Question 1

Given an interest rate of 8 percent per year,what is the value at date t = 9 of a perpetual stream of $500 annual payments that begins at date t = 17?

Accepted Answer

PV_{t = 17} = $500/.08 = $6,250PV_{t = 9} = $6,250/1.08^17-9 = $3,376.68NOTE: This is a correction to the original problem solution.

Question 2

You have just purchased a new warehouse.To finance the purchase,you've arranged for a 30-year mortgage loan for 80 percent of the $2,600,000 purchase price.The monthly payment on this loan will be $12,200.What is the effective annual rate on this loan?

Accepted Answer

Loan amount = $2,600,000 × 0.80 = $2,080,000 EAR = [1 + (.05797/12)]¹² - 1 = 5.95 percent

Question 3

Consider a firm with a contract to sell an asset 3 years from now for $90,000.The asset costs $71,000 to produce today.At what rate will the firm just break even on this contract?

Accepted Answer

$90,000 = $71,000 × (1 + r)³; r = 8.23 percent

Question 4

Your holiday ski vacation was great,but it unfortunately ran a bit over budget.All is not lost.You just received an offer in the mail to transfer your $5,000 balance from your current credit card,which charges an annual rate of 18.7 percent,to a new credit card charging a rate of 9.4 percent.You plan to make payments of $510 a month on this debt.How many less payments will you have to make to pay off this debt if you transfer the balance to the new card?

Accepted Answer

$5,000 = $510 × [(1 - {1 + (0.094/12)]}^t)/(0.094/12)]t = ln (1/0.9232)/ln 1.007833; t = 10.24 paymentsDifference = 10.72 - 10.24 = 0.48 payments

Question 5

You are considering two annuities,both of which pay a total of $20,000 over the life of the annuity.Annuity A pays $2,000 at the end of each year for the next 10 years.Annuity B pays $1,000 at the end of each year for the next 20 years.Which annuity has the greater value today?
 Is there any circumstance where the two annuities would have equal values as of today?
 Explain.

Accepted Answer

The answer of You are considering two annuities,both of which...

Question 6

You have your choice of two investment accounts.Investment A is a 5-year annuity that features end-of-month $2,500 payments and has an interest rate of 11.5 percent compounded monthly.Investment B is a 10.5 percent continuously compounded lump sum investment,also good for five years.How much would you need to invest in B today for it to be worth as much as investment A five years from now?

Accepted Answer

FVA = $2,500 × [{[1 + (0.115/12)]⁵ ^{× 12} -1}/(0.115/12)] = $201,462.23PV = $201,462.23 e^-1 ^{× 0.105} ^×5 = $119,176.06

Question 7

What is the present value of $1,100 per year,at a discount rate of 10 percent if the first payment is received 6 years from now and the last payment is received 30 years from now?

Accepted Answer

PV = $9,984.74/1.1⁵ = $6,199.74

Question 8

You want to buy a new sports car for $55,000.The contract is in the form of a 60-month annuity due at a 6 percent APR,compounded monthly.What will your monthly payment be?

Accepted Answer

The answer of You want to buy a new sports...

Question 9

Explain the difference between the effective annual rate (EAR)and the annual percentage rate (APR).Of the two,which one has the greater importance and why?

Accepted Answer

The answer of Explain the difference between the effective annual...

Question 10

You are looking at a one-year loan of $10,000.The interest rate is quoted as 8 percent plus 5 points.A point on a loan is simply 1 percent (one percentage point)of the loan amount.Quotes similar to this one are very common with home mortgages.The interest rate quotation in this example requires the borrower to pay 5 points to the lender up front and repay the loan later with 10 percent interest.What is the actual rate you are paying on this loan?

Accepted Answer

Loan amount received = $10,000 × (1 - .05) = $9,500Loan repayment amount = $10,000 × 1.08¹ = $10,800$10,800 = $9,500 × (1 + r)¹; r = 13.68 percent

Question 11

Kristie owns a perpetuity which pays $12,000 at the end of each year.She comes to you and offers to sell you all of the payments to be received after the 10^th year.Explain how you can determine the value of this offer.

Accepted Answer

The answer of Kristie owns a perpetuity which pays $12,000...

Question 12

Why might a borrower select an interest-only loan instead of an amortized loan,which would be cheaper?

Accepted Answer

The answer of Why might a borrower select an interest-only...

Quiz 6: Discounted Cash Flow Valuation