# Do you agree that if the required rate of return on a bond (rd) is greater than its coupon interest rate and will remain above that rate, then the market value of the bond will always be below its par value until the bond matures, at which time its m

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1. An investment offers $4,900 per **year** for 15 years, with the first payment
Occurring one year from now. If the **required** **return** is 8%, what is the
Present value of the investment? What would be the value if the payments
Occurred for 40 years? Forever?
15 years case
???????? ???????? ???????????????????????????? = ???? [
1/????
−
1
????(1 + ????)^????
]
???? = 4,900, ???? = 0.08, ???????????? ???? = 15
???????? = 4,900 [ (1/0.08) − (1/0.08(1 + 0.08)^15)]
= 41,941.45

2. Find the EAR in each of the following cases:
APR Compounding period EAR
7% Quarterly
16% Monthly
11% Daily (365 days in a year)
???????????? = (1 +
????
????
)
???? − 1
If m becomes infinite, ???????????? = ????
???? − 1
7% APR and quarterly compounding: ???? = 0.07, ???????????? ???? = 4
???????????? = (1 +
0.07/4
)^4
− 1
= 7.19%
16% APR and monthly compounding: ???? = 0.16, ???????????? ???? = 12
???????????? = (1 +
0.16/12 )^12
− 1
= 17.23%
11% APR and daily compounding: ???? = 0.11, ???????????? ???? = 365
???????????? = (1 +
0.11/365)^365
− 1
= 11.63%

3. Given an

**interest****rate**of 6.1% per year, what is the value at Date t=7 of a Perpetual stream of $2,500 annual payments that begins at Date t=15? ???????? ???????? ???????????????????????????????????????? = ???? ???? ???? = 2,500, ???????????? ???? = 0.061 3 PV of the perpetuity at date t=14 is 2,500/0.061 = 40,983.61. Discounting it back to date t=7, we Should have ????????7 = 40,983.61 (1+0.061)^7 = 27,077.12.4. Cohen has issued a

**bond**with the following characteristics: Par: $1,000; Time to maturity: 15 years; Coupon rate: 7%; Semiannual payment. What is The**price**of the bond if the YTM is 9%? ???????????????????? = 35 ∗ ( 1/0.045 − 1/0.045(1 + 0.045)^30) + 1,000/(1 + 0.045)^30 = 837.115. Jay, Inc. Has 7%

**coupon**bonds outstanding with semiannual payments and is Priced at par value. The Jay, Inc. Bond has 2 years to maturity. If interest rate Suddenly rises from 7% to 9%, what is the percentage change in the price of The bond? If interest rate increases to 9% ???????????????????????????????? = 35 ∗ (1/ 0.045 − 1/0.045(1 + 0.045)^4 ) + 1,000/(1 + 0.045)^4 = 964.12 ????ℎ???????????????? ???????? ???????????????????????????????? = 964.12 − 1,000/1,000 = −3.59%You purchase a bond with an invoice price of $950. The bond has a coupon
Rate of 6.8%, and there are 2 months to the next semiannual coupon date.
What is the clean price of the bond?
???????????????????? ???????????????????? = 950 − 1,000 ∗
0.068/2* ∗
4/6 = 927.33

1. A T-bill with face value $10,000 and 87 days to maturity is selling at a bank discount ask
Yield of 3.4%.
1) What is the price of the bill?
Price = 10,000 ∗ (1 − 3.4% ∗
87/360)
= 9,917.83

2. What is its bond equivalent yield?
Bond equivalent yield = (10,000 − 9,917.83/9,917.83) ∗ (365/87) = 3.48%

3. You purchase 100 shares of Argon Co. Today for $540 per

**share**. After one year, you sell The stock for $500 per share and collect $10 dividends per shareWhat is the dividend yield?
Dividend yield =
10/540
= 1.85%

What is the capital gain?
Capital gain = (500 − 540)/540
= −7.41%

What is the total return?
Total return = 1.85% − 7.41%
= −5.56%

4. Rachel opens a

**margin**account and purchases 400 shares of Ross Inc. At $40 per share. The initial margin requirement is 50%. The share price falls to $25 per share by the end Of the year.What is the remaining margin in the account?

Margin = (400 ∗ 25 − 400 ∗ 40 ∗ 50%)/(400 ∗ 25) = 20%

If the maintenance margin requirement is 30%, will she receive a margin call?
Yes, she will

How much will she have to put up to get back to 50% when her broker calls? Value of stock = 400 ∗ 25
= 10,000
Maximum borrowing = 10,000 ∗ 50%
= 5,000
Additional money required = 8,000 − 5,000
= 3,000

If she does not have any more cash, how many shares she has to sell to pay back the
Broker?
Assume she has to sell N shares
Value of remaining stock = (400 − N) ∗ 25
= 10,000 − 25????
Remaining loan = 8,000 − 25N
Margin = ((10,000 − 25????) − (8,000 − 25N))/(10,000 − 25????) = 50%
???? = 240

If price increases to $50 per share by the end of the year instead, how many more
Shares she can buy by borrowing more from her broker?
Assume she can buy Y more shares
Value of stock = (400 + Y) ∗ 50
= 20,000 + 50????
Maximum borrowing = 8,000 + 50Y
Margin =
((20,000 + 50????) − (8,000 + 50Y))/(20,000 + 50????) = 50%
???? = 80