you do not have access to the wholesale gold market)?

(c) What is the return on a cash-and-carry if you do loan out the gold, earning the lease rate?

10. Ann is looking for a fully amortizing 30 year Fixed Rate Mortgage with monthly payments for $3,200,000.

Mortgage A has a 4.38% interest rate and requires Ann to pay 1.5 points upfront.

Mortgage B has a 6% interest rate and requires Ann to pay zero fees upfront.

Assuming Ann makes payments for 30 years, what is Ann’s annualized IRR from mortgage A?

Firm X is being acquired by Firm Y for $35,000 worth of Firm Y stock (valued at the pre-merger current price of Y). Both firms are all-equity financed. The incremental value created by the merger is $2,500. Firm X has 2,000 shares of stock outstanding at $16 per share. Firm Y has 1,200 shares of stock outstanding at a price of $40 per share. What is the actual cost of the acquisition to Firm Y using company stock? Why is the actual cost less than $35,000?

A few years back, Dave and Jana bought a new home. They borrowed $230,415 at an annual fixed rate of 5.49% (15-year term) with monthly payments of $1,881.46. They just made their 50th payment, and the current balance on the loan is $208,555.87.
Interest rates are at an all-time low, and Dave and Jana are thinking of refinancing to a new 15-year fixed loan. Their bank has made the following offer: 15-year term, 3.0%, plus out-of-pocket costs of $2,937. The out-of-pocket costs must be paid in full at the time of refinancing.
Build a spreadsheet model to evaluate this offer. The Excel function:
=PMT(rate, nper, pv, fv, type)
calculates the payment for a loan based on constant payments and a constant interest rate. The arguments of this function are:
rate   = the interest rate for the loan
nper   = the total number of payments
pv   = present value (the amount borrowed)
fv   = future value [the desired cash balance after the last payment (usually 0)]
type   = payment type (0 = end of period, 1 = beginning of the period)
For example, for Dave and Jana’s original loan, there will be 180 payments (12*15 = 180), so we would use =PMT(0.0549/12, 180, 230415,0,0) = $1,881.46. Note that because payments are made monthly, the annual interest rate must be expressed as a monthly rate. Also, for payment calculations, we assume that the payment is made at the end of the month.
The savings from refinancing occur over time, and therefore need to be discounted back to current dollars. The formula for converting K dollars saved t months from now to current dollars is:
where r is the monthly inflation rate. Assume that r = 0.002 and that Dave and Jana make their payment at the end of each month.
Use your model to calculate the savings in current dollars associated with the refinanced loan versus staying with the original loan.
If required, round your answer to the nearest whole dollar amount. If your answer is negative use “minus sign”.

1.

a. You see the current 3-month T-bill quoted on a discount basis at 1.9425-1.9350. The T-bill has a $10,000 face value. The T-bill has 86 days until maturity. What price would you pay for one of these T-bills (disregarding transaction charges)? Enter the price you would pay rounded to the nearest cent.

b. You see the current 3-month T-bill quoted on a discount basis at 1.9325-1.9250. The T-bill has a $10,000 face value. The T-bill has 86 days until maturity. What is the bond equivalent ask yield? Enter the yield rounded to two digits in this format, 4.56%

c. You are an investor in the 34% marginal tax bracket. You are looking to invest some of your funds in a fixed income security. You see a Mecklenburg County municipal bond with a yield of 2.75%. The other bond you are considering is a Ford Motor Company corporate bond yielding 4.00%. On the basis of taxable equivalent yield, which bond would you choose?

d. You open a brokerage account and purchase 500 shares of MMM at $150.39 by borrowing half of the required funds (you pay for 250 shares and borrow enough to buy another 250 shares). You pay 6% annual interest on the borrowed money. At the end of one year, what price would trigger a margin call if the maintenance margin were set at 35% by the brokerage firm? Enter the margin call price by rounding to the nearest cent in this format, $123.45

1.

a. You are creating an index for the four following stocks:

What is the one day return for the index if it is price-weighted? Present your answer as the percent change from t=0 to t=1 to the nearest two decimals in this format, 1.23%

b.

What is the one day return for the index if it is market capitalization-weighted? Present your answer as the percent change from t=0 to t=1 to the nearest two decimals in this format, 1.23%

c.

Suppose that at the conclusion on t=1 trading day, stock ABC does a 2:1 stock split, what is the new divisor for your price-weighted index? Present your answer rounded to the nearest two digits like this, 1.23

Lisa Lasher buys 400 shares of stock on margin at $21 per share. If the margin requirement is 70 percent, how much must the stock rise for her to realize a 40-percent return on her invested funds? (Ignore dividends, commissions, and interest on borrowed funds.) Round your answer to the nearest cent.