Question: Consider the following spot and forward rate information from the Treasury spot rate curve (annualized rates on a BEY basis).
Period (years)
Rate
0.5
3.10%
1.0
3.50%
1.5
4.25%
2.0
4.95%
2.5
6.10%
3.0
6.50%
3.5
6.85%
4.0
7.15%
4.5
7.35%
5.0
7.55%
Using this information, what is the implied 6-month spot rate 4.5 years from now?
Calculate all yields on a BEY basis and annualize the 6-month rate.
Select an Answer: 9.70% 7.84% 7.52% 9.36% 9.16%
Rationale:
Given information from a spot rate curve, the 6-month forward rate can be found by utilizing the following formula:
Where:
zm + 1 = the one-period (six month) rate beginning (m + 1) periods from now
zm = the one-period (six month) rate beginning m periods from now
m = the beginning period sequence
In this example, you are required to extrapolate the 6-month forward rate beginning 4.5 years (or 9 periods) from now, given information about the prevailing spot interest rates. All of the necessary information has been provided, and the calculation of the required rate is as follows:
This is the implied 6-month forward rate beginning 4.5 periods from now. Doubling this rate will give us the annualized bond-equivalent 6-month rate, which is found as 9.36%.
An important note concerning our calculation: notice that it is the semi-annual yield being utilized in our calculation, and that this yield is found by dividing the annualized bond-equivalent yield by two. In this example, the annualized 4.5-year rate was provided as 7.35%, leading a BEY semiannual yield of 3.675%. Similarly, the 6-month forward rate was doubled to find the bond-equivalent annualized six month rate. While a rather simplistic measure, the BEY measurement is widely popular and utilized frequently by market participants.
2023-05-28
Question: Consider the following spot and forward rate information from the Treasury spot rate curve (annualized rates on a bond equivalent yield-BEY basis):
Time (years)
Rate
0.5
3.10%
1.0
3.50%
1.5
4.25%
2.0
4.95%
2.5
6.10%
3.0
6.50%
3.5
6.85%
4.0
7.15%
4.5
7.35%
5.0
7.55%
Using this information, what is the implied 6-month spot rate 3 years from now? (Calculate all yields on a BEY basis.)
Select an Answer: 4.97% 4.30% 1.70% 4.48% 1.19%
Rationale:
Given information from a spot rate curve, the 6-month forward rate can be found by utilizing the following formula:
Where:
zm + 1 = the one-period (six month) rate beginning (m + 1) periods from now
zm = the one-period (six month) rate beginning m periods from now
m = the beginning period sequence
In this example, you are required to extrapolate the 6-month forward rate beginning 3 years (or 6 periods) from now given information about the prevailing spot interest rates. All of the necessary information has been provided, and the calculation of the required rate is as follows:
f6 = (1.03425)7/(1.0325)6 − 1 = 0.0448 = 4.48%
This is the implied 6-month forward rate beginning 6 periods from now.
An important note concerning our calculation: notice that it is the semi-annual yield being utilized, and that this yield is found by dividing the annualized bond-equivalent yield by two. In this example, the annualized 3-year rate was provided as 6.50%, leading a BEY semiannual yield of 3.25%. Similarly, the semi-annual implied 6-month forward yield is doubled to reach the annualized bond-equivalent yield. While a rather simplistic measure, the BEY measurement is widely popular and utilized frequently by market participants.
2023-05-27
Question: A company has determined that its optimal capital structure consists of 40% debt and 60% equity.
Given the following information, calculate the marginal weighted average cost of capital when the capital budget is $40,000.
Interest rate on the firm's new debt = 7%
Net income = $40,000
Payout ratio = 50%
Tax rate = 40%
Stock price = $25
Growth rate = 0%
Shares outstanding = 10,000
Flotation cost on additional equity = 15%
Select an Answer: 11.81% 7.34% 7.20% 13.69% 14.28%
Rationale:
First, find the amount of equity and debt needed for a $40,000 budget:
We can find the amount of retained earnings = Net income × (1 − Payout ratio), or RE = $40,000 × 0.5 = $20,000.
We will need to find the cost of new common equity, because we only have $20,000 of equity on hand, and we need $4,000 more.
Find the dividend, Do = [0.5 × $40,000] / Number of shares = $20,000 / 10,000 = $2.00.
Then, find the cost of new equity:
ke = D1 / [Po(1 − f)] + g
= $2.00 / [ $25 × (1 − 0.15) ] + 0%
= 0.0941 or 9.41%.
Finally, calculate marginal WACC, using the cost of new equity, ke = 0.0941, and kd = 0.07, so:
WACC = D/A × (1 − Tax rate) × kd + E/A × ke
= 0.4 × (1 − 0.4) × 0.07 + 0.6 × 0.0941
= 0.0734, or 7.34%.
Note that because the marginal, not the average, WACC is being calculated, the cost of new equity, not the average cost of equity, is used.
2023-05-26
Question: A firm's dividend growth rate is 3.2% when the dividend payout ratio equals 37%. It is expected to pay a dividend of $2.2 next year.
If the cost of external equity for the firm equals 19.2% and the firm's stock is currently priced at $14.1, the flotation cost of equity equals ________.
Select an Answer: 2.50% 1.78% 0.89% 1.91%
Rationale:
If F is the percentage flotation cost and P is the amount of new equity raised per new share, then:
Ke = [D1 / P0(1 − f)] + g
where Ke is the cost of external equity. Here, g = 3.2%, D1 = $2.2, P = $14.1, and Ke = 19.2%.
Therefore, 19.2% = 2.2 / (14.1 × (1 − F)) + 3.2%. Solving for F gives F = 2.5%.
2023-05-25
Question: Consider the following information about two Treasury bills:
Treasury bill A is currently selling for $0.98733397 per $1 of par value and has 65 days from settlement until maturity.
Treasury bill B has 95 days until maturity and is trading at a discount yield of 7.2266%.
What is the yield on a discount basis for Treasury bill A? Further, what is the price per $1 of par value for Treasury bill B?
Rationale:
The first segment of this question asks for the yield on a discount basis.
Market participants conventionally quote Treasury bills using the yield on a discount basis, which utilizes the following formula:
d = (1 − p) × (360/Nsm)
Where:
p = the price per $1 of par value
Nsm = the number of days from settlement until the maturity of the bill
In this example, "p" is given as $0.98733397, and the number of days from settlement until maturity is 65. Inputting this information into the discount yield equation will lead to the following:
d = ($1 − $0.98733397) × (360 / 65) = 0.07015032, or 7.0150%
The second segment of this question requires that the equation above be manipulated such that we solve for "p" rather than "d." The price of this Treasury bill is found as follows:
