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

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%

3. PV of Stock with Dividends

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

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%

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%

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

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

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 = (1020.69–1000)/1000 = 2.069% (1 + real)*(1 + inflation) = 1 + nominal (1 + real)* 1.02069 = 1.05 Real =.028716 = 2.87%

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.

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

12. 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.

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

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%.

15. 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 = 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

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%

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

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.

19. IRR: Part (a)

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

21. 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