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Fundamentals of Finance Week 01 Quiz Answers

Module 1 Quiz

Q1. If the present value of $280 paid one year from now is $250, what is the one-year discount factor?

*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.

Q2. If the present value of $400 paid one year from now is $320, what is the one-year interest rate? (Note: this number is also known as the discount rate.)

*Make sure to input all percentage answers as numeric values without symbols, and use two decimal places of precision. For example, if the answer is 6%, then enter 0.06.

Q3. Lara Beal allocates wealth between two periods: youth and old age. Currently (in her youth) she has $8,000 in cash. She can lend and borrow at the bank at 15% (that is, lending $1 in youth will give her $1.15 in old age). Her only investment opportunity other than the bank is a project that costs $5,000 now in her youth and has a payoff of $6,000 in her old age. What is the most she can consume in her old age?

*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.

• Lara Beal allocates wealth between two periods: youth and old age. Currently (in her youth) she has $8,000 in cash. She can lend and borrow at the bank at 15

Q4. James Bennett also allocates wealth between youth and old age. He has no cash currently (in his youth), but will inherit $3000 in his old age. He can lend and borrow at the bank at 18% (that is, lending $1 in youth will give him $1.18 in old age). He has an investment opportunity that costs $12,000 now in his youth and has a payoff of $15,000 in his old age. This is the only investment opportunity available to him. What is the most he can consume in his youth?

*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.

The most amount that should be consumed in his youth is $15,254.23.

The calculation is as follows:

Present value × 1.18 = Future value

Present value × 1.18 = ($15,000 + $3,000)

So, the present value should be

= $18,000 ÷ $1.18

= $15,254.23

The present value is the value that represents today’s value.

Therefore we can conclude that the most amount that should be consumed in his youth is $15,254.23.

Q5. Which of the following investments do you prefer?

(a) Purchase a bond with a single payment of $1000 in ten years, for a price of $550.

(b) Invest $550 for ten years in PNC Bank at a guaranteed annual interest rate of 4.5%.

• (a) Purchase a Bond
• (b) Invest with PNC Bank

Q6. You have just applied for a 30-year $100,000 mortgage at a rate of 10%. What must the annual payment be?

*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.

using simple interest,

P.R.T/100

=> 100000 . 30 . 10 /100

=> $300,000

Q7. Suppose you are given a choice of the following two securities:

(a) an annuity that pays $10,000 at the end of each of the next 6 years;

or (b) a perpetuity that pays $10,000 forever, but the first cash payment is 11 years from today.

Which security do you choose if the annual interest rate is 5%?

• (a) an annuity that pays $10,000 at the end of each of the next 6 years
• (b) a perpetuity that pays $10,000 forever, but the first cash payment is 11 years from today

Q8. Assume the annual interest rate is 6%. Calculate the value of an investment that pays $100 every two years, starting two years from now and continuing forever.

*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.

principal amount =p

annual interest R= 6%

time t in a year

intrest amounts = p+t/ 100

for 2 years intrest amounts is 100 and time is 2

100= p×2×6/100

100×100/2×6=p

p=10000/ 12

=5000/6

=2500/3

=833.33

Q9. Suppose money invested in a hedge fund earns 1% per trading day. There are 250 trading days per year. What will be your annual return on $100 invested in the fund if the manager allows you to reinvest in the fund the 1% you earn each day?

*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.

since , daily earning puts into zero- interest-bearing , we didnt get any interest on daily earning .

now,

→ initial investment = $100 .

→ Earing per trading day = 1% of $100 = (1 * 100)/100 = $1 .

and,

→ Total total trading days = 250 .

so,

→ Total earing on trading days = 250 * 1 = $250 .

then,

→ Return after one year = initial investment + Total earing on trading days = $100 + $250 = $350 (Ans.)

Q10. Suppose money invested in a hedge fund earns 1% per trading day. There are 250 trading days per year. With an initial investment of $100, what will be your annual return assuming the manager puts all of your daily earnings into a zero-interest-bearing checking account and pays you everything earned at the end of the year?

*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.

Fundamentals of Finance Week 02 Quiz Answers

Module 2 Quiz

Q1. Suppose that you have purchased a 3-year zero-coupon bond with a face value of $1000 and a price of $850. If you hold the bond to maturity, what is your annual return?

*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision

Answer: Annual Return = ((Face Value – Purchase Price) / Purchase Price) * (1 / Number of Years) = (($1000 – $850) / $850) * (1 / 3) ≈ 0.0588 or 5.88%

Q2. Now suppose you have purchased a 3-year bond with a face value of $1000, a 7% annual coupon, and a price of $975. Is the yield to maturity greater or less than the annual return you computed for the bond in the previous question

• Yield to Maturity is GREATER than the Annual Return
• Yield to Maturity is LESS than the Annual Return

Q3. Suppose you bought a five-year zero-coupon Treasury bond for $800 per $1000 face value. What is the yield to maturity (annual compounding) on the bond?

*Make sure to input all percentage answers as numeric values without symbols, and use four decimal places of precision. For example, if the answer is 6%, then enter 0.0600.

Answer: Yield to Maturity = ((Face Value / Purchase Price) ^ (1 / Number of Years)) – 1 = (($1000 / $800) ^ (1 / 5)) – 1 ≈ 0.0589 or 5.89%

Q4. Suppose you bought a five-year zero-coupon Treasury bond for $800 per $1000 face value. Assume the yield to maturity on comparable bonds increases to 7% after you purchase the bond and remains there. Calculate your holding period return (annual return) if you sell the bond after one year.

*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.

Answer: Holding Period Return = ((Selling Price + Interest Earned) – Purchase Price) / Purchase Price = (($800 + ($800 * 0.07)) – $800) / $800 ≈ 0.1075 or 10.75%

Q5. Suppose you bought a five-year zero-coupon Treasury bond for $800 per $1000 face value. Assuming yields to maturity on comparable bonds remain at 7%, calculate your holding period return if you sell the bond after two years.

*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.

Answer: Holding Period Return = ((Selling Price + Interest Earned) – Purchase Price) / Purchase Price = (($800 + ($800 * 0.07 * 2)) – $800) / $800 ≈ 0.145 or 14.5%

Q6. Suppose you bought a five-year zero-coupon Treasury bond for $800 per $1000 face value. Suppose after 3 years, the yield to maturity on comparable bonds declines to 3%. Calculate the holding period return if you sell the bond at that time.

*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.

Answer: Holding Period Return = ((Selling Price + Interest Earned) – Purchase Price) / Purchase Price = (($1000 + ($800 * 0.03 * 2)) – $800) / $800 ≈ 0.25 or 25%

Q7. Assume the government issues a semi-annual bond that matures in 5 years with a face value of $1,000 a coupon yield of 10 percent. What would be the price if the yield to maturity (semi-annual compounding) on similar government bonds were 8%?

*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.

Answer:

Price = (C / (1 + (YTM / 2))) + (C / (1 + (YTM / 2))^2) + (C / (1 + (YTM / 2))^3) + (C / (1 + (YTM / 2))^4) + (FV / (1 + (YTM / 2))^5)

Where:

• C = Semi-annual coupon payment = (0.10 * $1000) / 2 = $50
• YTM = Yield to Maturity = 0.08 / 2 = 0.04 (semi-annual yield)
• FV = Face Value = $1,000

Price ≈ $1,023.89

Q8. For each of the bonds and reinvestment rates listed below calculate the amount of money accumulated at the end from a $1000 initial investment. Assume annual compounding.

Invest $1000 in a 5-year zero coupon bond with a yield to maturity of 9 percent.

*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.

Answer: Future Value = Present Value * (1 + Annual Interest Rate)^Number of Years Future Value = $1000 * (1 + 0.09)^5 ≈ $1,538.62

Q9. Bond A is a zero-coupon bond paying $100 one year from now. Bond B is a zero-coupon bond paying $100 two years from now. Bond C is a 10% coupon bond that pays $10 one year from now and $10 plus the $100 principal two years from now. The yield to maturity on bond A is 10%, and the price of bond B is $84.18. Assuming annual compounding, what is the price of Bond A?

*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision

Answer: Price of Bond A = $100 / (1 + 0.10) = $90.91

Q10. Bond A is a zero-coupon bond paying $100 one year from now. Bond B is a zero-coupon bond paying $100 two years from now. Bond C is a 10% coupon bond that pays $10 one year from now and $10 plus the $100 principal two years from now. The yield to maturity on bond A is 10%, and the price of bond B is $84.18. Assuming annual compounding, what is the yield to maturity on Bond B?

*Make sure to input all percentage answers as numeric values without symbols, and use four decimal places of precision. For example, if the answer is 6%, then enter 0.0600.

Answer: Yield to Maturity on Bond B = (Annual Interest Payment + (Face Value – Current Price) / Number of Years) / ((Face Value + Current Price) / 2) Yield to Maturity on Bond B = (0.10 * $100 + ($100 – $84.18) / 2) / (($100 + $84.18) / 2) Yield to Maturity

Fundamentals of Finance Week 03 Quiz Answers

Module 3 Quiz

Q1. Company TYK forecasts that it will begin paying dividends seven years from now, at which point dividends are $1 per share. Thereafter, dividends are expected to grow at a constant rate of 6% per year. The discount rate for TYK is 10%. How much would you pay for one share in Company TYK?

*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.

Answer: Price per Share = Dividend at Year 7 / (Discount Rate – Growth Rate) = $1 / (0.10 – 0.06) = $25.00

Q2. Golf Ball Inc. expects earnings to be $10,000 per year in perpetuity if it pays out all of its earnings in dividends. Suppose the firm has an opportunity to invest $1,000 of next year’s earnings to upgrade its machinery. It is expected that this upgrade will increase earnings in all future years (starting two years from now) by $140. Assume that Golf Ball’s next dividend is one year from now. The required rate of return is 12%.

What is the value of Golf Ball Inc. if it does not undertake the upgrade?

*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.

Answer: Value of Golf Ball Inc. (Without Upgrade) = Dividend Next Year / (Required Rate of Return – Growth Rate) = $10,000 / (0.12 – 0) = $83,333.33

Q3. Golf Ball Inc. expects earnings to be $10,000 per year in perpetuity if it pays out all of its earnings in dividends. Suppose the firm has an opportunity to invest $1,000 of next year’s earnings to upgrade its machinery. It is expected that this upgrade will increase earnings in all future years (starting two years from now) by $140. Assume that Golf Ball’s next dividend is one year from now. The required rate of return is 12%.

What is the value of Golf Ball Inc. if it undertakes the upgrade?

*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.

Answer:

Value of Golf Ball Inc. (With Upgrade) = (Dividend Next Year + Additional Earnings from Upgrade) / (Required Rate of Return – Growth Rate) Value of Golf Ball Inc (With Upgrade) = ($10,000 + $140) / (0.12 – 0) = $85,116.67

Q4. Suppose that the consensus forecast of security analysts of your favorite company is that earnings next year will be $5.00 per share. The company plows back 50% of its earnings and if the Chief Financial Officer (CFO) estimates that the company’s return on equity (ROE) is 16%. Assuming the plow back ratio and the ROE are expected to remain constant forever:

If you believe that the company’s required rate of return is 10%, what is your estimate of the price of the company’s stock?

*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.

Answer: Price per Share = (Earnings per Share / Required Rate of Return) + (Plowback Ratio * ROE / (Required Rate of Return – Growth Rate)) Price per Share = ($5.00 / 0.10) + (0.50 * 0.16 / (0.10 – 0)) = $50.00

Q5. Suppose that the consensus forecast of security analysts of your favorite company is that earnings next year will be $5.00 per share. The company plows back 50% of its earnings and if the Chief Financial Officer (CFO) estimates that the company’s return on equity (ROE) is 16%. Assuming the plow back ratio and the ROE are expected to remain constant forever:

Suppose you observe that the stock is selling for $50.00 per share, what would you conclude about either your belief of the stock’s required rate of return or the CFO’s estimate of the company’s return on equity? (select all that apply)

• the required rate of return is higher than originally expected
• the ROE on funds plowed back is less than originally estimated
• the ROE on funds plowed back is more than originally estimated
• the required rate of return is lower than originally expected

Q6. Suppose that the consensus forecast of security analysts of your favorite company is that earnings next year will be $5.00 per share. The company plows back 50% of its earnings and if the Chief Financial Officer (CFO) estimates that the company’s return on equity (ROE) is 16%. Assuming the plow back ratio and the ROE are expected to remain constant forever:

Suppose that you are confident that 10% is the required rate of return on the stock. What does the market price of $50.00 per share imply about the market’s estimate of the company’s expected return on equity? (please give a number)

*Make sure to input all percentage answers as numeric values without symbols, and use four decimal places of precision. For example, if the answer is 6%, then enter 0.0600.

Answer: Market’s Estimate of Expected Return on Equity = Required Rate of Return + (Plowback Ratio * (Required Rate of Return – Growth Rate)) Market’s Estimate of Expected Return on Equity = 0.10 + (0.50 * (0.10 – 0)) = 0.15 or 15%

Q7. Dividends on CCN corporations are expected to grow at a 9% per year. Assume that the discount rate on CCN is 12% and that the expected dividend per share in one year is $0.50. CCN has just paid a dividend, so the next dividend is the $0.50 to be paid one year from now.

Calculate today’s price per share for CCN.

*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.

Answer: Price per Share = (Next Year’s Dividend / (Discount Rate – Growth Rate)) = ($0.50 / (0.12 – 0.09)) = $16.67

Q8. Dividends on CCN corporations are expected to grow at a 9% per year. Assume that the discount rate on CCN is 12% and that the expected dividend per share in one year is $0.50. CCN has just paid a dividend, so the next dividend is the $0.50 to be paid one year from now.

Calculate the expected price per share 14 years from now. Assume that a dividend has just been paid.

*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.

Answer: Price per Share (14 years from now) = Next Year’s Dividend / (Discount Rate – Growth Rate) Price per Share (14 years from now) = $0.50 / (0.12 – 0.09) = $16.67

Q9. Dividends on CCN corporations are expected to grow at a 9% per year. Assume that the discount rate on CCN is 12% and that the expected dividend per share in one year is $0.50. CCN has just paid a dividend, so the next dividend is the $0.50 to be paid one year from now.

Assume that CCN’s return on equity (ROE) is 12%. What fraction of earnings must CCN be plowing back into the company?

*Make sure to input all fraction answers as such: (numerator)/(denominator)

\frac{1}{2}21​ = 1/2

Answer: Fraction of Earnings Plowed Back = (Required Rate of Return – Growth Rate) / ROE = (0.12 – 0.09) / 0.12 = 0.25 or 25%

Q10. Dividends on CCN corporations are expected to grow at a 9% per year. Assume that the discount rate on CCN is 12% and that the expected dividend per share in one year is $0.50. CCN has just paid a dividend, so the next dividend is the $0.50 to be paid one year from now.

Can CCN alter its price by altering the plowback ratio in the previous question?

• Yes
• No

Fundamentals of Finance Week 04 Quiz Answers

Module 4 Quiz

Q1. You are considering two possible marketing campaigns for a new product. The first marketing campaign requires an outlay next year of 2M, and then will pay 0.24M in all subsequent years. The second marketing campaign requires an outlay of 3M next year and then will pay 0.27M in all subsequent years.

What is the IRR for the first marketing campaign?

*Make sure to input all percentage answers as numeric values without symbols, and use four decimal places of precision. For example, if the answer is 6%, then enter 0.0600.

Answer: The IRR for the first marketing campaign is 12.0000%.

Q2. You are considering two possible marketing campaigns for a new product. The first marketing campaign requires an outlay next year of 2M, and then will pay 0.24M in all subsequent years. The second marketing campaign requires an outlay of 3M next year and then will pay 0.27M in all subsequent years.

What is the IRR for the second marketing campaign?

*Make sure to input all percentage answers as numeric values without symbols, and use four decimal places of precision. For example, if the answer is 6%, then enter 0.0600.

Answer: The IRR for the second marketing campaign is 9.0000%.

Q3. Suppose you have the following two mutually exclusive projects that you can carry out on the corner of 39th Street and Walnut Street: Build a daycare center or a health spa.

Suppose the daycare center has the following cash flows: An immediate cash outlay of $5,000 followed by inflows of $2500 in each of the next 3 years and zero thereafter.

Suppose the health spa has the following cash flows: An immediate outlay of $5000 followed by inflows of nothing in year one, $1000 in year 2 $7100 in year 3, and zero thereafter.

Is the IRR for the health spa lower or higher than the IRR for the daycare project?

• IRR for the health spa is LOWER than the IRR for the daycare project
• IRR for the health spa is HIGHER than the IRR for the daycare project

Q4. Suppose you have the following two mutually exclusive projects that you can carry out on the corner of 39th Street and Walnut Street: Build a daycare center or a health spa.

Suppose the daycare center has the following cash flows: An immediate cash outlay of $5,000 followed by inflows of $2500 in each of the next 3 years and zero thereafter.

Suppose the health spa has the following cash flows: An immediate outlay of $5000 followed by inflows of nothing in year one, $1000 in year 2 $7100 in year 3, and zero thereafter.

If you base your investment decision on which investment has the highest NPV, which do you choose when the discount rate is 15%?

• Daycare center
• Health Spa

Q5. Suppose you have the following two mutually exclusive projects that you can carry out on the corner of 39th Street and Walnut Street: Build a daycare center or a health spa.

Suppose the daycare center has the following cash flows: An immediate cash outlay of $5,000 followed by inflows of $2500 in each of the next 3 years and zero thereafter.

Suppose the health spa has the following cash flows: An immediate outlay of $5000 followed by inflows of nothing in year one, $1000 in year 2 $7100 in year 3, and zero thereafter.

If you base your investment decision on which investment has the highest NPV, which do you choose when the discount rate is 5%?

• Daycare center
• Health Spa

Q6. You are considering the following two mutually exclusive investments:

Project	Year 0	Year 1	Year 2
A	-$80	0	$120
B	-$40	$28	$28

Which project has the higher NPV if the required rate of return is 5%?

• NPV_ANPVA​
• NPV_BNPVB​

Q7. You are considering the following two mutually exclusive investments:

Project	Year 0	Year 1	Year 2
A	-$80	0	$120
B	-$40	$28	$28

Which project has the higher NPV if the required rate of return is 15%?

• NPV_ANPVA​
• NPV_BNPVB​

Q8. You are considering the following two mutually exclusive investments:

Project	Year 0	Year 1	Year 2
A	-$80	0	$120
B	-$40	$28	$28

Is the IRR of Project B larger or smaller than the IRR of Project A?

• The IRR of Project B is LARGER than the IRR of Project A
• The IRR of Project B is SMALLER than the IRR of Project A

Q9. TEME is a manufacturer of toy construction equipment. If it pays out all of its earnings as dividends, it will have earnings of 0.3 million per quarter in perpetuity. Suppose that the discount rate, expressed as an effective annual rate (EAR), is 16%. TEME pays dividends quarterly.

What is the value of TEME if it continues to pay out all of its earnings as dividends? Assume that the next dividend is paid one quarter from now.

*Make sure to input the answer without any currency symbols, or commas, and remove M as the Million value.

e.g. 6,000,000 = 6M, so the answer should be written as 6

Answer: The value of TEME, if it continues to pay out all of its earnings as dividends, is 1.875M.

Q10. TEME is a manufacturer of toy construction equipment. If it pays out all of its earnings as dividends, it will have earnings of 0.3 million per quarter in perpetuity. Suppose that the discount rate, expressed as an effective annual rate (EAR), is 16%. TEME pays dividends quarterly.

Suppose that TEME is considering a one-time expansion into toy xylophones. It is estimated that this will cost 1M. Assume that this cost will be incurred at the end of the year, one year from now. As a result of expansion, earnings in subsequent quarters (i.e. starting in 1 year and 1 quarter from now) would be 0.05 million higher than without the expansion. Calculate the value of TEME if it undertakes the investment.

*Make sure to input the answer without any currency symbols, or commas, and remove M as the Million value.

e.g. 6,000,000 = 6M, so the answer should be written as 6

Answer: The value of TEME, if it undertakes the investment in toy xylophones, is 1.870M.

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