Chapter 26: Q16RQ (page 1464)
Question: What is an annuity? How does it differ from a lump sum payment?
Answer
An annuity is an equal monetary payment, while a lump sum payment is a one-time payment.
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You are planning for early retirement. You would like to retire at age 40 and have enough money saved to be able to withdraw \(220,000 per year for the next 30 years (based on family history, you think you will live to age 70). You plan to save by making 20 equal annual instalments (from age 20 to age 40) into a fairly risky investment fund that you expect will earn 8% per year. You will leave the money in this fund until it is completely depleted when you are 70 years old.
Requirements
1. How much money must you accumulate by retirement to make your plan work? (Hint: Find the present value of the \)220,000 withdrawals.)
2. How does this amount compare to the total amount you will withdraw from the investment during retirement? How can these numbers be so different?
Using payback, ARR, and NPV with unequal cash flows
Hughes Manufacturing, Inc. has a manufacturing machine that needs attention. The company is considering two options. Option 1 is to refurbish the current machine at a cost of \(2,600,000. If refurbished, Hughes expects the machine to last another eight years and then have no residual value. Option 2 is to replace the machine at a cost of \)3,800,000. A new machine would last 10 years and have no residual value. Hughes expects the following net cash inflows from the two options:
Year | Refurbish current machine | Purchase new machine |
1 | \(1,760,000 | \)2,970,000 |
2 | 440,000 | 490,000 |
3 | 360,000 | 410,000 |
4 | 280,000 | 330,000 |
5 | 200,000 | 250,000 |
6 | 200,000 | 250,000 |
7 | 200,000 | 250,000 |
8 | 200,000 | 250,000 |
9 | 250,000 | |
10 | 250,000 | |
Total | \(3,640,000 | \)5,700,000 |
Hughes uses straight-line depreciation and requires an annual return of 10%.
Requirements
1. Compute the payback, the ARR, the NPV, and the profitability index of these two options.
2. Which option should Hughes choose? Why?
What is the decision rule for IRR?
What is the decision rule for NPV?
How is IRR calculated with unequal net cash inflows?
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