Test 2 solution sketches Note for multiple-choice questions: Choose the closest answer

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 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=( )/3 = 4.133% Avg bond return=( )/3 = 2.567% Difference = – = 1.566%

PV of Stock with Dividends

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 / ( )] = $8.80

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% = * (X – 1.25) 8.75 = 2.5X – X = 4.75%

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%

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/ ,000/(1.14) ,000/(1.14) ,000/(1.14) 4 PV = $459,464

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/( )=$50,000 P.I. = 50,000/50,000 = 1

Real Rate of Return with Inflation According to the CPI, a bundle that cost $1,000 in 2011 would cost $1, in If an investment received a nominal rate of return of 5% between 2011 and 2012, what is the real rate of return? Inflation = ( –1000)/1000 = 2.069% (1 + real)*(1 + inflation) = 1 + nominal (1 + real)* = 1.05 Real = = 2.87%

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.

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

Growing Savings Danica is trying to save up enough money for her son’s 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.

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/( ) * [1–(1.05/1.08) 9 ] $10,000= * X X = $1,339.59

PV of Growing Annuity The current date is May 22, 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%.

PV of Growing Annuity In what year will Benson’s account have a PV of $8,500? Growing annuity formula will not work (r=g) PV = *1000 = $8,500 Answer is May 22, Year 0PV = $ Year 1PV = $1050/1.05 = $ Year 2PV = $1050*1.05/(1.05) 2 = $1000 ……… 2012Year 8PV = $1000

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 = % Monthly rate = (1.15) 1/12 – 1 = %

Stock Value If the first dividend were paid in 3 months: PV = $5/ = $ Since the first dividend is in 2 months: PV = * = $142.26

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.

IRR: Part (a)

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<0, which means it is a parabola that opens down (positive NPV is between the two roots).

IRR: Part (b) Option 2: Choose values in each range (r.2) and show what the NPV is for those discount rates. Example: r=0  NPV = -$2 million r=.1  NPV = $0.826 million r=1  NPV = -$38 million