An investment costs $800 initially, then earns $300 in years 2, 3, and 4. The annual interest rate is 4%. Which of the following statements about this investment is correct? The investment should be made, since its payback period is three years. The investment should not be made because its net present value is negative. The investment would become more attractive if the interest rate increased. The investment should be made, since the total amount earned is greater than the cost.
You are considering buying a house. Your mortgage requires monthly payments of $2,500 for 360 months. The interest rate is fixed at 4%. What is the present discounted value of your mortgage? $62,499.95 $2,500 $62,500 $900,000
What is the option value of waiting? the increase in the net present value from postponing an investment until uncertainty about the investment returns is reduced the use of a risk-free discount rate for the evaluation of risky investments the interest rate that causes the net present value of an investment to equal zero the difference between the present discounted value calculated from using the nominal interest rate and the real interest rate
Adam has wealth of $40,000 as long as his business does not burn down. However, there is a 50% probability that his business will burn down and cause a $30,000 loss, leaving him with $10,000 of wealth. Adam's utility function is given by U = W0.5, where W is wealth. What is the maximum price that Adam would pay for full insurance that covers the potential $30,000 loss? [Hint: The maximum price equals the actuarially fair premium plus the risk premium.] $22,500 $17,500 $12,500 $15,500
| An investment costs $800 initially, then earns $300 in years 2, 3, and 4. The annual interest rate is 4%. Which of the following statements about this investment is correct? | |||||||||
|
| You are considering buying a house. Your mortgage requires monthly payments of $2,500 for 360 months. The interest rate is fixed at 4%. What is the present discounted value of your mortgage? | |||||||||
|
| What is the option value of waiting? | |||||||||
|
| Adam has wealth of $40,000 as long as his business does not burn down. However, there is a 50% probability that his business will burn down and cause a $30,000 loss, leaving him with $10,000 of wealth. Adam's utility function is given by U = W0.5, where W is wealth. What is the maximum price that Adam would pay for full insurance that covers the potential $30,000 loss? [Hint: The maximum price equals the actuarially fair premium plus the risk premium.] | |||||||||
|
Related questions
Net Present Value-Unequal Lives
Al a Mode, Inc., is considering one of two investment options. Option 1 is a $42,000 investment in new blending equipment that is expected to produce equal annual cash flows of $14,000 for each of seven years. Option 2 is a $48,000 investment in a new computer system that is expected to produce equal annual cash flows of $18,000 for each of five years. The residual value of the blending equipment at the end of the fifth year is estimated to be $9,000. The computer system has no expected residual value at the end of the fifth year.
| Present Value of $1 at Compound Interest | |||||
| Year | 6% | 10% | 12% | 15% | 20% |
| 1 | 0.943 | 0.909 | 0.893 | 0.870 | 0.833 |
| 2 | 0.890 | 0.826 | 0.797 | 0.756 | 0.694 |
| 3 | 0.840 | 0.751 | 0.712 | 0.658 | 0.579 |
| 4 | 0.792 | 0.683 | 0.636 | 0.572 | 0.482 |
| 5 | 0.747 | 0.621 | 0.567 | 0.497 | 0.402 |
| 6 | 0.705 | 0.564 | 0.507 | 0.432 | 0.335 |
| 7 | 0.665 | 0.513 | 0.452 | 0.376 | 0.279 |
| 8 | 0.627 | 0.467 | 0.404 | 0.327 | 0.233 |
| 9 | 0.592 | 0.424 | 0.361 | 0.284 | 0.194 |
| 10 | 0.558 | 0.386 | 0.322 | 0.247 | 0.162 |
| Present Value of an Annuity of $1 at Compound Interest | |||||
| Year | 6% | 10% | 12% | 15% | 20% |
| 1 | 0.943 | 0.909 | 0.893 | 0.870 | 0.833 |
| 2 | 1.833 | 1.736 | 1.690 | 1.626 | 1.528 |
| 3 | 2.673 | 2.487 | 2.402 | 2.283 | 2.106 |
| 4 | 3.465 | 3.170 | 3.037 | 2.855 | 2.589 |
| 5 | 4.212 | 3.791 | 3.605 | 3.352 | 2.991 |
| 6 | 4.917 | 4.355 | 4.111 | 3.784 | 3.326 |
| 7 | 5.582 | 4.868 | 4.564 | 4.160 | 3.605 |
| 8 | 6.210 | 5.335 | 4.968 | 4.487 | 3.837 |
| 9 | 6.802 | 5.759 | 5.328 | 4.772 | 4.031 |
| 10 | 7.360 | 6.145 | 5.650 | 5.019 | 4.192 |
Assume there is sufficient capital to fund only one of the projects. Determine which project should be selected, comparing the (a) net present values and (b) present value indices of the two projects, assuming a minimum rate of return of 15%. Use the present value tables appearing above.
a. Determine the net present values of the two projects.
| Blending Equipment | Computer System | |
| Total present value of cash flows | $ | $ |
| Less amount to be invested | $ | $ |
| Net present value | $ | $ |
b. Determine the present value indices of the two projects. If required, round the present value index to two decimal places.
| Present Value Index | |
| Blending Equipment | |
| Computer System |
Which project should be selected? (If both present value indices are the same, either project will grade as correct.)
Computer System
Feedback
a. For each investment, determine the present value of the cash flows at 15% for 5 years, Exhibit 5. Use the residual value of the Blending Equipment to equate useful lives (Exhibit 2). Subtract the amount to be invested.
b. Divide the total present value of the cash flows by the amount to be invested. What do the present value indexes indicate about the net present values?
Learning Objective 3, Learning Objective 4.
Check My Work
Question 1
Mary purchases a U.S. Treasury bond; the bond is:
| An asset for the government but a liability for Mary. | |
| An asset of the U.S. government as well as an asset for Mary. |
| A liability of the U.S. government and an asset for Mary. | |
| An asset for Mary but not a liability of the U.S. Government. |
Question 2
More detailed financial instruments tend to be:
| More costly because they will cost more to create. | |
| Less costly because they can be standardized more easily. |
| More desirable than less detailed ones, no matter what the price. | |
| Less costly because all possible contingencies are covered |
Question 3
Considering the value of a financial instrument, the more likely it is the payment will be made:
| The less valuable is the financial instrument because it is highly liquid. | |
| The more valuable the financial instrument. |
| The greater the uncertainty; therefore the less valuable is the financial instrument | |
| The less valuable is the instrument because risk is lower. |
Question 4
Most of the buying and selling in primary markets:
| Is done by the Federal Reserve. | |
| Is in the public view. |
| Involves an investment bank. | |
| Is highly transparent and closely monitored by the SEC. |
Question 5
Derivative markets exist to allow for:
| Cash receipts from the sale of bonds. | |
| Reduced information asymmetry. |
| Direct transfers of common stocks for bonds. | |
| Reduced risk from volatile prices. |
Question 6
Compound interest is the idea:
| That you get an interest deduction for paying your loan off early. | |
| That you get an interest deduction if you take out a loan for longer than one year. |
| That interest rates will rise on larger loans. | |
| That you get interest on interest |
Question 7
Suppose Paul borrows $4000 for one year from his grandfather who charges Paul 7% interest. At the end of the year Paul will have to repay his grandfather:
| $4,280 | |
| $4,350 |
| None of the above | |
| $4,290 |
Question 8
The value of $100 left in a certificate of deposit for four years that earns 4.5% annually will be:
| $119.25 | |
| $145.00 |
| $120.00 | |
| $117.00 |
Question 9
The relationship between present value and the interest rate could best be described as:
| A direct relationship, they both move together | |
| An inverse relationship, as i increases, PV decreases. |
| None of the above. | |
| An unclear relationship, whether it is direct or inverse depends on the interest rate. |
Question 10
At any fixed interest rate, an increase in time, n, until a payment is made:
| Has no impact on the present value since the interest rate is fixed. | |
| Reduces the present value. |
| None of the above. | |
| Increases the present value. |
