Yield Questions

Question 1

An investor expects a stock currently selling for $20 per share to increase to $25 by year-end. The dividend last year was $1 but he expects this year’s dividend to be $1.25. What is the expected holding period return on this stock?

Answer 1

“Return = [dividend + (end − begin)] / beginning price
R = [1.25 + (25 − 20)] / 20 = 6.25 / 20 = 0.3125
“

Question 2

An investor is considering investing in Tawari Company for one year. He expects to receive $2 in dividends over the year and feels he can sell the stock for $30 at the end of the year. To realize a return on the investment over the year of 14%, the price the investor would pay for the stock today is closest to:

Answer 2

“HPR = [Dividend + (Ending price − Beginning price)] / Beginning price
0.14 = [2 + (30 − P)] / P
1.14P = 32 so P = $28.07
“

Question 3

Banca Hakala purchases two front row concert tickets over the Internet for $90 per seat. One month later, the rock group announces that it is dissolving due to personality conflicts and the concert that Hakala has tickets for will be the “farewell” concert. Hakala sees a chance to raise some quick cash, so she puts the tickets up for sale on the same internet site. The auction closes at $250 per ticket. After paying a 10% commission to the site on the amount of the sale and paying $10 in shipping costs, Hakala’s one-month holding period return is approximately:

Answer 3

“The holding period return is calculated as: (ending price – beginning price +/- any cash flows) / beginning price. Here, the beginning and ending prices are given. The other cash flows consist of the commission of 0.10 × $250 × 2 tickets = $50 and the shipping cost of $10 (total for both tickets).
Thus, her one-month holding period return is: [(2 × $250) – (2 × $90) – $50 − $10] / (2 × $90) = 1.44, or approximately 144%.
“

Question 4

An investor buys a 10 3/8 treasury note for 103 11/32 and sells it one year later for 101 13/32. What is the holding period yield?

Answer 4

“103 11/32 = 103.344% or $1,033.44
101 13/32 = 101.406% or $1,014.06
A coupon of 10 3/8 = 10.375% or $103.75
The rate of return equals the [(ending cash flows − the beginning cash flows) / beginning price] × 100 =
[(1014.06 + 103.75 − 1033.44) / 1033.44] × 100 = 8.16%
“

Question 5

A bond that pays $100 in interest each year was purchased at the beginning of the year for $1,050 and sold at the end of the year for $1,100. An investor’s holding period return is:

Answer 5

Input into your calculator: N = 1; FV = 1,100; PMT = 100; PV = -1,050; CPT → I/Y = 14.29

Question 6

When Annette Famigletti hears that a baseball-loving friend is coming to visit, she purchases two premium-seating tickets for $45 per ticket for an evening game. As the date of the game approaches, Famigletti’s friend telephones and says that his trip has been cancelled. Fortunately for Famigletti, the tickets she holds are in high demand as there is chance that the leading Major League Baseball hitter will break the home run record during the game. Seeing an opportunity to earn a high return, Famigletti puts the tickets up for sale on an internet site. The auction closes at $150 per ticket. After paying a 10% commission to the site (on the amount of the sale) and paying $8 total in shipping costs, Familgletti’s holding period return is approximately:

Answer 6

The holding period return is calculated as: (ending price − beginning price +/- any cash flows) / beginning price. Here, the beginning and ending prices are given. The other cash flows consist of the commission of $30 (0.10 × 150 × 2 tickets) and the shipping cost of $8 (total for both tickets). Thus, her holding period return is: (2 × 150 − 2 × 45 − 30 − 8) / (2 × 45) = 1.91, or approximately 191%.

Question 7

An investor sold a 30-year bond at a price of $850 after he purchased it at $800 a year ago. He received $50 of interest at the time of the sale. The annualized holding period return is:

Answer 7

“The holding period return (HPR) is calculated as follows:
HPR = (Pt − Pt-1 + Dt) / Pt
where:
Pt = price per share at the end of time period t
Dt = cash distributions received during time period t.
Here, HPR = (850 − 800 + 50) / 800 = 0.1250, or 12.50%.
“

Question 8

A stock is currently worth $75. If the stock was purchased one year ago for $60, and the stock paid a $1.50 dividend over the course of the year, what is the holding period return?

Answer 8

(75 − 60 + 1.50) / 60 = 27.5%.

Question 9

If an investor bought a stock for $32 and sold it one year later for $37.50 after receiving $2 in dividends, what was the holding period return on this investment?

Answer 9

“HPR = [D + End Price − Beg Price] / Beg Price
HPR = [2 + 37.50 − 32] / 32 = 0.2344.
“

Question 10

A bond was purchased exactly one year ago for $910 and was sold today for $1,020. During the year, the bond made two semi-annual coupon payments of $30. What is the holding period return?

Answer 10

“HPY = (1,020 + 30 + 30 – 910) / 910 = 0.1868 or 18.7%.
________________________________________
“

Question 11

An investor buys one share of stock for $100. At the end of year one she buys three more shares at $89 per share. At the end of year two she sells all four shares for $98 each. The stock paid a dividend of $1.00 per share at the end of year one and year two. What is the investor’s time-weighted rate of return

Answer 11

“The holding period return in year one is ($89.00 − $100.00 + $1.00) / $100.00 = -10.00%.
The holding period return in year two is ($98.00 − $89.00 + $1.00) / $89 = 11.24%.
The time-weighted return is [{1 + (-0.1000)}{1 + 0.1124}]1/2 – 1 = 0.06%.
“

Question 12

An investor buys one share of stock for $100. At the end of year one she buys three more shares at $89 per share. At the end of year two she sells all four shares for $98 each. The stock paid a dividend of $1.00 per share at the end of year one and year two. What is the investor’s money-weighted rate of return?

Answer 12

“T = 0: Purchase of first share = -$100.00
T = 1: Dividend from first share = +$1.00
Purchase of 3 more shares = -$267.00
T = 2: Dividend from four shares = +4.00
Proceeds from selling shares = +$392.00
The money-weighted return is the rate that solves the equation:
$100.00 = -$266.00 / (1 + r) + 396.00 / (1 + r)2.
CFO = -100; CF1 = -266; CF2 = 396; CPT → IRR = 6.35%.
“

Question 13

An investor buys four shares of stock for $50 per share. At the end of year one she sells two shares for $50 per share. At the end of year two she sells the two remaining shares for $80 each. The stock paid no dividend at the end of year one and a dividend of $5.00 per share at the end of year two. What is the difference between the time-weighted rate of return and the money-weighted rate of return?

Answer 13

“T = 0: Purchase of four shares = -$200.00
T = 1: Dividend from four shares = +$0.00
Sale of two shares = +$100.00
T = 2: Dividend from two shares = +$10.00
Proceeds from selling shares = +$160.00
The money-weighted return is the rate that solves the equation:
$200.00 = $100.00 / (1 + r) + $170.00 / (1 + r)2.
Cfo = -200, CF1 = 100, Cf2 = 170, CPT → IRR = 20.52%.
The holding period return in year one is ($50.00 − $50.00 + $0.00) / $50.00 = 0.00%.
The holding period return in year two is ($80.00 − $50.00 + $5.00) / $50 = 70.00%.
The time-weighted return is [(1 + 0.00)(1 + 0.70)]1/2 − 1 = 30.38%.
The difference between the two is 30.38% − 20.52% = 9.86%.
“

Question 14

Robert Mackenzie, CFA, buys 100 shares of GWN Breweries each year for four years at prices of C$10, C$12, C$15 and C$13 respectively. GWN pays a dividend of C$1.00 at the end of each year. One year after his last purchase he sells all his GWN shares at C$14. Mackenzie calculates his average cost per share as [(C$10 + C$12 + C$15 + C$13) / 4] = C$12.50. Mackenzie then uses the internal rate of return technique to calculate that his money-weighted annual rate of return is 12.9%. Has Mackenzie correctly determined his average cost per share and money-weighted rate of return?

Answer 14

“Because Mackenzie purchased the same number of shares each year, the arithmetic mean is appropriate for calculating the average cost per share. If he had purchased shares for the same amount of money each year, the harmonic mean would be appropriate. Mackenzie is also correct in using the internal rate of return technique to calculate the money-weighted rate of return. The calculation is as follows:
Time Purchase/Sale Dividend Net cash flow
0 -1,000 0 -1,000
1 -1,200 +100 -1,100
2 -1,500 +200 -1,300
3 -1,300 +300 -1,000
4 400 × 14 = +5,600 +400 +6,000
CF0 = −1,000; CF1 = −1,100; CF2 = −1,300; CF3 = −1,000; CF4 = 6,000; CPT → IRR = 12.9452.
“

Question 15

Miranda Cromwell, CFA, buys ₤2,000 worth of Smith & Jones PLC shares at the beginning of each year for four years at prices of ₤100, ₤120, ₤150 and ₤130 respectively. At the end of the fourth year the price of Smith & Jones PLC is ₤140. The shares do not pay a dividend. Cromwell calculates her average cost per share as [(₤100 + ₤120 + ₤150 + ₤130) / 4] = ₤125. Cromwell then uses the geometric mean of annual holding period returns to conclude that her time-weighted annual rate of return is 8.8%. Has Cromwell correctly determined her average cost per share and time-weighted rate of return?

Answer 15

“Because Cromwell purchases shares each year for the same amount of money, she should calculate the average cost per share using the harmonic mean. Cromwell is correct to use the geometric mean to calculate the time-weighted rate of return. The calculation is as follows:
Year Beginning price Ending price Annual rate of return
1 ₤100 ₤120 20%
2 ₤120 ₤150 25%
3 ₤150 ₤130 −13.33%
4 ₤130 ₤140 7.69%
TWR = [(1.20)(1.25)(0.8667)(1.0769)]1/4 − 1 = 8.78%. Or, more simply, (140/100)1/4 − 1 = 8.78%.
“

Question 16

An investor buys a share of stock for $200.00 at time t = 0. At time t = 1, the investor buys an additional share for $225.00. At time t = 2 the investor sells both shares for $235.00. During both years, the stock paid a per share dividend of $5.00. What are the approximate time-weighted and money-weighted returns respectively?

Answer 16

“Time-weighted return = (225 + 5 − 200) / 200 = 15%; (470 + 10 − 450) / 450 = 6.67%; [(1.15)(1.0667)]1/2 − 1 = 10.8%
Money-weighted return: 200 + [225 / (1 + return)] = [5 / (1 + return)] + [480 / (1 + return)2]; money return = approximately 9.4%
Note that the easiest way to solve for the money-weighted return is to set up the equation and plug in the answer choices to find the discount rate that makes outflows equal to inflows.
Using the financial calculators to calculate the money-weighted return: (The following keystrokes assume that the financial memory registers are cleared of prior work.)
TI Business Analyst II Plus®
• Enter CF0: 200, +/-, Enter, down arrow
• Enter CF1: 220, +/-, Enter, down arrow, down arrow
• Enter CF2: 480, Enter, down arrow, down arrow,
• Compute IRR: IRR, CPT
• Result: 9.39
“

Question 17

On January 1, Jonathan Wood invests $50,000. At the end of March, his investment is worth $51,000. On April 1, Wood deposits $10,000 into his account, and by the end of June, his account is worth $60,000. Wood withdraws $30,000 on July 1 and makes no additional deposits or withdrawals the rest of the year. By the end of the year, his account is worth $33,000. The time-weighted return for the year is closest to:

Answer 17

“To calculate the time-weighted return:
Step 1: Separate the time periods into holding periods and calculate the return over that period:
Holding period 1: P0 = $50.00
D1 = $5.00
P1 = $75.00 (from information on second stock purchase)
HPR1 = (75 − 50 + 5) / 50 = 0.60, or 60%
Holding period 2: P1 = $75.00
D2 = $7.50
P2 = $100.00
HPR2 = (100 − 75 + 7.50) / 75 = 0.433, or 43.3%.
Step 2: Use the geometric mean to calculate the return over both periods
Return = [(1 + HPR1) × (1 + HPR2)]1/2 − 1 = [(1.60) × (1.433)]1/2 − 1 = 0.5142, or 51.4%.”

Question 18

A 10% coupon bond was purchased for $1,000. One year later the bond was sold for $915 to yield 11%. The investor’s holding period yield on this bond is closest to:

Answer 18

“HPY = [(interest + ending value) / beginning value] − 1
= [(100 + 915) / 1,000] − 1
= 1.015 − 1 = 1.5%
“

Question 19

A Treasury bill with a face value of $1,000,000 and 45 days until maturity is selling for $987,000. The Treasury bill’s bank discount yield is closest to:

Answer 19

“The actual discount is 1.3%, 1.3% × (360 / 45) = 10.4%
The bank discount yield is computed by the following formula, r = (dollar discount / face value) × (360 / number of days until maturity) = [(1,000,000 − 987,000) / (1,000,000)] × (360 / 45) = 10.40”

Question 20

What is the effective annual yield for a Treasury bill priced at $98,853 with a face value of $100,000 and 90 days remaining until maturity?

Answer 20

“HPY = (100,000 − 98,853) / 98,853 = 1.16%
EAY = (1 + 0.0116)365/90 − 1 = 4.79%
“

Question 21

A T-bill with a face value of $100,000 and 140 days until maturity is selling for $98,000. What is the effective annual yield (EAY)?

Answer 21

The EAY takes the holding period yield and annualizes it based on a 365-day year accounting for compounding. HPY = (100,000 − 98,000) / 98,000 = 0.0204. EAY = (1 + HPY)365/t − 1 = (1.0204)365/140 − 1 = 0.05406 = 5.41%.

Question 22

A T-bill with a face value of $100,000 and 140 days until maturity is selling for $98,000. What is the money market yield?

Answer 22

“The money market yield is equivalent to the holding period yield annualized based on a 360-day year. = (2,000 / 98,000)(360 / 140) = 0.0525, or 5.25%.
________________________________________
“

Question 23

A T-bill with a face value of $100,000 and 140 days until maturity is selling for $98,000. What is the Holding Period yield?

Answer 23

The holding period yield is the return the investor will earn if the T-bill is held to maturity. HPY = (100,000 – 98,000) / 98,000 = 0.0204, or 2.04%.

Question 24

A T-bill with a face value of $100,000 and 140 days until maturity is selling for $98,000. What is the bank discount yield?

Answer 24

Actual discount is 2%, annualized discount is: 0.02(360 / 140) = 5.14%

Question 25

A Treasury bill (T-bill) with a face value of $10,000 and 219 days until maturity is selling for 97.375% of face value. Which of the following is closest to the holding period yield on the T-bill if held until maturity?

Answer 25

“The formula for holding period yield is: (P1 − P0 + D1) / (P0), where D1 for a T-bill is zero (it does not have a coupon). Therefore, the HPY is: ($10,000 − $9,737.50) / ($9,737.50) = 0.0270 = 2.70%.
Alternatively (100 / 97.375) − 1 = 0.02696.
“

Question 26

A Treasury bill (T-bill) with a face value of $10,000 and 44 days until maturity has a holding period yield of 1.1247%. Which of the following is closest to the effective annual yield on the T-bill?

Answer 26

The formula for the effective annual yield is: ((1 + HPY)365/t) − 1. Therefore, the EAY is: ((1.011247)(365/44)) − 1 = 0.0972, or 9.72%

Question 27

A Treasury bill (T-bill) with 38 days until maturity has a bank discount yield of 3.82%. Which of the following is closest to the money market yield on the T-bill?

Answer 27

“The formula for the money market yield is: [360 × bank discount yield] / [360 − (t × bank discount yield)]. Therefore, the money market yield is: [360 × 0.0382] / [360 − (38 × 0.0382)] = (13.752) / (358.548) = 0.0384, or 3.84%.
Alternatively: Actual discount = 3.82%(38 / 360) = 0.4032%.
T-Bill price = 100 − 0.4032 = 99.5968%.
HPR = (100 / 99.5968) − 1 = 0.4048%.
MMY = 0.4048% × (360 / 38) = 3.835%.
“

Question 28

A Treasury bill has 40 days to maturity, a par value of $10,000, and was just purchased by an investor for $9,900. Its holding period yield is closest to:

Answer 28

The holding period yield is the return that the investor will earn if the bill is held until it matures. The holding period yield formula is (price received at maturity − initial price + interest payments) / (initial price) = (10,000 − 9,900 + 0) / (9,900) = 1.01%. Recall that when buying a T-bill, investors pay the face value less the discount and receive the face value at maturity.

Question 29

A Treasury bill (T-bill) with a face value of $10,000 and 137 days until maturity is selling for 98.125% of face value. Which of the following is closest to the bank discount yield on the T-bill?

Answer 29

“The formula for bank discount yield is: (D / F) × (360 / t). Actual discount is 1 − 0.98125 = 0.01875. Annualized is: 0.01875 × (360 / 137) = 0.04927
________________________________________
“

Question 30

What is the yield on a discount basis for a Treasury bill priced at $97,965 with a face value of $100,000 that has 172 days to maturity?

Answer 30

($2,035 / $100,000) × (360 / 172) = 0.04259 = 4.26% = bank discount yield.

Question 31

A Treasury bill has 40 days to maturity, a par value of $10,000, and is currently selling for $9,900. Its effective annual yield is closest

Answer 31

The effective annual yield (EAY) is based on a 365-day year and accounts for compound interest. EAY = (1 + holding period yield)365/t − 1. The holding period yield formula is (price received at maturity − initial price + interest payments) / (initial price) = (10,000 − 9,900 + 0) / (9,900) = 1.01%. EAY = (1.0101)365/40 − 1 = 9.60%.

Question 32

The bank discount of a $1,000,000 T-bill with 135 days until maturity that is currently selling for $979,000 is:

Answer 32

($21,000 / 1,000,000) × (360 / 135) = 5.6%.

Question 33

An investor has just purchased a Treasury bill for $99,400. If the security matures in 40 days and has a holding period yield of 0.604%, what is its money market yield

Answer 33

The money market yield is the annualized yield on the basis of a 360-day year and does not take into account the effect of compounding. The money market yield = (holding period yield)(360 / number of days until maturity) = (0.604%)(360 / 40) = 5.436%.

Question 34

The effective annual yield (EAY) for a T-bill maturing in 150 days is 5.04%. What are the holding period yield (HPY) and money market yield (MMY) respectively?

Answer 34

The EAY takes the holding period yield and annualizes it based on a 365-day year accounting for compounding. The HPY = (1 + 0.0504)150/365 = 1.2041 − 1 = 2.04%. Using the HPY to compute the money market yield = HPY × (360/t) = 0.0204 × (360/150) = 0.04896 = 4.90%.

Question 35

A Treasury bill, with 80 days until maturity, has an effective annual yield of 8%. Its holding period yield is closest to:

Answer 35

The effective annual yield (EAY) is equal to the annualized holding period yield (HPY) based on a 365-day year. EAY = (1 + HPY)365/t − 1. HPY = (EAY + 1)t/365 − 1 = (1.08)80/365 − 1 = 1.70%.

Question 36

The holding period yield for a T-Bill maturing in 110 days is 1.90%. What are the equivalent annual yield (EAY) and the money market yield (MMY) respectively?

Answer 36

The EAY takes the holding period yield and annualizes it based on a 365-day year accounting for compounding. (1 + 0.0190)365/110 − 1 = 1.06444 − 1 = 6.44%. Using the HPY to compute the money market yield = HPY × (360 / t) = 0.0190 × (360 / 110) = 0.06218 = 6.22%.

Question 37

If the money market yield is 3.792% on a T-bill with 79 days to maturity, what is the holding period yield?

Answer 37

The holding period yield can be calculated from the money market yield as: (money market yield) ÷ (360 ÷ t). Therefore, the HPY is (0.03792) × (79 ÷ 360) = 0.0083 = 0.83%.

Question 38

A broker calls with a proposal to buy a Treasury bill (T-bill) with 186 days to maturity. He says the effective annual yield on the T-bill is 4.217%. What is the holding period yield if you hold the bill until maturity?

Answer 38

To calculate the HPY from the EAY, the formula is: (1 + EAY)(t/365) − 1. Therefore, the HPY is: (1.04217)(186/365) − 1 = 0.0213, or 2.13%.

Question 39

If the holding period yield on a Treasury bill (T-bill) with 197 days until maturity is 1.07%, what is the effective annual yield?

Answer 39

To calculate the EAY from the HPY, the formula is: (1 + HPY)(365/t) − 1. Therefore, the EAY is: (1.0107)(365/197) − 1 = 0.0199, or 1.99%.

Question 40

The effective annual yield for an investment is 10%. What is the yield for this investment on a bond-equivalent basis?

Answer 40

“First, the annual yield must be converted to a semiannual yield. The result is then doubled to obtain the bond-equivalent yield.
Semiannual yield = 1.10.5 − 1 = 0.0488088.
The bond-equivalent yield = 2 × 0.0488088 = 0.097618.
“

Question 41

The holding period yield of a T-bill that has a bank discount yield of 4.70% and a money market yield of 4.86% and matures in 240 days is closest

Answer 41

4.86 × (240/360) = 3.24%.

Question 42

What is the effective annual yield of a T-bill that has a money market yield of 5.665% and 255 days to maturity

Answer 42

“Holding Period Yield = 4.0127% = 5.665% × (255 / 360)
Effective Annual Yield = (1.040127)365/255 = 1.0571 − 1 = 5.79%.
“

Question 43

A Treasury bill has 90 days until its maturity and a holding period yield of 3.17%. Its effective annual yield is closest to:

Answer 43

The effective annual yield (EAY) is equal to the annualized holding period yield (HPY) based on a 365-day year. EAY = (1 + HPY)365/t − 1 = (1.0317) 365/90 − 1 = 13.49%.

Question 44

A Treasury bill, with 45 days until maturity, has an effective annual yield of 12.50%. The bill’s holding period yield is closest to:

Answer 44

The effective annual yield (EAY) is equal to the annualized holding period yield (HPY) based on a 365-day year. EAY = (1 + HPY)365/t − 1. HPY = (EAY + 1)t/365 − 1 = (1.125)45/365 − 1 = 1.46%.