Test 2 solution sketches Note for multiple-choice questions:
Choose the closest answer
Slide 2
Average Equity Risk Premium In 1985, the country of Urce had
average bond returns of 2.5%, followed by 3.6% in 1986 and 1.6% in
1987. The average return on stocks in these years was 5.7%, -3.8%,
and 10.5%. What was the average equity risk premium in Urce over
this 3-year period? (Use the arithmetic mean.) Avg stock
return=(5.7-3.8+10.5)/3 = 4.133% Avg bond return=(2.5+3.6+1.6)/3 =
2.567% Difference = 4.133 2.567 = 1.566%
Slide 3
PV of Stock with Dividends
Slide 4
PV of Stock with Growing Dividend Organ Power Chicken will not
pay its first dividend until 5 years from today. This dividend will
be $1, with each subsequent payment increasing by 8.5%. What is the
PV of the stock if the effective annual discount rate is 15%? PV =
[1 / (1.15) 4 ] * [1 / (.15-.085)] = $8.80
Slide 5
CAPM Expected Return Treehouse of Antacid stock has a beta
value of 2.5 and an expected return of 10%. The risk-free rate of
return is currently 1.25%. What is the expected return on the
market? 10% = 1.25 + 2.5 * (X 1.25) 8.75 = 2.5X 3.125 X =
4.75%
Slide 6
Geometric Average Return A portfolio of stock is worth $500
today. It was worth $450 one year ago, $440 two years ago, and $435
three years ago. What is the geometric average rate of return over
the last three years? (500/435) 1/3 1 = 4.75%
Slide 7
Lottery Payments The Saw Mill Gum lottery will pay Elianna
$100,000 today. Each subsequent payment will be $10,000 higher than
the one before. Her final payment will be $140,000. What is the PV
of these payments if her effective annual discount rate is 14%? PV
= 100,000 + 110,000/1.14 + 120,000/(1.14) 2 + 130,000/(1.14) 3 +
140,000/(1.14) 4 PV = $459,464
Slide 8
Profitability Index Bumble Bloop canned sardines buy a machine
that costs $50,000 today. The machine leads to positive cash flows
in the future, starting at $5,000 in one year and subsequent annual
cash flows that increase by 5% forever. What is the profitability
index of this machine if the effective annual discount rate is 15%?
PV of cash flows = 5000/(.15-.05)=$50,000 P.I. = 50,000/50,000 =
1
Slide 9
Real Rate of Return with Inflation According to the CPI, a
bundle that cost $1,000 in 2011 would cost $1,020.69 in 2012. If an
investment received a nominal rate of return of 5% between 2011 and
2012, what is the real rate of return? Inflation =
(1020.691000)/1000 = 2.069% (1 + real)*(1 + inflation) = 1 +
nominal (1 + real)* 1.02069 = 1.05 Real =.028716 = 2.87%
Slide 10
Balloon Payment Clayton is taking out an interest-only home
loan for $100,000 today. (His monthly payments will only cover the
interest.) He will make 120 monthly payments starting in one month,
and a final balloon payment 10 years from today.
Slide 11
Balloon Payment How much will this balloon payment be if the
stated annual interest rate is 12%, compounded monthly? Balance at
the beginning of each month is $100,000 Balloon payment is
$100,000
Slide 12
Growing Savings Danica is trying to save up enough money for
her sons racing lessons 10 years from now. The PV of the costs of
the racing lessons is $10,000. She will save $X one year from
today, and increase this amount by 5% each year for a total of 9
years. The total savings will be exactly enough to cover the racing
lessons.
Slide 13
Growing Savings Find X if the effective annual discount rate is
8%. $10,000=X * 1/(r - g) * [1((1+g)/(1+r)) 9 ] $10,000=X *
1/(.08-.05) * [1(1.05/1.08) 9 ] $10,000=7.46499 * X X =
$1,339.59
Slide 14
PV of Growing Annuity The current date is May 22, 2013. Today,
Benson will deposit $500 into a bank account that earns 5%
effective annual interest. In the future, he will make annual
deposits on the same date each year. The next deposit will be
$1,050, and each deposit growing by 5%.
Slide 15
PV of Growing Annuity In what year will Bensons account have a
PV of $8,500? Growing annuity formula will not work (r=g) PV = 500
+ 8*1000 = $8,500 Answer is May 22, 2021 2013Year 0PV = $500
2014Year 1PV = $1050/1.05 = $1000 2015Year 2PV = $1050*1.05/(1.05)
2 = $1000 2012Year 8PV = $1000
Slide 16
Stock Value Almond Tar Fireplaces will pay quarterly dividends
of $5 every 3 months, starting 2 months from now. What is the PV of
this stock if the effective annual discount rate is 15%? Quarterly
rate = (1.15) 1/4 1 = 3.55581% Monthly rate = (1.15) 1/12 1 =
1.17149%
Slide 17
Stock Value If the first dividend were paid in 3 months: PV =
$5/.0355581 = $140.62 Since the first dividend is in 2 months: PV =
140.62 * 1.0117149 = $142.26
Slide 18
Internal Rates of Return There is a potentially-profitable gold
mine in the Purple Elephant Hills. The company would have to pay
$200 million today to open the mine. One year from today, all of
the gold extracted will be sold for $450 million. Two years from
today, costs of $252 million must be paid to seal the mine. There
are no other costs or benefits.
Slide 19
IRR: Part (a)
Slide 20
IRR: Part (b) For what discount rates should the mine be
opened? Show all work to justify your answer. Answer: 0.05 < r
< 0.20 Option 1: Equation for NPV (0=-100r 2 +25r-1) has
a=-100