March 21

Money Borrowed

  • Money borrowed for one year carries interest of 5.o, money borrowed two years is 6.o, and money borrowed for two years carries an interest rate of 7.0 per year. First year costs are $2,000,000 and expect no additional revenue. In the second year, costs will be $5,000,000 but have 30 percent chance of generating $10,000,000 in additional revenue, a 20 percent chance of generating $6,000,000 in additional revenue, and a fifty percent chance of not being to sell anything because your contractor is behind schedule. In the final year, you have a fifty percent chance of $2,000,000 in additional costs (The contractor is a friend of your boss and you can't sue for breach of contract). and a fifty percent chance that you finished paying the bills in the second year. You have fifty percent chance that revenue in the third year will be $2,000,000, a thirty percent chance it will be $5,000,000 and a 20 percent chance it will be $12,000,000. At that point salvage won't be worth the trouble. How do you decide if this is a viable project?


  • Excellent answer, very detailed and thorough.


  • There are two concepts that are used in evaluating this project. The first is Expected Value. This is calculated by taking the probabilities that a set of cash flows will occur and multiplying each cash flow by its probability to arrive at an expected cash flow. The second is Net Present Value. This is obtained by adding the expected net cash flows together after discounting them based on when they occur. First, we need to calculate the Expected Value for the expenses and revenues for each year. Year 1: -$2 million in costs with no revenue. Year 2: -$5 million in costs with a 30% chance of $10,000,000 in revenue, a 20% chance of $6,000,000 in revenue, and a 50% chance of no revenue. The expected revenue = 0.3 ($10 million) + 0.2 ($6 million) + 0.5 (zero dollars) = $4.2 million. Year 3: a 50% chance of -$2 million in costs and a 50% chance of zero dollars in costs. The expected costs = 0.5 (-$2 million) + 0.5 (zero dollars) = -$1 million. A 50% chance of $2,000,000 in revenue, a 30% chance of $5,000,000 in revenue, and a 20% chance of $12,000,000 in revenue yields an expected revenue of 0.5 ($2 million) + 0.3 ($5 million) + 0.2 ($12 million) = $4.9 million So, we now have expected costs and revenues for each year. These are: Year 1: costs of -$2 million; revenue of zero dollars Year 2: costs of -$5 million; revenue of $4.2 million Year 3: costs of -$1 million; revenue of $4.9 million Now we calculate the net cash flows for each year by adding the costs and revenues together. This yields: Year 1: cash flow of -$2 million Year 2: cash flow of -$800,000 Year 3: cash flow of $3.9 million There is no salvage value, so there are no additional cash flows. Now we use the Net Present Value formula and the interest rates that were given to discount the cash flows back to the present so that we can evaluate the attractiveness of the project. If the Net Present Value is positive, then the project is generally viewed as being worth doing. The Net Present Value formula is calculated by taking the future values and dividing them by (1 + i)^n where i is the interest rate for the period and n is the number of periods from the present time. So, the Net Present Value = -$2 million/1.05^1 + -$800,000/1.06^2 + $3.9 million/1.07^3 = $566,802.66. Because the Net Present Value is positive, this is a viable project, assuming one can withstand the risks of the most negative possible outcomes. Sincerely, Wonko Source: "Principles of Engineering Economy," Eighth Edition, by Grant, Ireson, and Leavenworth, John Wiley & Sons, 1990


  • Elmarto: Money borrowed for first year is 5.0%, two years carries an interest of 6.0% and three years at 7.0%


  • Hi douger! I think there is a typo in the first sentence. It says: "Money borrowed for one year carries interest of 5.o, money borrowed two years is 6.o, and money borrowed for two years carries an interest rate of 7.0 per year" So, money borrowed for two years carries an interest rate of 6.0% or 7.0% ? Also, I assume that in the cases where you mention 5.0 and 6.0 you're also referring to the interest rate in a "per year" basis. Is this correct? If you can clarify this, I think I can help you with this question. Best wishes! elmarto







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