Quiz 3 solution sketches
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Transcript of Quiz 3 solution sketches
Quiz 3 solution sketches
1:00 Lecture, Version A
Note for multiple-choice questions: Choose the closest
answer
Finite PV Someone tells you that there is a
stock that will have an annual growth rate of dividend payments of 55%, and the annual discount rate for the stock is 40%. Which of the following statements is correct? (Assume that dividends are paid annually starting one year from today.)
Finite PV A: The stock is finitely valued if we
assume that dividends will be paid forever. No (g>r means infinite PV of
perpetuity) B: The stock is finitely valued if we
assume that dividends will be paid only for 100 years. Yes (each PV is finite)
Finite PV C: No stock can ever have dividend
growth of 55% from one year to the next. No, high growth rate is possible in any
year D: The PV of the stock is $0.
No, PV is positive since the dividend>0.
E: Both (A) and (B) No, because (A) is false.
Sample Standard Deviation A sample of 3 stocks has rates of
return of 8%, 5%, and 2%. What is the standard deviation of this sample? Avg = (8 + 5 + 2)/3 = 5% Variance
= 1/2*[(.08-.05)2 + (.05-.05)2 + (.02-.05)2]= 1/2*[.0018] = .0009
S.D. = (.0009)1/2 = .03 S.D. = 3%
Expected NPV Mariah plans to open a new car
dealership. She will buy a plot of land today for $900,000. She will have to spend $800,000 for cars today. Starting one year from today, she will have positive cash flows (undiscounted) of $200,000 every year. The last of these positive cash flows will be 10 years from today.
Expected NPV There is a clause in the contract
that 10 years from today, the land must be sold to a university. If economic times are good, the plot will sell for $2 million. If not, the plot must be sold for $900,000. If the effective annual discount rate is 5% and you believe the probability of good economic times is 50%, what is the NPV of this investment?
Expected NPV (in $millions) NPV = -0.9 – 0.8 + .2/.05 (1 –
1/1.0510) + 0.5 *2*(1/1.0510) + 0.5*0.9(1/1.0510)
NPV = 0.7345 NPV = $734,500
Semiannual Bond Coupons A bond pays coupons of $60
annually, starting six months from today, until the bond matures (with the last coupon on the maturity date). The bond will mature 3½ years from today and pay a face value of $500. What is the PV of this bond if the appropriate effective annual interest rate for this bond is 8%?
Semiannual Bond Coupons PV = 60/(1.08)1/2 + 60/(1.08)3/2 +
60/(1.08)5/2 + 560/(1.08)7/2 PV = $588.46
Zero-Coupon Bond Value A zero-coupon bond will mature 5
years from today. The promised payment at maturity is $10,000. The current market rate (as an effective annual interest rate) is 12%. What is the current value of owning this bond? X * (1.12)5 = 10,000 X = 10,000/(1.12)5
X = $5674.27
Change in Bond Value You currently own a zero-coupon
bond with maturity date in 18 months. The bond will pay $3,000 on the maturity date. The effective annual rate of return for this bond at the beginning of today is 9%. At the end of the day the rate drops to 8%. How much does the value of the bond change today?
Change in Bond Value PV @ 9% = 3000/(1.09)3/2 =
$2,636.22 PV @ 8% = 3000/(1.08)3/2 =
$2,672.92 r decreases PV increases Change in PV = 2672.92 – 2636.22 Change in PV = $36.70
Payback Period Method Use the undiscounted payback
period method, with the cutoff date 10 years, 4 months from now. (In other words, the payback period is 10 years, 4 months.) The effective annual discount rate is 37.934%. Which of the following offers should be picked if someone uses this method?
Payback Period Method A: A one-time payment of $5,000
today B: $600 every year forever,
starting 1 year from now C: $1,100 every 2 years, starting
today D: $8,000 every 10 years, starting
8 years from now E: $20,000 every 20 years, starting
11 years from now
Payback Period Method Undiscounted future value at 10y
4m: A: $5,000 B: $600 * 10 = $6,000 C: $1,100 * 6 = $6,600 D: $8,000 E: $0 (first payment not until year 20)
Using the undiscounted payback period method, one should choose option D
Price-to-Earnings Ratio Stocks A and B have the same
annual discount rate, and would each pay the same dividend if they acted as cash cows. Stock A has no growth opportunities with positive NPV. Stock B has many growth opportunities with positive NPV. Which of the following statements is true if both companies maximize the value of their stock?
Price-to-Earnings Ratio A: Stock A will have a lower price-to-
earnings ratio than Stock B B: Stock A will have a higher price-to-
earnings ratio than Stock B C: Both stocks will have the same price-
to-earnings ratio D: Stock A will have a higher price-to-
earnings ratio than Stock B if the growth opportunities are small enough
E: None of the above
Price-to-Earnings Ratio Price per share / Earnings per share
= 1/R + NPVGO/EPS 1/R is positive and the same for
both NPVGO is positive for B and zero
for A A’s P-E ratio < B’s P-E ratio, so the
correct response is A
Growing Dividends Goliath Galloping Ghost, Inc. will
pay its first dividend two years from today, and will pay annually thereafter forever. The first dividend payment (in 2 years) is $5 per share. Each of the next two dividend payments will be 30% higher than the previous payment. After that, dividend payments will grow at 6% per year forever.
Growing Dividends What is the PV of this stock if the
effective annual interest rate is 13%? Year 2: PV = 5/1.132 = $3.92 Year 3: PV = 5*1.3/1.133 = $4.50 Year 4: PV = 5*1.32/1.134 = 8.45/1.134 =
$5.18 Years 5+: FV in year 4
= 8.45*1.06/(.13 – .06) = $127.96 Years 5+: PV = 127.96/1.134 = $78.48 Sum of PVs = $92.08