Homework #7
Show your work for full credit
- (1pt) What is the payback period for the following set of cash flows?
| Year |
Cash Flow |
| 0 |
-$10,000 |
| 1 |
$3,000 |
| 2 |
$4,000 |
| 3 |
$5,000 |
In calculating the payback period, it is critical to find the time the project has recovered its initial investment. In a period of 3 years, the project has created: –
= $3,000 + $4,000 + $5,000
= $12,000 in cash flows.
The project will be required to add $2,000 in the third year to make the total cash flows of the invested amount.
In the third year, the project’s cash flows will be $3,000.
Payback period = 2 + ($2000/$5,000)
= 2.4 years
- (1pt) A firm evaluates all of its projects by applying the IRR rule. If the required return is 5%, should the firm accept the following project?
| Year |
Cash Flow |
| 0 |
-$110,000 |
| 1 |
$40,000 |
| 2 |
$40,000 |
| 3 |
$40,000 |
NPV = -110,000 + (40,000/(1+.05)) + (40,000/(1+.05)^2) + (40,000/(1+.05)^3)
= -110,000 + 38,095.238 + 36,281.179 + 34,553.504
= – 1,070.079
NO, the firm should not accept the project since the NPV is negative.
- (2pts) What is the NPV for the following set of cash flows if the relevant discount rate is 10%? What is the profitability index? Should the firm accept the project?
| Year |
Cash Flow |
| 0 |
-$40,000 |
| 1 |
$10,000 |
| 2 |
$15,000 |
| 3 |
$25,000 |
NPV for the project, if the required return is 10 percent
NPV = -40,000 + (10,000/1.10) + (15,000/1.10^2) + (25,000/1.10^3)
= -40,000 + 9,090.909 + 12,396.694 + 18,782.870
= $270.473
YES, the firm should accept this project since the NPV is positive.
Profitability index at 10%
PI = PV of future cash flows / investment, investment = $40,000
PV = (10,000/(1+.1)) + (15,000/(1+.1)^2) +( 25,0000/(1+.1)^3)
= 9,090.909 + 12,396.694 + 18,782.870
= 40,270.473
So, PI = 40,270.473/40,000
= 1.0068%
- (1pt) If two projects are mutually exclusive, is it ever correct to select the project with a lower internal rate of return (IRR)? Explain.
No, a project manager should always select the project with a higher IRR. So long as the initial cost of the project is the same, the project with a higher IRR creates more opportunities and potential benefits for the owner. As mutually exclusive, it implies that two projects cannot run simultaneously. Therefore, the selection of a project with higher IRR creates better chances for the company to generate more profit and sustainability of its future operations as compared to lower IRR projects.
- (1pt) Under what circumstances is it necessary to use the modified internal rate of return (MIRR) instead of the internal rate of return (IRR)? Explain.
The use of MIRR instead of IRR entails the flexibility it provides to the project. The need for more flexibility is essential to give a project more allowance for returns generation as expected in the initial objectives. The MIRR enhances and builds more control of a project over the assumed reinvestment rate. This is informed by future cash flow of a project that must be determined to more effective than the formerly implemented project. The reinvestment of cash flows at the IRR gives a company a firm grip to control the profits and benefits of a project.
- (1pt) A stock had an initial price of $10, paid a dividend of $1 per share during the year, and had an ending price of $14. Compute the percentage return, capital gain, and dividend yield.
Dividend yield = 1/10 = .10
Capital gain = 14-10 = $4
Percentage return = 4/10 = .40 or 40%.
- (1pt) Your portfolio that has $200,000 invested in Stock A and $100,000 invested in Stock B. If the expected returns on these stocks are 10% and 14%, respectively, what is the expected return on the portfolio?
Stock A = $200,000
Expected returns = 10%
Stock B = $100,000
Expected returns = 14%
Total amount for Stock A = 110/100 * 200,000 = 220,000
Total amount for Stock B = 114/100 * 100,000 = 114,000
Total amount for the portfolio = $334,000
Initial investment for the portfolio = $200,000 + $100,000 = $300,000
Expected returns on the portfolio = $334,000 – $300,000
= $34,000
- (2pts) Describe at least two economic trends that contributed to the Great Depression. Try to use financial terminology from class in your answer.
Suggested problems:
Subsequent to the Great Depression, there was a rapid stock market crash of the 1929. This was prompted by the banks’ failures for controlled remittances and regulation of financial management. The situation further became worse with stock market prices eroding to the lowest points ever in history. Investors at the time were prompted to experience extensive losses with adverse effects on the financial capacity. The level of resilience was undermined by the drought that lasted throughout the 1930s. The situation made the economic industry experiences profound socioeconomic effects including massive unemployment, loss of property and possession, banks closure, and near bankruptcy for millions of citizens. The culmination of extensive unequal distribution of wealth in the society saw a growth of the poor and minimal increase in the class of the rich. Therefore, the country’s consumption rate deteriorating positing a state where economic sustainability was unfavorable.
- If a project with conventional cash flows has a payback period less than its life, can you definitively state the algebraic sign of the NPV? Why or why not?
When the payback period is less than the project’s life it implies that the NPV is positive for a zero discount rate. This indicates that the project is bound to have a, IRR that is greater than the discount rate. Therefore, we can definitively state that the algebraic sign of the NPV is positive of the discount rate < IRR.
- Ed has to choose between Project A and Project B, which are mutually exclusive. Project A has an initial cost of $28,000 and an internal rate of return of 16 percent. Project B has an initial cost of $47,000 and an internal rate of return of 12 percent. Explain why the selection of the project with the higher internal rate of return could be a faulty decision.
Project A
Initial cost = $28,000
IRR = 16%
Project B
Initial cost = $47,000
IRR = 12%
The selection of the project with a higher IRR would be a faulty decision based on the comparison of the gains generated. The total gains generated by Project A would accumulate to $4,480 as compared to $5,640 for Project B. This illustrates that, despite having a lower IRR Project B’s greater initial investment cost can yield higher returns in the same period as Project A with a higher IRR.
- Describe the concept of a risk premium. What is the risk-free rate?
Risk premium entails the expected return on investment an asset is bound generate in the excess of the risk-free rate of return. The risk premium is paid to the investors as a form of compensation for tolerating an extra risk. Risk-free rate is the guaranteed rate of return that is experienced as a result of an investment with zero risk. Such an investment is bound to endure zero risk. Therefore, there is no risk of loss from the investment.
- Critically evaluate the following statement: Playing the stock market is like gambling. Such speculative investing has no social value, other than the pleasure people get from this form of gambling.
The comparison of stock market can only befit the context of gambling should the investor fail to conduct adequate research on the financial performance of a firm, investment choices, and strategic developments and their impacts on the firm. This is referred to as speculative investment that constitute of investing based on the fluctuations of stocks and a gut feeling and intention of generating potentially good returns due to variations in the market. As an investor, this can be misleading and inappropriate. In return, it adds no social values as the gambling is informed taking random chances. The conduct of extensive research on financial performances and understanding different contexts and how they affect market share prices is a critical task. This surpasses gambling context as is essential to the society. Therefore, stock market equation to gambling only befits the lack of research and utilizing the gut feeling to guide taking chances based on market fluctuations of different stocks.
- What is the historical real return on long-term government bonds? On long-term corporate bonds?
The real rate of return is used to describe the inflation adjusted rate of return that is exerted on securities. To attain the real rate of return, the inflation rate is subtracted from the nominal rate of return. The purchasing power provides the necessary mechanism for the inflation rate and nominal rate of returns to differ. On long-term government bonds, the subtraction of inflation rate from the nominal rate of return provides the real return rate over a long period of time. The long-term government bond is calculated to stand at 5.80%. The long-term corporate bond is calculated to stand at 6.20%.
- You bought a stock three months ago for $34.18 per share. The stock paid no dividends. The current share price is $35.07. What is the APR of your investment? The EAR?
Annual Percentage Rate (APR)
Calculation of 3-month rate =
($35.07 – 34.18) / $34.18 = .260 or 2.60%.
APR = 2.60*4 = 10.40%
EAR = 1.026038^4-1 = .10829 or 10.829%
- What are the portfolio weights for a portfolio that has 135 shares of Stock A that sell for $71 per share and 95 shares of Stock B that sell for $84 per share?
Portfolio weight =?
Stock A shares = 135
Sell = $71
Stock B shares = 95
Sell = $84
Total value of stocks = 135(71) + 95(84)
= $9,585 + $7,980 = $17,565
The portfolio weight for each stock, therefore; –
Stock A = 135($71) / $17,565
= .5457
Stock B = 95($84) / $17,565
= .4543
- You have $10,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 14% and Stock Y with an expected return of 11%. If your goal is to create a portfolio with an expected return of 12.4%, how much money will you invest in Stock X? In Stock Y?
Stock X expected return = 14%
Stock Y expected return = 11%
Portfolio with expected return = 12.4% i.e., .124
In the case, the question provides the expected return of each asset and the expected return of the portfolio. Then, we are asked to find the weight of each asset. The total weight of a portfolio must equal 1 (100%), then, the weight of Stock Y = Minus one the weight of Stock X.
That is, E(Rp) equation; – .124 = .14xX + .11(1 – xX)
.124 = .14xX + .11 – .11xX
.014 = .03xX
xX = .4667
Investment value of Stock X = .4667 * $10,000
= $4,667
Investment value of Stock Y = (1-.4667) * $10,000
= $5,333
- You purchased 250 shares of a particular stock at the beginning of the year at a price of $68. The stock paid a dividend of $2 per share, and the stock price at the end of the year was $77. What was your dollar return on this investment?
Dollar return of the investment = Value of shares * Change in price/share and dividend per share received
Total dollar return = 250 ($77 – $68 + 2)
= $2,750.00
