The video introduces the concept of valuing cash flows using the time value of money principle and demonstrates how to compute present value in R. It starts by defining a cash‑flow vector (e.g., eight entries from time 0 to 7) and explains that the timing of each cash flow and the interest rate are crucial for valuation. The tutorial explains that a euro today is worth more than a euro in the future because it can earn interest; a constant interest rate I (e.g., 3%) leads to a growth factor (1+I)^k and a corresponding discount factor V^k = 1/(1+I)^k. Using R, the presenter shows how to build a discount‑factor vector, multiply it element‑wise with the cash‑flow vector, and sum the results to obtain the present value of the entire cash‑flow stream. Example calculations illustrate that €500 at time 0 remains €500, while €200 at time 7 discounts to about €162.6. The tutorial ends with a call for viewers to practice valuing cash flows in R.
Chapters
In financial transactions, cash flows from one party to another. This first video explains you how to value cash flows. To set the scene, fix a capital unit, say €1, and a time unit, say 1 year. Our notation uses 0 to denote the present moment that's right now, and K refers to k time units in the future. The amount of money to be received or paid at time K is ck. That's the cash flow at time k. Here's an example of a sequence of cash flows. This vector has eight entries. The first one corresponds to time 0 and the last one to time 7. You create this vector in R with entries 500, 400, 300 and then repeat 205 times using the wrap function. The length of the vector cash flows is 8. As expected. The timeline at the bottom shows a general notation for a cash flow vector which starts from c0 at time 0 and runs up to cn at time n. The length of this vector is n 1. It is crucial to value a cash flow vector. Two things are the timing of cash flows and the time value of money. The time value of money implies that a euro that is available to you right now is worth more than a euro that is promised to you in the future. That's because the euro that you own today can be invested and grow. This growth is determined by the interest rate. Let's assume a constant interest rate, say I. This is the interest earned over a one time period. The timeline on the left illustrates how €1 at time zero grows to 1.03 Euro at time one. At the right side, the discount vector V describes the inverse operation. €1 at time 1 discounts to 1, 1, I € or V € at time 0. That's 0.€97. In our example, you can extend this idea to k time periods instead of just one. The timeline on the left shows how €1 at time 0 grows to 1i to the power k euro at time k. Or in terms of V, the discount vector. That's V to the power minus K euro. In the R code, you see how this works. With k equals 2 and a rate of 3%, you obtain 1.06 Euro at time 2. The timeline on the right shows how 1 Euro at time k discounts to V to the power K€ at time 0. From the R code, you learn that €1 at time 2 is worth 0.€94 at time 0. Your goal is now to calculate the value at time 0 of the cash flows on this timeline. The first cash flow, €500, is at time 0 and the last one, €200 is at time 7. This value at time 0 is called the present value. You find it by discounting each cash flow to time zero and then taking the sum. Define the interest rate I of 3% and the corresponding discount vector v. The vector discount Factors stores the applicable discount factors obtained by raising V to the power 0 to 7, and cash flows stores the cash flows from time 0 to 7. By multiplying both vectors element wise, you obtain the present value of each of the cash flows. For example, 200 Euro at times 7 is worth 162.6 Euro at the present time. Finally, to obtain the present value of the entire cash flow vector sum the discounted cash flows from the previous step. Now it's your turn to value some cash flows in R.
