DISCOUNTED CASH FLOW VALUATION
Concepts Review and Critical Thinking Questions
1. As you increase the length of the time involved, what happens to the present value of an annuity? What happens to the future value?
2. Tri-State Megabucks Lottery advertises a $10 million grand prizes. The winner receives $500,000 today and 19 annual payments if $500,000. A lump sum option of $5 million payable immediately is also available. Is this deceptive advertising?
3. Suppose you won the Tri-State Megabucks Lottery in the previous question. What factors should you take into account in deciding whether you should take the annuity option or the lump sum option?
4. Havana, Inc has identified an investment project with the following cash flows. If the discount rate is 8% what is the future value of these cash flows in year 4? What is the future value at an interest rate of 11% at 24%
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Year
|
Cash Flow $
|
|
1
|
1,075
|
|
2
|
1,235
|
|
3
|
1,510
|
|
4
|
1,965
|
5. An investment offers $6,700 per year for 15 years, with the first payment occurring 1 year from now. If the required return is 8%, what is the value of the investment? What would the value be if the payment occurred for 40 years? For 75 years? Forever?
6. Curly's Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $25,000 per year forever. If the required return on this investment is 6%, how much will you pay for the policy?
7. Find the EAR in each of the following cases:
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Stated Rate (APR)
|
Number of times compounded
|
Effective Rate (EAR)
|
|
10 %
|
Quarterly
|
|
|
17
|
Monthly
|
|
|
13
|
Daily
|
|
|
9
|
Semiannually
|
|
8. Magnus Credit Corp wants to earn an effective annual return on its consumer loans of 17% per year. The bank uses daily compounding on its loans. What interest rate is the bank required by law to report to potential borrowers? Explain why this rate is misleading to an uninformed borrower.
9. You want to buy a new sport coupe for $68,500, and the finance office at the dealership has quoted you a 5.9% APR loan for 60 months to buy the car. What will your monthly payments be? What is the effective annual rate on this loan?
10. One of your customers is delinquent on his account payable balance. You've mutually agreed to a repayment schedule of $500 per month. You will charge 1.4% per month interest on the overdue balance. If the current balance is $17,340, how long it take for the account to be paid off?
11. You have received a credit card application from Shady Bank Savings and Loan offering an introductory rate of 1.8% per year, compounded monthly for the first six month, increasing thereafter to 18% compounded monthly. Assuming you transfer the $10,000 balance from your existing credit card and make no subsequent payments, how much interest that you owe at the end of the first year?
12. You are saving to buy a $195,000 house. There are two competing bank in your area, both offering certificates of deposit yielding 5.5%. How long will it take your initial $85,000 investment to reach the desired level at First Bank, which pays simple interest? How long at Second Bank, which compounds interest monthly?