Download presentation

Presentation is loading. Please wait.

Published byJeremy Glenn Modified over 2 years ago

1
Summer 2012 Test 2 solution sketches

2
1(a) You are paid $500 per year for three years, starting today. If the stated annual discount rate is 5%, compounded continuously, what is the total present value of the three payments? PV = $500 + $500/exp(0.05) + $500/exp(0.05 * 2) = $1,428.03

3
1(b) If Jacob takes out a mortgage of $300,000 and only pays off the interest incurred each month, how much will his monthly payment be if the effective annual interest rate is 17%? The 12 th root of 1.17 is 1.0131696 Monthly rate is 1.31696% Monthly payment is $300,000(0.0131696) $3,950.88

4
1(c) Stark’s Sizzling Steaks is considering opening a new location in Walla Walla, WA. In order to open, $2 million must be invested today. If the restaurant opens, the yearly operating profits are $300,000 per year forever, starting 1 year from today. (Profits are achieved only once a year in this example.) For what discount rates would the net present value be positive if the new restaurant is opened? All numbers are in millions of dollars –2 + 0.3/r > 0 r < 0.15

5
2 Belly Batteries, Inc. Belly Batteries, Inc. has just paid out its annual dividend of $5 earlier today. The annual dividend will go up by 10% each of the next 5 years, followed by no growth after that. What will the price of this stock be 3 years from today if the effective annual discount rate is 9%? (Note: Provide the price AFTER the dividend has been paid.) Note that we need to calculate the future value, 3 years from today Also note that payments made between now and Year 3 are NOT counted in the value of the stock

6
2 Belly Batteries, Inc. Dividend in Year 4 $5(1.1) 4 = $7.3205 FV in Year 3 dollars: $7.3205/1.09 = $6.7161 Dividend in Years 5 onward $5(1.1) 5 = $8.0525 FV in Year 3 dollars for all dividends paid in Years 5 onward (note that we have to discount the perpetuity formula used by 1 year) ($8.05255/0.09)(1/1.09) = $82.0851 Total of all dividends paid in Years 4 onward: Add up bolded numbers $88.80 (rounded to the nearest cent)

7
3: A sample of a stock’s returns over the past five years was 200%, 20%, -40%, 40%, -100%. (a) What is the geometric average return over the five-year period? The fifth root of (1+2)(1+.2)(1-.4)(1+.4)(1-1), minus 1 0 – 1 = -1 = -100%

8
3: A sample of a stock’s returns over the past five years was 200%, 20%, -40%, 40%, -100%. (b) What is the standard deviation of this sample? Arithmetic mean is (2+.2-.4+.4-1)/5 0.24 = 24% Variance (note that we lose a degree of freedom since we have a sample here) (1/4)[(2-.24) 2 + (.2-.24) 2 + (-.4-.24) 2 + (.4-.24) 2 + (-1-.24) 2 ] 1.268 Standard deviation is the square root of the variance 1.126, or 112.6%

9
3: A sample of a stock’s returns over the past five years was 200%, 20%, -40%, 40%, -100%. (c) If someone invested $100 in this stock five years ago, how much would this stock be worth today? Two ways to find the answer $100(1+2)(1+.2)(1-.4)(1+.4)(1-1) = 0 You have a negative 100% return in your final year, which means you lose your entire amount You are left with 0

10
4: Nominal return/inflation/real return In 1946, the nominal return for large- company stocks was –8.18%, and the Consumer Price Index (CPI) went up by 18.13%. Assuming that the CPI represents the inflation rate, what was the real rate of return of large-company stocks in 1946? 1 + nominal = (1 + real)(1 + inflation) 1 – 0.0818 = (1 + real)(1 + 0.1813) Solve for real to be -0.22272 or -22.272%

11
5 Lotta Love/Soren Lotta Love will receive many payments from Soren. She will receive $1,000 today, $2,000 two years from today, $X four years from today and $4,000 every year for 8 years, starting six years from today. The present value of all payments is $40,000, and her effective annual discount rate is 24%. Find X. PV of all future payments (including today’s) must be $40,000

12
5 Lotta Love/Soren 40,000 = 1,000 + 2,000/1.24 2 + X/1.24 4 + (4000/.24)[1 – 1/1.24 8 ]/1.24 5 Solve for X $78,092.93 Annuity formula 5 years of discounting

13
6 Zero-coupon bond A zero-coupon bond is purchased for $900 at 10 am today, with a face value of $1,100 to be paid two years from today. Later today, at 1 pm, the yield to maturity (calculated on a yearly basis) changes to 12%. How much does the value of the bond change between 10 am and 1 pm? (Make sure to clearly state if the value goes up or down.) The new value is $1,100/1.12 2 = $876.91 The old value was $900 The change in value $876.91 - $900 = -$23.09 Down by $23.09

Similar presentations

OK

Chapter 6 The Time Value of Money— Annuities and Other Topics.

Chapter 6 The Time Value of Money— Annuities and Other Topics.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on water our life line screening Ppt on 7 wonders of the world 2013 Ppt on drupal content management system Ppt on online banking system project Differential display ppt on ipad Free download ppt on chemical bonding Ppt on metro rail in hyderabad Ppt on internet services for class 10 Ppt on uses of plants for grade 1 Ppt on trans-siberian railway route