[MUSIC] Now let me show you how you can use these same formulas to solve several of the real world puzzles I posed to you in our very first lecture. Remember the refrigerator problem? In that problem, you have a choice between a new energy efficient refrigerator which costs $750 or the cheaper model at $500. If you buy the energy efficient refrigerator, your electricity bill will be $120 a year cheaper over the five-year life of the refrigerator. Assuming an interest rate of 8%, which refrigerator should you buy? Assuming of course, that you'll make your choice purely on economic grounds, rather than upon any possible concern about saving energy. Here again is the math. The next present value of the investment is calculated by first subtracting the purchase price of the cheaper refrigerator from the purchase price of the more expensive refrigerator. To get the net additional investment required to buy the more expensive model. This is $250 which we put a minus sign in front of because it is an investment outlay. Then we simply calculate the time value of the savings, which turns out to be $479. Subtracting $250 from this, yields a positive NPV of $229. Clearly the seemingly more expensive refrigerator turns out to actually be cheaper from net present value perspective. Now how about an investment in a different kind of capital. Your own human capital. To illustrate this, lets recall the dilemma of Priscilla and Phil from our first lecture. As a family they are trying to decide whether Phil should quit his job in order to enter a two year program for his MBA. Phil's situation is this, he's 45 years old and his making good money at his job as a salesman at a medical equipment company, $50,000 a year. Nonetheless, Phil feels stuck in his job, knowing that he can never advance further in his company or his career without additional education. However, with an MBA degree, Phil could move into the corporate side of the company and make at least $85,000 a year, right up until retirement at age 55. Unfortunately, the MBA program he wants to enroll in will cost him $80,000. $40,000 a year, and he will have to borrow money to do it, as well as quit his job. Fortunately, Priscilla brings home a decent salary, one big enough to support Phil and their two children over the next two years. So the only question they have is whether it makes financial sense for Phil to take this major step. So what should Priscilla and Phil do, assuming an interest rate of 6%? OK, here's the numbers. Did you remember to count Phil's foregone salary as an opportunity cost of entering the program? That's $50,000 per year for two years. And that plus the $40,000 tuition for two years gives an annual cost of Phil's investment in human capital of $90,000. Properly discounting this sum at a 6% interest rate over the two-year period yields a net investment cost of $165,903 in Net Present Value terms. Now, let's look at the other side of the investment coin. Phil's incremental income from getting his MBA will be $35,000 per year, which is the difference between his current and future salary. However, his new salary won't start until year three. Properly discounting this income flow through year ten, when Phil reaches retirement, yields $193,434. So, what's the NPV of Phil and Priscilla's investment? That's right, it's positive $27,531, which is simply the difference between the NPV of the investment outlay and the NPV of the income stream. So Phil should go get his MBA. But, would that still be the case if interest rates were 12%?
