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# Finance: Chapter 3 TVM: expected return, PV, annuity, EAR

Chpt. 3 TVM

1. How long does it take a present value amount to triple if the expected return is 9%?
a. 8.00 periods
b. 8.04 periods
c. 12.00 periods
d. 12.75 periods
e. insufficient information to compute

2. What is the PV of a 5-year annuity due (payments at beginning of period, aka annuity in advance) of \$550 if the required return is 6.5%
a. 2286
b. 2434
c. 2750
d. 2582
e. insufficient information to compute

3. You have just taken out a 30 year, \$120,000 mortgage on your new home. This mortgage is to be repaid in 360 equal monthly installments. If the stated (nominal) annual interest rate is 14.75 percent, what is the amount of the INTEREST portion of the FIRST monthly installment?
a. \$1,475
b. \$1,472
c. \$1,493
d. \$17,700
e. insufficient information to compute

4. What is the EAR for a 9.5% APR with continuous compounding?
a. 7.48%
b. 9.5%
c. 9.97%
d. 10.99%
e. insufficient information to compute

5. Williams Inc. is expected to pay a \$3 dividend next year and that dividend is expected to grow at 4% every year thereafter. If the discount rate is 10%, what would be the present value of the expected dividend stream (aka the expected price of the firm's stock)?
a. 50.00
b. 30.00
c. 0.50
d. 75.00
e. 55.00

6. Your salary next year is expected to be \$40,000. Assume you expect your salary to grow at a steady rate of 4% per year for another 25 years. If the appropriate cost of capital (aka discount rate) is 9%, what is the PV today of your future salary cashflow stream? [For simplicity, assume the salary amounts are at the end of each of the next 25 years.] Answer to nearest \$1000.
a. 246,000
b. 247,000
c. 391,000
d. 553,000
e. 800,000

7. Chrysler is offering a choice of either 48 month 2.0% APR financing, OR \$2000 cash back if you pay "cash" on a car purchase. The stated price is \$25,000. If you can obtain bank financing at 5.75% APR (monthly compounding), what would be the implied monthly loan payments if use your bank for financing and thus drop the price by the \$2000 cash rebate? Assume 48 month term for the bank loan also.
a. 815
b. 2168
c. 616
d. 538
e. insufficient information to compute

8. You are offered the opportunity to buy a note for \$10,000. The note is certain to pay \$2000 at the end of each of the next 10 years. If you buy the note, what rate of interest will you receive on this investment (to nearest %)
a. 15%
b. 100%
c. 20%
d. 16%
e. insufficient information to compute

9. Next year you will begin receiving \$155 dollars per year in perpetuity from your grandparent's family trust fund (first payment is exactly 1 year from today). You consider these payments essentially risk free and have decided to discount them at a constant risk free rate of 6.5%. What is the present value today of these future cash flows? (Hint: draw a time line to illustrate exactly the cash flows for this problem.)
a. 1353
b. 2385
c. 1270
d. 146

10. In 10 years you will begin receiving \$155 dollars per year in perpetuity from your grandparent's family trust fund (first payment is exactly 10 years from today). You consider these payments essentially risk free and have decided to discount them at a constant risk free rate of 6.5%. What is the present value today of these future cash flows? (Hint: draw a time line to illustrate exactly the cash flows for this problem.)
a. 1353
b. 2385
c. 1270
d. 146

#### Solution Preview

See attached files.

1. How long does it take a present value amount to triple if the expected return is 9%?
a. 8.00 periods
b. 8.04 periods
c. 12.00 periods
d. 12.75 periods
e. insufficient information to compute

Assume PV = \$1.00, FV = \$3.00 (\$1 x 3)

FV = PV (1+i)n where PV is the present value
FV is the future value
i is the interest rate
n is the period

3 = 1(1 + 0.09)n
3 = (1.09)n
LN 3 = n LN 1.09
1.10 = n(0.09)
n = 1.10/0.09
n = 12.75

2. What is the PV of a 5-year annuity due (payments at beginning of period, aka annuity in advance) of \$550 if the required return is 6.5%
a. 2286
b. 2434
c. 2750
d. 2582
e. insufficient information to compute

PVA = W x 1 - 1 where PVA is the present value
(1 + R)N-1 W is the amount received each quarter
R R is the interest rate
N is the period

PVA = 550 x 1 - 1 + \$550
(1 + 0.065)5-1
0.065

PVA = 1,884.19 + 550 = 2,434.19

3. You have just taken out a 30 year, \$120,000 mortgage on your new home. This mortgage is to be repaid in 360 equal monthly installments. If the stated (nominal) annual interest rate is 14.75 percent, what is the amount of the INTEREST portion of the FIRST monthly installment?
a. \$1,475
b. \$1,472
c. \$1,493
d. \$17,700
e. insufficient ...

#### Solution Summary

This solution is comprised of a detailed explanation to answer how long does it take a present value amount to triple if the expected return is 9%.

\$2.19