Practice problems that allow students to click on answers to see if they are correct and see solutions

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It is a series of practice problems that allow students to click on answers to see if they are correct and see solutions.  The example of how it works is first and the code follows.

 EXAMPLE:

Security Valuation Practice Problems

Click on an answer to check it.

1. A bond has a 6% coupon rate, matures in exactly 8 years, pays interest semi-annually and has a face value of $1,000. If current market conditions have bonds of similar risk and maturity priced to return 5%, what will this bond sell for? Hint: Is the 6% coupon a premium over current rates?

A. $1,000.00 Incorrect. This result requires the coupon rate to equal the current market rate.

B. $1,064.63 Incorrect. This answer doesn't include semi-annual compounding. For example, the Excel formula might have been =PV(5%,8,60,1000,0). But it needs to adjust the RATE and the NPER inputs for semi-annual compounding.

C. $1,065.28 Correct. The Excel formula is: =PV(2.5%,16,30,1000,0)

 

2. A bond has a 6% coupon rate, matures in exactly 8 years, pays interest semi-annually and has a face value of $1,000. If current market conditions have bonds of similar risk and maturity priced to return 6%, what will this bond sell for? Hint: Is the 6% coupon a premium over current rates?

A. $1,000.00 Correct. Since the coupon rate equals the current market rate or bond will sell at par or at its face value of $1,000.

B. $1,064.63 Incorrect. This answer requires discounting at a rate lower than the market rate of 6%.

C. $1,105.28 Incorrect. This answer requires discounting at a rate lower than the market rate of 6%.

 

3. A bond has a 6% coupon rate, matures in exactly 8 years, pays interest semi-annually and has a face value of $1,000. If its current market price is $939.53, what is this bond's yield-to-maturity? Hint: Is the yield higher or lower than the 6% coupon rate?

A. 5.5% Incorrect. Since the bond is selling at a discount the YTM must be greater than the coupon rate of 6%.

B. 6.4% Incorrect. Discounting the bond's features at this rate results in a price of $975.26 = PV(3.2%,16,30,1000,0). The correct YTM will discount the bond to the $939.53 price.

C. 7.0% Correct. The Excel formula is: =RATE(16,30,-939.53,1000,0,4%) = 3.5% Since this is a semi-annual rate w double it to get a 7.0% annual rate. We can check our answer:=PV(3.5%,16,30,1000,0)=$939.53

 

4. A bond has a 7% coupon rate, matures in exactly 8 years, pays interest semi-annually and has a face value of $1,000. Current market conditions for bonds of similar risk and maturity price these bonds to return 6%, so this bond sells for $1,062.81. If interest rates suddenly drop to 5% what will happen to the bond's price?

A. Decreases to $1,000 Incorrect. This result requires the coupon rate to equal the current market rate.

B. Increases to $1,129.26 Incorrect. This answer doesn't include semi-annual compounding. For example, the Excel formula might have been =PV(5%,8,70,1000,0). But it needs to have the RATE, PMT and the NPER inputs adjusted for semi-annual compounding.

C. Increases to $1,130.55 Correct. The Excel formula is: =PV(2.5%,16,30,1000,0)=$1,130.55

 

5. An investor purchased a bond for $1,000 at issuance. The bond has a 6% coupon rate, matures in exactly 15 years, pays interest semi-annually and has a face value of $1,000. If the investor must sell the bond today, and current market conditions have bonds of similar risk and maturity priced to return 5%, what price will he sell the bond for?

A. $1,000.00 Incorrect. This result requires the coupon rate to equal the current market rate.

B. $1,064.63 Incorrect. This answer doesn't include semi-annual compounding. For example, the Excel formula might have been =PV(5%,8,60,1000,0). But it needs to adjust the RATE and the NPER inputs for semi-annual compounding.

C. $1,065.28 Correct. The Excel formula is: =PV(2.5%,16,30,1000,0)

 

6. A bond has a 7% coupon rate, matures in exactly 17 years, pays interest semi-annually and has a face value of $1,000. Current market rates for bonds of this risk profile are 5%, so the bond should sell for $1,227.24 (You can check this). However, the bond is callable in exactly 3 years. Since the coupon rate of 7% is far above the current market rate of 5%, investors are pricing the bond as if it will be called. What price are investors paying for the bond if they will receive a call premium of $1,140 instead of the $1,000 face value and the bond is called in exactly 3 years?

A. $980.00 Incorrect. The bond has to be selling for more than $1,000 since the coupon rate is far above the current market rate..

B. $1,175.80 Correct. The Excel formula is =PV(2.5%,6,35,1140,0). This reflects 2.5%: the semi-annual equivalent of the 5% current market rate. 6: The semi-annual periods for 3 years until the bond is called. 35: the semi-annual coupon payments or interest payments. 1140: The amount that investors will receive if the bond is called, a $140 call premium over the $1,000 face value.

C. $1,227.24 Incorrect. This is the value of the bond ignoring its callability. The Excel formula is: =PV(2.5%,34,35,1000,0) Notice that the face value is the $1,000 standard face value without the call premium.

 

7. A bond has a 6% coupon rate, matures in exactly 8 years, pays interest semi-annually and has a face value of $1,000. If current market conditions have bonds of similar risk and maturity priced to return 7%, what will this bond sell for? Hint: Is the 6% coupon a premium over current rates?

A. $939.53 Correct. The Excel formula is =PV(3.5%,16,30,1000,0)

B. $1,000.00 Incorrect. This answer ddoesn't adjust for the market rate of 7%.

C. $1,065.28 Incorrect. The Excel formula is: =PV(3.5%,16,30,1000,0) The Rate inlut should be half of 7%.

 

8. A bond has a 6% coupon rate, matures in exactly 20 years, pays interest semi-annually and has a face value of $1,000. If I buy the bond for $1,000 today and it is called in 2 years with a $120 call premium, what is my rate of return? Hint: Use the Excel RATE function, but think about whether this is an annual or semi-annual rate. To check your answer the discounted futre cash flows should equal the purchase price of $1,000. If you have done the problem correctly, the Rate result is a semi-annual rate. To turn it into the exact annual rate we need to compute (1+Rate)² - 1 , so a semi-annual rate of 5% becomes an annual rate of (1.05)² - 1 = 0.1025 = 10.25% a little higher than the doubled rate.

A. 5.75% Incorrect. This is the semi-annual rate.

B. 6% Incorrect. This result requires the payment on the called bond to be $1,000 but there is a call premium so the rate should be higher than the coupon rate.

C. 11.837% Correct. The Excel formula is: =RATE(4,30,-1000,1120,0,) =0.057 which is th semi-annual rate. Turning this into the annual rate (1.0575)2 - 1 (or =1.0575^2 - 1 in Excel) = 011837319 = 11.837%

 

9. A share of preferred stock pays a $2.50 annual dividend. If the stock is priced to return 10% what is its price today?

A. $15.00 Incorrect. Preferred stock is a perpetuity so is valued as

B. $25.00 Correct. Preferred stock is a perpetuity so is valued as .

C. $30.00 Incorrect. Preferred stock is a perpetuity so is valued as

 

10. General Products has just paid a $1.50 annual dividend. Investor expect the dividend to grow 3% per year indefinitely. If investors require a 12% return from securities of this risk, what is General Products' stock price today?

A. $12.50 Incorrect. This result doesn't grow the dividend one period as is required by the Gordon Constant Dividend Growth model. $P_0=\frac{Div\:x\:\left(1+g\right)}{\left(r\:-\:g\right)}\:\:\:$

B. $12.875 Incorrect. This answer doesn't subtract the growth rate from the required rate of return in the denominator as required by the Gordon Constant Dividend Growth model. $P_0=\frac{Div\:x\:\left(1+g\right)}{\left(r\:-\:g\right)}\:\:\:$

C. $17.17 Correct. Using the Gordon Constant Dividend Growth model. $P_0=\frac{Div\:x\:\left(1+g\right)}{\left(r\:-\:g\right)}\:\:\:=\frac{1.50x1.03}{0.12-0.03}=\frac{1.545}{0.09}=17.166667$

 

11. ACME common stock sells for $28.60 per share. Its most recent annual dividend was $2.20. If investors demand a 12% required rate of return from the stock, what dividend growth rate are they assuming the company will have?

A. 3% Incorrect. At a growth rate of 3%the price would be (2.20x1.035)/(.12-.035) =$26.79

B. 4% Correct. In the dividend growth model $P_0=\frac{Div\:x\:\left(1+g\right)}{\left(r\:-\:g\right)}\:\:\:so\:g=\frac{Pr\:-\:D}{P\:+\:D}$. Inserting numbers we have $\frac{28.60\:x\:0.12\:-\:2.2}{28.6\:+\:2.20}=\:0.04$

C. $4.31% Incorrect. This answer occurs if you forget to increase the value of the dividend.

 

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