96 Brooks ◼ Financial Management: Core Concepts, 4e
13. Annuity due. Reginald is about to lease an apartment for the year. The landlord wants
the lease payments paid at the start of the month. The twelve monthly payments are
$1,300 per month. The landlord says he will allow Reginald to prepay the rent for the
entire year with a discount. The one-time annual payment due at the beginning of the
lease is $14,778. What is the implied monthly discount rate for the rent? If Reginald is
earning 1.5% on his savings monthly, should he pay by month or take the one annual
payment?
14. Timeline of cash flow and application of time value of money. Mauer Mining
Company leases a special drilling press with annual payments of $150,000. The
contract calls for rent payments at the beginning of each year for a minimum of six
years. Mauer Mining can buy a similar drill for $750,000 but will need to borrow the
funds at 8%.
a. Show the two choices on a time line with the cash flow.
b. Determine the present value of the lease payments at 8%.
c. Should Mauer Mining lease or buy this drill?
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15. Perpetuities. The Canadian government has once again decided to issue a consol (a
bond with a never-ending interest payment and no maturity date). The bond will pay
$50 in interest each year (at the end of the year) but never return the principal. The
current discount rate for Canadian government bonds is 6.5%. What should this bond
sell for in the market? What if the interest rate should fall to 4.5%? Rise to 8.5%? Why
does the price go up when interest rates fall? Why does the price go down when interest
rates rise?
ANSWER
16. Perpetuities. The Stack has just written and recorded the single greatest rock song ever
made. The boys in the band believe that the royalties from this song will pay the band a
handsome $200,000 every year forever. The record studio is also convinced that the
song will be a smash hit and that the royalty estimate is accurate. The record studio
wants to pay the band upfront and not make any more payments for the song. What
should the record company offer the band if they use a 5% discount rate, a 7.5%
discount rate, or a 10% discount rate?
100 Brooks ◼ Financial Management: Core Concepts, 4e
6
$15,423.33
$4.068.63
$1,542.33
$2,526.30
$12,897.03
7
$12,897.03
$4.068.63
$1,289.70
$2,778.93
$10,118.09
8
$10,118.09
$4.068.63
$1,011.81
$3,056.83
$7,061.27
9
$7,061.27
$4.068.63
$706.13
$3,362.51
$3,698.76
10
$3,698.76
$4.068.63
$369.88
$3,698.76
$0.00
Note that all payments, interest for year, principal paid, and ending balance are rounded to
nearest cent.
22. Amortization. Loan Consolidated Incorporated (LCI) is offering a special one-time
package to reduce Custom Autos’ outstanding bills to one easy–to-handle payment plan.
LCI will pay off the current outstanding bills of $242,000 for Custom Autos if Custom
Autos will make an annual payment to LCI at a 10% interest rate over the next fifteen
years. First, what are the annual payments and the remaining balance of the loan at the
end of each year (should Custom Autos want to pay off the loan early)? Second, when
will the balance be half paid off? Finally, what is the total interest expense on the loan
over the fifteen years?
$242,000.00
$234,383.35
$234,383.35
$226,005.03
$226,005.03
$216,788.86
$216,788.86
$206,651.11
$206,651.11
$195,499.57
$195,499.57
$183,232.87
$183,232.87
$169,739.50
$169,739.50
$154,896.80
$154,896.80
$138,569.82
10
$138,569.82
$120,610.15
11
$120,610.15
$100,854.51
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23. Waiting period with an ordinary annuity. Fill in the missing waiting periods (years) or
number of payments in the following table for an ordinary annuity stream.
Number of
Payments or
Years
Annual Interest
Rate
Future Value
Annuity
Present Value
6%
0
$250.00
$2,867.48
8%
$5,794.62
$400.00
0
10%
0
$636.48
$6,000.00
4%
$100,000.00
$80.80
0
ANSWER
