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Problem Set 01

 
In all cases, the student is to provide and identify the data used to solve these problems.
 

Problem 1

 
The Black Knight plans to purchase a Honda Civic worth $20,000. Which of the two 5-year deals described below should the Black Knight take (show the calculations):
 
a. Lancelot, the sales manager for King Arthur Motors, offers to take 10% off the price, and lend the Black Knight the balance at the regular financing rate of 9% annually.
 
b. Lancelot, offers to lend the Black Knight $20,000 (without a discount) at a rate of 3% annually.
 

Problem 2

 
Curly, Larry and Moe purchased a condo in Las Vegas last year for $250,000. The Three Stooges put $50,000 down, taking on a mortgage of $200,000 at 10% on a 30-year term loan (with monthly payments). Since last year, interest rates have dropped to 9%. The Three Stooges can refinance their mortgage at this rate, with a closing cost of 3% of the loan. Their opportunity cost is 8%. Ignore tax effects and any repayment toward the principle in the last year since it is negligible.
 
a. What are their monthly payments on their current mortgage (at 10%)?
 
b. What would their monthly payments be if they refinance with a mortgage at 9% (with a 30-year term loan)?
 
c. The Three Stooges plan to stay in this condo for the next 5 years. With the refinancing cost (3% of the mortgage), should they refinance their mortgage?
 
d. How much would interest rates have to drop before it makes sense to refinance their mortgage (assuming they stay in the house for five years)?

Problem 3

 
Dorothy, now living in Oz, is 35 years old today. She expects to retire at age 65 and The Wizard says that she will live to be 100 years old. She wants to return to the Kanas when she retires. Dorothy estimates that it will cost $ 300,000 to make the move (on her 65th birthday) and that her living expenses will be $30,000 a year, starting at the end of year 66 and continuing through the end of year 100.
 
a. Assuming that interest rates are at 8%, how much will Dorothy need to have saved by her retirement date to be able to afford her retirement plan?
 
b. She already has $50,000 in savings. If Dorothy invests this money, tax-free, at 8% a year, how much would she need to save each year for the next 30 years to be able to afford her retirement?
 
c. If she does not have any current savings and does not expect to save any money for the next 5 years, how much would she have to set aside each year after that to be able to afford her retirement, assuming interest rates are at 8%?
 

Problem 4

 
Wonderland has hired Alice to operate its pension fund for. Wonderland currently has $5 million in the fund and expects to have cash inflows of $2 million a year for the first 5 years followed by cash outflows of $ 3 million a year for the next 5 years. Assume that interest rates are at 8%.
 
a. How much money will be left in the fund at the end of the tenth year?
 
b. If Wonderland must pay a perpetuity after the tenth year (starting in year 11 and going through infinity) from the balance left in the pension fund, what could Wonderland afford to pay?
 

Problem 5

 
Peter Pan, an investment advisor, has Captain Hook as a client. The Captain has $250,000 in savings, is 55 years old and expects to work for 10 more years, stealing $100,000 a year. He expects to make a return of 5% on his investments for the foreseeable future. (Peter can ignore taxes since Hook does not pay any taxes.)
 
a. Once Hook retires 10 years from now, he intends to withdraw $80,000 a year for the following 25 years (his actuary tells him he will live to be 90 years old). How much would Hook need in the bank 10 years from now to be able to carry out his retirement plan?
 
b. How much of Hook’s income would he need to save each year for the next 10 years to afford these withdrawals ($80,000 a year) after the tenth year?
 
c. If Pan assumes that interest rates decline to 4% ten years from now, by how much, if any, would Hook have to lower his annual withdrawal, assuming that he still plans to withdraw cash each year for the next 25 years?
 

FORMAT FOR HOMEWORK PROBLEMS AND PROBLEM SETS

 
1. State the Problem(s)
 
What is the future value of $2,700 in four years if the interest rate is 10%?
 
The problem is to calculate the future value
 
2. Determine and show the data
I = 10
N = 4
PV = 2700
PMT = 0
FV = ?
 
3. Determine the model (formulas)
FV = PV (1+i)n
 
4. Calculate the Solution
Use a calculator. Place the result in the proper format ($, %, etc.)
 
5. Communicate the Analysis
Write the analysis by putting your solution in the context of the problem statement:
 
The future value of $2,700 in four years with an interest rate of 10% is $3,953.07.

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