Winter 2007

Solutions

Type A Exam

Numerical questions (2 points each)

1. (Q. 5 in B) What is the present value of the following payment stream, discounted at 8 percent annually: $1,000 at the end of year 1, $2,000 at the end of year 2, and $3,000 at the end of year 3?

A)$5,022.11

B)$5,144.03

C)$5,423.87

D)$5,520.00

Answer A

PV = [pic]

= $925.93 + $1,714.68 + $2,381.50

= $5,022.11

2. (Q. 6 in B) What is the present value of a four-year annuity of $100 per year that begins two years from today if the discount rate is 9 percent?

A)$297.22

B)$323.86

C)$356.85

D)$388.97

Answer A

PV1 = $100 [pic]

= $100 [3.2397]

PV1 = $323.97

PV0 = [pic]

= $297.22

3. (Q. 7 in B) $3,000 is deposited into an account paying 10 percent annually, to provide three annual withdrawals of $1,206.34 beginning in one year. How much remains in the account after the second withdrawal?

A)$587.32

B)$1,096.67

C)$1,206.34

D)$1,326.97

Answer B

[pic]

4. (Q. 8 in B) Approximately how much should be accumulated by the beginning of retirement to provide a $2,500 monthly check (to be paid at the end of each month) that will last for 25 years, during which time the fund will earn 8 percent interest with monthly compounding?

A)$261,500

B)$323,800

C)$578,700

D)$690,000

Answer B

The monthly interest rate is 8% / 12 = 0.667%

PV = $2,500 × [1/0.00667 – 1/(0.00667(1.00667300))] = $2,500 [129.52]

= $323,800.

5. (Q. 1 in B) An investor buys a ten-year, 7 percent coupon bond for $1,050, holds it for one year and then sells it for $1,040. What was the investor's rate of return over the 1-year holding period? Assume coupons are paid annually.

A)5.71 percent

B)6.00 percent

C)6.67 percent

D)7.00 percent

Answer A

Return on bond = (Interest coupon + Capital gain) / Purchase price of bond.

In our example there was a capital loss of $10 given that the selling price of the bond ($1,040) was less than the purchase price of the bond ($1,050).

Rate of return = ($70 - $10)/$1,050 = 5.71%.

6. (Q. 2 in B) A bond with 10 years until maturity, an 8 percent coupon rate, and an 8 percent original yield to maturity increased in price to $1,107.83 yesterday. What appears to have happened to interest rates? Coupons are paid annually.

A)Rates increased by 2.00 percent.

B)Rates decreased by 2.00 percent.

C)Rates increased by 0.72 percent.

D)Rates decreased by 1.50 percent.

Answer D

$1,107.83 = $80[pic]

i = 6.5%, yield to maturity was 8.0% prior to the price change. Therefore the rates have decreased by 1.5%.

7. (Q. 3 in B) Which of the following statements is correct about a stock currently selling for $50 per share that has a 16 percent expected return and a 10 percent expected capital appreciation?

A)Its expected dividend exceeds the actual dividend. B)Its expected return will exceed the actual return. C)It is expected to pay $3 in dividends for next year. D)It is expected to pay $8 in dividends for next year.

Answer C

Expected return = expected dividend yield + expected capital appreciation 16% = expected dividend yield + 10%

6% = expected dividend yield

$50 share price × 6% = $3 expected dividend payment

8. (Q. 4 in B) An investor receives a 15 percent total return by purchasing a stock for $40 and selling it after one...