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Time Value of Money (Challenge assignment)

(These problems need a little more thinking, and drawing a complete, correct time line is the best way to start.) a) To get credit, you must show a complete (i.e. fully labeled incorporating all of the information in the problem, plus highlighting the unknown to be solved for) and correct time line, as we did in class for the ten short problem. b) You must provide a numerical answer, or at least indicate (e.g. using numerical values of the time value of money factors) all of the components of a correct final numerical answer. c) The work must be very neat, else you will not get any credit. d) Of the two problems below, Mack Aroni The Bank Robber is an easier problem. For Western Timber, you will need to first treat just the first paragraph as a full problem by itself, and solve for how much timber should be cut at the end of each year. And only then should you use the information in the second paragraph which incorporates dollar values.

1. Mack Aroni, a bank robber, is worried about his retirement. He decides to start a savings account. Mack annually deposits his net share of the loot, which consists of $70,000 per year, for 3 years beginning January 1, 1985. Mack is arrested on January 4, 1987 (after making the third deposit) and spends the rest of 1987 and most of 1988 in jail. He escapes in September of 1988. He resumes his savings plan with semiannual deposits of $25,000 each beginning January 1, 1989. Assume that the banks interest rate was 8% compounded annually from January 1, 1985 through January 1, 1988, and 10% per annum compounded semiannually thereafter. When Mack retires on January 1, 1992 (six months after his last deposit), what is the balance in his savings account?

2. Western Timber Company acquires a tract of land on long-term lease and a lumber concession permitting it to cut equal quantities of timber (assume all in one big cutting at the end of each year) for ten years, but it must return the land to the government at the end of ten years with at least half a million cubic feet of timber standing. Currently, there are a million cubic feet of standing timber, and it is estimated that the forest grows at ten per cent per year. Assuming that the timber can be sold for $100/cu. ft, and that the relevant discount rate for Western Timber is 6% for the first 6 years, and 8% thereafter, if it does the best it can for itself, what is the present value of future cash flows of Western Timber Company?

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